%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW179+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:04:44 AM UTC 2026
% Result : Theorem 270.34s 270.64s
% Output : Proof 270.48s
% 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__0960_A_060_061_Acmod_Ac_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
file('theBenchmark.p',fact__0960_A_060_061_Acmod_Ac_096) ).
fof(fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
file('theBenchmark.p',fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))),
file('theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
file('theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(fact_norm__add__less,axiom,
! [V_s,V_y,V_r,V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ),
file('theBenchmark.p',fact_norm__add__less) ).
fof(fact_norm__mult__less,axiom,
! [V_s,V_y,V_r,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)) ) ) ),
file('theBenchmark.p',fact_norm__mult__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_zero__less__two,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),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_not__sum__squares__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_norm__one,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_norm__one) ).
fof(fact_norm__not__less__zero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_not__real__square__gt__zero,axiom,
! [V_x_2] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_real__le__refl,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
file('theBenchmark.p',fact_real__le__refl) ).
fof(fact_real__le__linear,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
file('theBenchmark.p',fact_real__le__linear) ).
fof(fact_real__le__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ),
file('theBenchmark.p',fact_real__le__trans) ).
fof(fact_real__le__antisym,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
=> V_z = V_w ) ),
file('theBenchmark.p',fact_real__le__antisym) ).
fof(fact_less__eq__real__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__less__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__less__def) ).
fof(fact_real__norm__def,axiom,
! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
file('theBenchmark.p',fact_real__norm__def) ).
fof(fact_real__add__left__mono,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ),
file('theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))),
file('theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_split__mult__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_split__mult__pos__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_comm__mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__comm__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( 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_2),V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__le__square,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> 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__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> 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)
=> ~ 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_norm__ge__zero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
file('theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_mult__left__le__imp__le,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__right__le__imp__le,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__left__less__imp__less,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_mult__right__less__imp__less,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__less__le__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
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)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_mult__left__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> 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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> 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_abs__eq__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring__abs(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ),
file('theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_abs__mult__pos,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( 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),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = 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_norm__le__zero__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_norm__mult__ineq,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
file('theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [V_y_2,V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [V_y_2,V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_norm__triangle__ineq,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
file('theBenchmark.p',fact_norm__triangle__ineq) ).
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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,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_linorder__neqE__linordered__idom,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_real__mult__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)),
file('theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_real__mult__commute,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z),
file('theBenchmark.p',fact_real__mult__commute) ).
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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
=> c_Orderings_Oord__class_Oless(T_a,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_divisors__zero,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_mult__eq__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_mult__right_Ozero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_mult_Ozero__right,axiom,
! [V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(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_Ozero__right) ).
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__left_Ozero,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_mult_Ozero__left,axiom,
! [V_b,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult_Ozero__left) ).
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_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_combine__common__factor,axiom,
! [V_c,V_b,V_e,V_a,T_a] :
( class_Rings_Osemiring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ),
file('theBenchmark.p',fact_combine__common__factor) ).
fof(fact_mult__left_Oadd,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(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_H),V_b)) ),
file('theBenchmark.p',fact_mult_Oadd__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),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = 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_mult__right_Oadd,axiom,
! [V_y,V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ),
file('theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(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),V_b_H)) ),
file('theBenchmark.p',fact_mult_Oadd__right) ).
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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
file('theBenchmark.p',fact_abs__mult__self) ).
fof(fact_abs__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
file('theBenchmark.p',fact_abs__mult) ).
fof(fact_abs__one,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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_real__mult__left__cancel,axiom,
! [V_b_2,V_a_2,V_ca_2] :
( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_real__mult__right__cancel,axiom,
! [V_b_2,V_a_2,V_ca_2] :
( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_real__mult__1,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z,
file('theBenchmark.p',fact_real__mult__1) ).
fof(fact_real__add__mult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)),
file('theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_abs__norm__cancel,axiom,
! [V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ),
file('theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__comm__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_zero__less__mult__pos2,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_mult__pos__neg2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ 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_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_zero__less__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> 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)
=> ~ 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)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
=> 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_less__add__one,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,V_a,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_abs__mult__less,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),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_norm__eq__zero,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__eq__zero) ).
fof(fact_norm__zero,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_norm__zero) ).
fof(fact_norm__mult,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ),
file('theBenchmark.p',fact_norm__mult) ).
fof(fact_real__mult__less__mono2,axiom,
! [V_y,V_x,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)) ) ),
file('theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_real__mult__order,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ),
file('theBenchmark.p',fact_real__mult__order) ).
fof(fact_real__mult__less__iff1,axiom,
! [V_y_2,V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_m,axiom,
! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),v_m____) ),
file('theBenchmark.p',fact_m) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [V_y,V_x,V_c,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
=> V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_rabs__ratiotest__lemma,axiom,
! [V_y,V_x,V_c] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
=> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_rabs__ratiotest__lemma) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_abs__triangle__ineq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ),
file('theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_abs__of__pos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ),
file('theBenchmark.p',fact_abs__of__pos) ).
fof(fact_zero__less__abs__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_pCons,axiom,
? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
file('theBenchmark.p',fact_pCons) ).
fof(fact_zero__reorient,axiom,
! [V_x_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
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_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_add__left__cancel,axiom,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2)
<=> V_b_2 = V_ca_2 ) ),
file('theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__right__cancel,axiom,
! [V_ca_2,V_a_2,V_b_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2)
<=> V_b_2 = V_ca_2 ) ),
file('theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__ab__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = 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_one__reorient,axiom,
! [V_x_2,T_a] :
( class_Groups_Oone(T_a)
=> ( c_Groups_Oone__class_Oone(T_a) = V_x_2
<=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_one__reorient) ).
fof(fact_abs__idempotent,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
file('theBenchmark.p',fact_abs__idempotent) ).
fof(fact_add__0__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> 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)
=> 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_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> 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)
=> 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_add__le__cancel__right,axiom,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,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_ca_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
=> 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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__less__cancel__right,axiom,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless(T_a,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_ca_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
=> 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)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__less__imp__less__left) ).
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_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__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_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_abs__zero,axiom,
! [T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> 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_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_abs__eq__0) ).
fof(fact_abs__ge__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_abs__le__D1) ).
fof(fact_abs__add__abs,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
file('theBenchmark.p',fact_abs__add__abs) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,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_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),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_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
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)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__less__le__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_abs__ge__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> 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)
=> ~ c_Orderings_Oord__class_Oless(T_a,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_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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)
=> 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),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)
=> 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),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_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 )
=> c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != 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_even__less__0__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_even__less__0__iff) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [B_m] :
~ ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m) ),
file('theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_order__refl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__refl) ).
fof(fact_poly__1,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_poly__1) ).
fof(fact_poly__add,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__add) ).
fof(fact_add__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ),
file('theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_mult__poly__add__left,axiom,
! [V_r,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ),
file('theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_le__fun__def,axiom,
! [V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_linorder__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__linear) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_x_2 = V_y_2
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_order__eq__refl,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( V_x = V_y
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__eq__refl) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_ord__eq__le__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__le__trans) ).
fof(fact_xt1_I3_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I3_J) ).
fof(fact_ord__le__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__le__eq__trans) ).
fof(fact_xt1_I4_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I4_J) ).
fof(fact_order__antisym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( 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__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I5_J,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( 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_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_le__funE,axiom,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_linorder__le__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_linorder__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( V_x != V_y
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__cases) ).
fof(fact_order__less__asym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__asym) ).
fof(fact_xt1_I10_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_order__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> 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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( V_b = V_c
=> 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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__less__eq__trans) ).
fof(fact_xt1_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
=> 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
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> 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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ~ 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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ),
file('theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( 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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_x != V_y ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__less,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ 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)
=> ( 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
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,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_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x_2 != V_y_2
<=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_order__less__irrefl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__less__irrefl) ).
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_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)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = 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_poly__eq__iff,axiom,
! [V_q_2,V_pa_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
<=> V_pa_2 = V_q_2 ) ),
file('theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_poly__zero,axiom,
! [V_pa_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
<=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_poly__zero) ).
fof(fact_xt1_I8_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_xt1_I7_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__less__le__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I11_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_a != V_b
=> 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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_a != V_b
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__less__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_xt1_I12_J,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> 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
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> 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_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> 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)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_order__le__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,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_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless(T_a,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_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
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_double__eq__0__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_add__0__iff,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_add__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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_crossproduct__eq,axiom,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
<=> ( V_y_2 = V_z_2
| V_w_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [V_b,V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_crossproduct__noteq,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_ca_2 != V_d_2
& V_a_2 != V_b_2 )
<=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ),
file('theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = 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_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_poly__0,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_poly__0) ).
fof(fact_poly__mult,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__mult) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(fact_mult_Opos__bounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact_mult__left_Ononneg__bounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
fof(fact_mult__right_Ononneg__bounded,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
fof(fact_mult_Ononneg__bounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult_Ononneg__bounded) ).
fof(fact_mult__left_Obounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ),
file('theBenchmark.p',fact_mult__left_Obounded) ).
fof(fact_less__fun__def,axiom,
! [V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
fof(fact_mult__poly__0__right,axiom,
! [V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_mult__poly__0__left,axiom,
! [V_q,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_order__root,axiom,
! [V_a_2,V_pa_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_order__root) ).
fof(fact_mult_Obounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ),
file('theBenchmark.p',fact_mult_Obounded) ).
fof(fact_mult__right_Obounded,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ),
file('theBenchmark.p',fact_mult__right_Obounded) ).
fof(fact_norm__sgn,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( V_x = c_Groups_Ozero__class_Ozero(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
file('theBenchmark.p',fact_norm__sgn) ).
fof(fact_poly__rec__0,axiom,
! [T_a,V_z_2,V_f_2,T_b] :
( class_Groups_Ozero(T_b)
=> ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
=> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2 ) ),
file('theBenchmark.p',fact_poly__rec__0) ).
fof(fact_field__le__mult__one__interval,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( ! [B_z] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z)
=> ( c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x),V_y) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_field__le__mult__one__interval) ).
fof(fact_sgn__sgn,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ),
file('theBenchmark.p',fact_sgn__sgn) ).
fof(fact_sgn__zero__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_sgn__zero__iff) ).
fof(fact_sgn__0__0,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_sgn__0__0) ).
fof(fact_sgn__zero,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__vector(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_sgn__zero) ).
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__mult,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ),
file('theBenchmark.p',fact_sgn__mult) ).
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_sgn__one,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_sgn__one) ).
fof(fact_sgn__less,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_sgn__less) ).
fof(fact_sgn__greater,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_sgn__greater) ).
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)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ),
file('theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_abs__sgn,axiom,
! [V_k,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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_real__sgn__pos,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sgn__pos) ).
fof(fact_sgn__pos,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( 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_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_less__zeroE,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_less__zeroE) ).
fof(fact_le0,axiom,
! [V_n] : 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_field__le__epsilon,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( ! [B_e] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_e)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e)) )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_field__le__epsilon) ).
fof(fact_coeff__1,axiom,
! [V_n,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_coeff__1) ).
fof(fact_norm__diff__triangle__ineq,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ),
file('theBenchmark.p',fact_norm__diff__triangle__ineq) ).
fof(fact_sgn__neg,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( 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) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_sgn__neg) ).
fof(fact_nat__diff__split__asm,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,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 = 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)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_nat__diff__split,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
<=> ( ! [B_d] :
( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
=> hBOOL(hAPP(V_P_2,B_d)) )
& ( 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_diff__add__0,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ),
file('theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_diff__0__eq__0,axiom,
! [V_n] : 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_zero__less__diff,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_zero__less__diff) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_diff__self__eq__0,axiom,
! [V_m] : 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_diff__less,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ),
file('theBenchmark.p',fact_diff__less) ).
fof(fact_diffs0__imp__equal,axiom,
! [V_n,V_m] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( 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_less__or__eq__imp__le,axiom,
! [V_n,V_m] :
( ( V_m = V_n
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_less__diff__iff,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ),
file('theBenchmark.p',fact_less__diff__iff) ).
fof(fact_diff__less__mono,axiom,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ),
file('theBenchmark.p',fact_diff__less__mono) ).
fof(fact_le__neq__implies__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( V_m != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_diff__is__0__eq_H,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> 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_less__imp__le__nat,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_diff__is__0__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ( V_ma_2 != V_n_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__less__le) ).
fof(fact_diff__0,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ),
file('theBenchmark.p',fact_diff__0) ).
fof(fact_nat__less__cases,axiom,
! [V_P_2,V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
=> ( ( V_ma_2 = V_n_2
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
fof(fact_diff__less__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ),
file('theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_less__not__refl3,axiom,
! [V_t,V_s] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
=> V_s != V_t ),
file('theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> V_m != V_n ),
file('theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__irrefl__nat,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_linorder__neqE__nat,axiom,
! [V_y,V_x] :
( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_nat__neq__iff,axiom,
! [V_n_2,V_ma_2] :
( V_ma_2 != V_n_2
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_less__not__refl,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__not__refl) ).
fof(fact_add__lessD1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
=> 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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
=> 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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__less__add1) ).
fof(fact_add__diff__inverse,axiom,
! [V_n,V_m] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_less__diff__conv,axiom,
! [V_k_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_not__add__less2,axiom,
! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i),
file('theBenchmark.p',fact_not__add__less1) ).
fof(fact_diff__def,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_diff__def) ).
fof(fact_ab__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_ab__diff__minus) ).
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)
=> c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_diff__minus__eq__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_poly__diff,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__diff) ).
fof(fact_poly__minus,axiom,
! [V_x,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
file('theBenchmark.p',fact_poly__minus) ).
fof(fact_minus__real__def,axiom,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
file('theBenchmark.p',fact_minus__real__def) ).
fof(fact_real__diff__def,axiom,
! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
file('theBenchmark.p',fact_real__diff__def) ).
fof(fact_expand__poly__eq,axiom,
! [V_q_2,V_pa_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( V_pa_2 = V_q_2
<=> ! [B_n] : hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_a,V_q_2),B_n) ) ),
file('theBenchmark.p',fact_expand__poly__eq) ).
fof(fact_coeff__minus,axiom,
! [V_n,V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)) ),
file('theBenchmark.p',fact_coeff__minus) ).
fof(fact_coeff__inject,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Ocoeff(T_a,V_x_2) = c_Polynomial_Ocoeff(T_a,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_coeff__inject) ).
fof(fact_coeff__diff,axiom,
! [V_n,V_q,V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)) ),
file('theBenchmark.p',fact_coeff__diff) ).
fof(fact_minus__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ),
file('theBenchmark.p',fact_minus__minus) ).
fof(fact_minus__diff__eq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ),
file('theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_equation__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) ),
file('theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
<=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( class_Groups_Oab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
=> ( V_a_2 = V_b_2
<=> V_ca_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_norm__triangle__ineq2,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_le__refl,axiom,
! [V_n] : 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] : 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] : 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_diff__le__self,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m),
file('theBenchmark.p',fact_diff__le__self) ).
fof(fact_nat__le__linear,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| 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
=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> 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_diff__le__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ),
file('theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
=> 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_eq__diff__iff,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
<=> V_ma_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [V_n,V_m,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = 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_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ),
file('theBenchmark.p',fact_le__diff__iff) ).
fof(fact_add__leE,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ),
file('theBenchmark.p',fact_add__leE) ).
fof(fact_add__leD1,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
file('theBenchmark.p',fact_add__leD2) ).
fof(fact_add__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
file('theBenchmark.p',fact_add__le__mono) ).
fof(fact_diff__add__assoc2,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ),
file('theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_add__diff__assoc2,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_le__imp__diff__is__add,axiom,
! [V_k_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
<=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ),
file('theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_le__add__diff__inverse2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_le__diff__conv2,axiom,
! [V_i_2,V_j_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ),
file('theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_add__diff__assoc,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_le__add__diff__inverse,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,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__le__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_add__le__mono1) ).
fof(fact_le__add__diff,axiom,
! [V_m,V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ),
file('theBenchmark.p',fact_le__add__diff) ).
fof(fact_trans__le__add2,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
file('theBenchmark.p',fact_trans__le__add2) ).
fof(fact_trans__le__add1,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__le__add1) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_le__diff__conv,axiom,
! [V_i_2,V_k_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) ),
file('theBenchmark.p',fact_le__diff__conv) ).
fof(fact_diff__diff__right,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ),
file('theBenchmark.p',fact_diff__diff__right) ).
fof(fact_le__iff__add,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) ),
file('theBenchmark.p',fact_le__iff__add) ).
fof(fact_le__Suc__ex__iff,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
<=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ),
file('theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_le__add1,axiom,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
file('theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_le__add2) ).
fof(fact_diff__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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)
=> 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_a] :
( class_Groups_Oab__group__add(T_a)
=> ( V_a_2 = V_b_2
<=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_right__minus__eq) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_d_2) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_minus__zero,axiom,
! [T_a] :
( class_Groups_Ogroup__add(T_a)
=> 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_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
<=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ),
file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_equal__neg__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_neg__equal__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_diff__eq__diff__less,axiom,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_le__imp__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ),
file('theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_neg__le__iff__le,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_minus__le__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ),
file('theBenchmark.p',fact_minus__le__iff) ).
fof(fact_le__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ),
file('theBenchmark.p',fact_le__minus__iff) ).
fof(fact_less__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
fof(fact_minus__less__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,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_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_mult_Odiff__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(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),V_b_H)) ),
file('theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [V_y,V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ),
file('theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult_Odiff__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(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_H),V_b)) ),
file('theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_diff__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ),
file('theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_add__diff__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ),
file('theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_minus__mult__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> 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),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)
=> 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),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) ),
file('theBenchmark.p',fact_minus__mult__left) ).
fof(fact_mult_Ominus__right,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_mult__right_Ominus,axiom,
! [V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)) ),
file('theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_mult__left_Ominus,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) ),
file('theBenchmark.p',fact_mult__left_Ominus) ).
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),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),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),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),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_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
<=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_square__eq__iff) ).
fof(fact_minus__add__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ),
file('theBenchmark.p',fact_minus__add) ).
fof(fact_add__minus__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ),
file('theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_minus__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ),
file('theBenchmark.p',fact_minus__add__cancel) ).
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) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_abs__minus__commute,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ),
file('theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_norm__minus__commute,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ),
file('theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_abs__minus__cancel,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
file('theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_norm__minus__cancel,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ),
file('theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_abs__poly__def,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) ) ) ),
file('theBenchmark.p',fact_abs__poly__def) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_sgn__minus,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ),
file('theBenchmark.p',fact_sgn__minus) ).
fof(fact_norm__triangle__ineq3,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(fact_le__iff__diff__le__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_minus__le__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__0__le__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__less__nonneg,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_less__minus__self__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_right__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,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_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
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)
=> c_Groups_Oplus__class_Oplus(T_a,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)
=> c_Groups_Oplus__class_Oplus(T_a,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)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ),
file('theBenchmark.p',fact_minus__unique) ).
fof(fact_add__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ),
file('theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_mult__diff__mult,axiom,
! [V_b,V_a,V_y,V_x,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ominus__class_Ominus(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_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ),
file('theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [V_b,V_a,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Ominus__class_Ominus(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_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ),
file('theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
<=> V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,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_ca_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
<=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_square__eq__1__iff,axiom,
! [V_x_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
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)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_abs__triangle__ineq2__sym,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,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)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,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)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,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_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,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)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),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_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_abs__less__iff) ).
fof(fact_real__le__eq__diff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_real__minus__mult__self__le,axiom,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)),
file('theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_real__add__eq__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ),
file('theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_real__add__minus__iff,axiom,
! [V_a_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = V_a_2 ),
file('theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_coeff__0,axiom,
! [V_n,T_a] :
( class_Groups_Ozero(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_coeff__0) ).
fof(fact_abs__le__interval__iff,axiom,
! [V_ra_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) ) ),
file('theBenchmark.p',fact_abs__le__interval__iff) ).
fof(fact_abs__minus__add__cancel,axiom,
! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))),
file('theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_coeff__add,axiom,
! [V_n,V_q,V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)) ),
file('theBenchmark.p',fact_coeff__add) ).
fof(fact_sgn__poly__def,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_sgn__poly__def) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) ) ),
file('theBenchmark.p',fact_le__add__iff2) ).
fof(fact_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) ) ),
file('theBenchmark.p',fact_less__add__iff2) ).
fof(fact_less__add__iff1,axiom,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2) ) ),
file('theBenchmark.p',fact_less__add__iff1) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [V_x,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_abs__minus__le__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = 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)
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
& ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = 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)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ),
file('theBenchmark.p',fact_abs__of__neg) ).
fof(fact_abs__triangle__ineq4,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ),
file('theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ),
file('theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_norm__diff__ineq,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_norm__triangle__ineq4,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))) ),
file('theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(fact_real__0__le__add__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
file('theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
file('theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_sgn__real__def,axiom,
! [V_a] :
( ( V_a != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) )
& ( V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_sgn__real__def) ).
fof(fact_real__sgn__def,axiom,
! [V_x] :
( ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__sgn__def) ).
fof(fact_real__0__less__add__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
file('theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
file('theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_abs__real__def,axiom,
! [V_a] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) ) ),
file('theBenchmark.p',fact_abs__real__def) ).
fof(fact_real__abs__def,axiom,
! [V_r] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) ) ),
file('theBenchmark.p',fact_real__abs__def) ).
fof(fact_abs__sum__triangle__ineq,axiom,
! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))),
file('theBenchmark.p',fact_abs__sum__triangle__ineq) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le__0__eq,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_le__0__eq) ).
fof(fact_mult__le__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_mult__le__cancel2,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_gr0I,axiom,
! [V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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_mult__less__mono2,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> 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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> 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_gr__implies__not0,axiom,
! [V_n,V_m] :
( 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_mult__cancel2,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel2) ).
fof(fact_mult__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
& 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_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) ),
file('theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__is__0,axiom,
! [V_n_2,V_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__is__0) ).
fof(fact_less__nat__zero__code,axiom,
! [V_n] : ~ 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_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_nat__0__less__mult__iff,axiom,
! [V_n_2,V_ma_2] :
( 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_ma_2),V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) ) ),
file('theBenchmark.p',fact_nat__0__less__mult__iff) ).
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_neq0__conv,axiom,
! [V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_not__less0,axiom,
! [V_n] : ~ 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_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_add__eq__self__zero,axiom,
! [V_n,V_m] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
=> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_add__is__0,axiom,
! [V_n_2,V_ma_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_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] : 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_add__gr__0,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) ) ),
file('theBenchmark.p',fact_add__gr__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [V_n] : 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_sgn__if,axiom,
! [V_x,T_a] :
( class_Groups_Osgn__if(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( ~ 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_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) )
& ( 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_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_abs__diff__less__iff,axiom,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
<=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) ) ) ),
file('theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)),
file('theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
file('theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_nat__less__add__iff2,axiom,
! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_nat__less__add__iff1,axiom,
! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2) ) ),
file('theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__add__commute,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
file('theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
file('theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_diff__add__inverse2,axiom,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__add__inverse,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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_nat__add__assoc,axiom,
! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
file('theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_diff__diff__left,axiom,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
file('theBenchmark.p',fact_diff__diff__left) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
<=> V_ma_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_nat__add__right__cancel,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
<=> V_ma_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_diff__cancel,axiom,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__commute,axiom,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j),
file('theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__mult__distrib,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = 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_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_diff__mult__distrib2,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = 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_nat__mult__commute,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
file('theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_nat__mult__1,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_nat__mult__1) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [V_n_2,V_ma_2] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_nat__mult__1__right,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [V_n_2,V_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_add__mult__distrib,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = 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),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = 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] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_nat__mult__eq__cancel__disj,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_ma_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_nat__eq__add__iff2,axiom,
! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( 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_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
<=> V_ma_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) ) ),
file('theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_nat__diff__add__eq2,axiom,
! [V_n,V_m,V_u,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ),
file('theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_nat__le__add__iff2,axiom,
! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__eq__add__iff1,axiom,
! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( 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_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2) = V_n_2 ) ),
file('theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__diff__add__eq1,axiom,
! [V_n,V_m,V_u,V_i,V_j] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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__le__add__iff1,axiom,
! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2) ) ),
file('theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_complex__diff__def,axiom,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
file('theBenchmark.p',fact_complex__diff__def) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( 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_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> V_ma_2 = V_n_2 ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_natceiling__add__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_natceiling__add__one) ).
fof(fact_natfloor__add__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_natfloor__zero) ).
fof(fact_zero__le__natfloor,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),
file('theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_natfloor__mono,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ),
file('theBenchmark.p',fact_natfloor__mono) ).
fof(fact_natfloor__one,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_natfloor__one) ).
fof(fact_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_natceiling__zero) ).
fof(fact_zero__le__natceiling,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),
file('theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_natceiling__mono,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ),
file('theBenchmark.p',fact_natceiling__mono) ).
fof(fact_natceiling__one,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_natceiling__one) ).
fof(fact_natfloor__neg,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_natfloor__neg) ).
fof(fact_natceiling__neg,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_natceiling__neg) ).
fof(fact_le__natfloor__eq__one,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ),
file('theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natceiling__le__eq__one,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_le__mult__natfloor,axiom,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))) ) ),
file('theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,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_I5_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_natceiling__eq,axiom,
! [V_x,V_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_natceiling__eq) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) ),
file('theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ),
file('theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_natfloor__real__of__nat,axiom,
! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
file('theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_natceiling__real__of__nat,axiom,
! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
file('theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_real__of__nat__inject,axiom,
! [V_ma_2,V_n_2] :
( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
<=> V_n_2 = V_ma_2 ),
file('theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
file('theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [V_n_2] :
( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_real__of__nat__less__iff,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ),
file('theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_real__of__nat__le__iff,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ),
file('theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_real__of__nat__mult,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_real__of__nat__add,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__1) ).
fof(fact_real__natceiling__ge,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))),
file('theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
fof(fact_real__of__nat__diff,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ),
file('theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_real__natfloor__le,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ),
file('theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_le__natfloor,axiom,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ),
file('theBenchmark.p',fact_le__natfloor) ).
fof(fact_natceiling__le,axiom,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
file('theBenchmark.p',fact_natceiling__le) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
file('theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_nat__less__real__le,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ),
file('theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_le__natfloor__eq,axiom,
! [V_a_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2) ) ),
file('theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_natceiling__le__eq,axiom,
! [V_a_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)) ) ),
file('theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_natfloor__subtract,axiom,
! [V_x,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ),
file('theBenchmark.p',fact_natfloor__subtract) ).
fof(fact_real__natfloor__gt__diff__one,axiom,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),
file('theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
fof(fact_natceiling__subtract,axiom,
! [V_x,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
file('theBenchmark.p',fact_natceiling__subtract) ).
fof(fact_less__natfloor,axiom,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ),
file('theBenchmark.p',fact_less__natfloor) ).
fof(fact_natfloor__add,axiom,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ),
file('theBenchmark.p',fact_natfloor__add) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [V_n,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ),
file('theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_natfloor__eq,axiom,
! [V_x,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(V_x) = V_n ) ),
file('theBenchmark.p',fact_natfloor__eq) ).
fof(fact_natceiling__add,axiom,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
file('theBenchmark.p',fact_natceiling__add) ).
fof(fact_reals__Archimedean6,axiom,
! [V_r] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
=> ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r) ) ),
file('theBenchmark.p',fact_reals__Archimedean6) ).
fof(fact_compl__le__compl__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_compl__mono,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ),
file('theBenchmark.p',fact_compl__mono) ).
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_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_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_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( class_Groups_Ominus(T_a)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,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_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,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_b,T_a] :
( class_Groups_Ouminus(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,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)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ),
file('theBenchmark.p',fact_double__compl) ).
fof(fact_lemma__interval,axiom,
! [V_b,V_x,V_a] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
=> ? [B_d] :
( ! [B_y] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,V_b)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a,B_y) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ) ) ),
file('theBenchmark.p',fact_lemma__interval) ).
fof(fact_ex__least__nat__less,axiom,
! [V_n_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(V_P_2,V_n_2))
=> ? [B_k] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
=> ~ hBOOL(hAPP(V_P_2,B_i)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) ) ) ),
file('theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_less__poly__def,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
<=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ),
file('theBenchmark.p',fact_less__poly__def) ).
fof(fact_not__pos__poly__0,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('theBenchmark.p',fact_not__pos__poly__0) ).
fof(fact_pos__poly__add,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,V_p)
=> ( c_Polynomial_Opos__poly(T_a,V_q)
=> c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ),
file('theBenchmark.p',fact_pos__poly__add) ).
fof(fact_pos__poly__mult,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,V_p)
=> ( c_Polynomial_Opos__poly(T_a,V_q)
=> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ),
file('theBenchmark.p',fact_pos__poly__mult) ).
fof(fact_less__eq__poly__def,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
<=> ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_less__eq__poly__def) ).
fof(fact_pos__poly__total,axiom,
! [V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| c_Polynomial_Opos__poly(T_a,V_p)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_pos__poly__total) ).
fof(fact_lemma__interval__lt,axiom,
! [V_b,V_x,V_a] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
=> ? [B_d] :
( ! [B_y] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,V_b)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,B_y) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ) ) ),
file('theBenchmark.p',fact_lemma__interval__lt) ).
fof(fact_lemmaCauchy,axiom,
! [V_X_2,V_M_2,T_a,T_b] :
( ( class_Orderings_Oord(T_a)
& class_RealVector_Oreal__normed__vector(T_b) )
=> ( ! [B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))) ) ) ),
file('theBenchmark.p',fact_lemmaCauchy) ).
fof(fact_reals__Archimedean3,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ! [B_y] :
? [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x)) ),
file('theBenchmark.p',fact_reals__Archimedean3) ).
fof(fact_decseq__def,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Odecseq(T_a,V_X_2)
<=> ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ),
file('theBenchmark.p',fact_decseq__def) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)) ),
file('theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_Bseq__def,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) ),
file('theBenchmark.p',fact_Bseq__def) ).
fof(fact_norm__power__ineq,axiom,
! [V_n,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)) ),
file('theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),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_norm__power,axiom,
! [V_n,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ),
file('theBenchmark.p',fact_norm__power) ).
fof(fact_poly__power,axiom,
! [V_x,V_n,V_p,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ),
file('theBenchmark.p',fact_poly__power) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [V_q,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_realpow__minus__mult,axiom,
! [V_x,V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ),
file('theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_realpow__num__eq__if,axiom,
! [V_m,V_n,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),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),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_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_power__strict__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> 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_one__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> 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_nat__zero__less__power__iff,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ),
file('theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
=> ( 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))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [V_n_2,V_x_2] :
( 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_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_zpower__zadd__distrib,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),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_power__real__of__nat,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_real__of__nat__power,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n),
file('theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_natfloor__power,axiom,
! [V_n,V_x] :
( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ),
file('theBenchmark.p',fact_natfloor__power) ).
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),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_field__power__not__zero,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_power__mult__distrib,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
file('theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_power__commutes,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__commutes) ).
fof(fact_power__one,axiom,
! [V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__one) ).
fof(fact_power__mult,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ),
file('theBenchmark.p',fact_power__mult) ).
fof(fact_power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ),
file('theBenchmark.p',fact_power__abs) ).
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_power__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> 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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> 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)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> 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_one__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> 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__eq__0__iff,axiom,
! [V_n_2,V_a_2,T_a] :
( ( class_Rings_Ozero__neq__one(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Omult__zero(T_a)
& class_Power_Opower(T_a) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_power__inject__exp,axiom,
! [V_n_2,V_ma_2,V_a_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
<=> V_ma_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
fof(fact_power__0,axiom,
! [V_a,T_a] :
( class_Power_Opower(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__0) ).
fof(fact_power__add,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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_abs__power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)) = 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_power__less__imp__less__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( 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))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_power__less__power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> 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)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> 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_zero__le__power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)) ),
file('theBenchmark.p',fact_zero__le__power__abs) ).
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),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),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__minus) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( 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))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
<=> 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__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_power__Suc__less,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
file('theBenchmark.p',fact_power__Suc__less) ).
fof(fact_power__strict__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> 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__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)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> 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__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
<=> 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__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( 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))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_Bseq__iff2,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_k] :
( ? [B_x] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) ) ),
file('theBenchmark.p',fact_Bseq__iff2) ).
fof(fact_Bseq__iff3,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_k] :
( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) ) ),
file('theBenchmark.p',fact_Bseq__iff3) ).
fof(fact_power__power__power,axiom,
! [T_a] :
( class_Power_Opower(T_a)
=> c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ),
file('theBenchmark.p',fact_power__power__power) ).
fof(fact_zero__le__zpower__abs,axiom,
! [V_n,V_x] : 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)),
file('theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_zle__diff1__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
<=> 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_zless__le,axiom,
! [V_w_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
<=> ( V_z_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) ) ),
file('theBenchmark.p',fact_zless__le) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_le__imp__0__less,axiom,
! [V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ),
file('theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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_zadd__zless__mono,axiom,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ),
file('theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_odd__nonzero,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_zadd__0,axiom,
! [V_z] : 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] : 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_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_zmult__1,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zmult__1) ).
fof(fact_zmult__1__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zmult__1__right) ).
fof(fact_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_abs__zmult__eq__1,axiom,
! [V_n,V_m] :
( 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)
=> 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_zadd__zmult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
file('theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = 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_zless__add1__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,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
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_zadd__strict__right__mono,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ),
file('theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_zless__linear,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
file('theBenchmark.p',fact_zless__linear) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_int__0__less__1) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_zmult__zless__mono2,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
=> 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_odd__less__0,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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))
<=> 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_zabs__less__one__iff,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,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_zdiff__zmult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = 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_zmult__zminus,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = 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_zdiff__zmult__distrib2,axiom,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = 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_zminus__0,axiom,
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_zsgn__def,axiom,
! [V_i] :
( ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( ~ 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_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( 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_less__bin__lemma,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_zabs__def,axiom,
! [V_i] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) ) ),
file('theBenchmark.p',fact_zabs__def) ).
fof(fact_power_Opower_Opower__0,axiom,
! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,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_decr__lemma,axiom,
! [V_z,V_x,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z) ),
file('theBenchmark.p',fact_decr__lemma) ).
fof(fact_incr__lemma,axiom,
! [V_x,V_z,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,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_zminus__zadd__distrib,axiom,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_diff__int__def,axiom,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,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] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
file('theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_zminus__zminus,axiom,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
file('theBenchmark.p',fact_zminus__zminus) ).
fof(fact_zadd__assoc,axiom,
! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
file('theBenchmark.p',fact_zadd__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
file('theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_zadd__commute,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_zle__antisym,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
=> ( 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ),
file('theBenchmark.p',fact_zle__trans) ).
fof(fact_zle__linear,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| 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] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
file('theBenchmark.p',fact_zle__refl) ).
fof(fact_zadd__left__mono,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ),
file('theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_self__quotient__aux1,axiom,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_self__quotient__aux2,axiom,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_q__pos__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> 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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,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))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
=> 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] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = 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_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
=> 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] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = 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_Orderings_Oord__class_Oless(tc_Int_Oint,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))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> 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__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> 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_zero__less__power__nat__eq,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
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_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> 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_tsub__def,axiom,
! [V_x,V_y] :
( ( ~ 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) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ),
file('theBenchmark.p',fact_tsub__def) ).
fof(fact_BseqI,axiom,
! [V_X_2,V_K_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)
=> ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
=> c_SEQ_OBseq(T_a,V_X_2) ) ) ),
file('theBenchmark.p',fact_BseqI) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_tsub__eq,axiom,
! [V_x,V_y] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ),
file('theBenchmark.p',fact_tsub__eq) ).
fof(fact_BseqD,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
=> ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) ),
file('theBenchmark.p',fact_BseqD) ).
fof(fact_decr__mult__lemma,axiom,
! [V_k_2,V_P_2,V_d_2] :
( 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,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2))) )
=> ( 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,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] :
( 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2))) )
=> ( 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,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_realpow__pos__nth__unique,axiom,
! [V_a,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> ? [B_x] :
( ! [B_y] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) )
=> B_y = B_x )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) ) ) ),
file('theBenchmark.p',fact_realpow__pos__nth__unique) ).
fof(fact_realpow__pos__nth,axiom,
! [V_a,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> ? [B_r] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) ) ) ),
file('theBenchmark.p',fact_realpow__pos__nth) ).
fof(fact_ln__realpow,axiom,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x)) ),
file('theBenchmark.p',fact_ln__realpow) ).
fof(fact_ln__one,axiom,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_ln__one) ).
fof(fact_ln__less__self,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),V_x) ),
file('theBenchmark.p',fact_ln__less__self) ).
fof(fact_ln__inj__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
=> ( c_Transcendental_Oln(V_x_2) = c_Transcendental_Oln(V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_ln__inj__iff) ).
fof(fact_ln__less__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_ln__less__cancel__iff) ).
fof(fact_ln__le__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_ln__le__cancel__iff) ).
fof(fact_ln__ge__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)) ),
file('theBenchmark.p',fact_ln__ge__zero) ).
fof(fact_ln__gt__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)) ),
file('theBenchmark.p',fact_ln__gt__zero) ).
fof(fact_ln__gt__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ),
file('theBenchmark.p',fact_ln__gt__zero__iff) ).
fof(fact_ln__eq__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Transcendental_Oln(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_ln__eq__zero__iff) ).
fof(fact_ln__less__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('theBenchmark.p',fact_ln__less__zero__iff) ).
fof(fact_ln__less__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
file('theBenchmark.p',fact_ln__less__zero) ).
fof(fact_ln__gt__zero__imp__gt__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ) ),
file('theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).
fof(fact_ln__ge__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ),
file('theBenchmark.p',fact_ln__ge__zero__iff) ).
fof(fact_ln__ge__zero__imp__ge__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ) ),
file('theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).
fof(fact_ln__mult,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y)) ) ),
file('theBenchmark.p',fact_ln__mult) ).
fof(fact_ln__add__one__self__le__self,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x) ),
file('theBenchmark.p',fact_ln__add__one__self__le__self) ).
fof(fact_incseq__def,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Oincseq(T_a,V_X_2)
<=> ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) ) ) ),
file('theBenchmark.p',fact_incseq__def) ).
fof(fact_int__val__lemma,axiom,
! [V_k_2,V_f_2,V_n_2] :
( ! [B_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,V_n_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_f_2,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)) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,hAPP(V_f_2,V_n_2))
=> ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,V_n_2) ) ) ) ),
file('theBenchmark.p',fact_int__val__lemma) ).
fof(fact_nat0__intermed__int__val,axiom,
! [V_k_2,V_f_2,V_n_2] :
( ! [B_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,V_n_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_f_2,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)) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,hAPP(V_f_2,V_n_2))
=> ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,V_n_2) ) ) ) ),
file('theBenchmark.p',fact_nat0__intermed__int__val) ).
fof(fact_BseqI2_H,axiom,
! [V_K_2,V_X_2,V_N_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( ! [B_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2,B_n)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2) )
=> c_SEQ_OBseq(T_a,V_X_2) ) ),
file('theBenchmark.p',fact_BseqI2_H) ).
fof(fact_lemma__NBseq__def,axiom,
! [V_X_2,T_b] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_lemma__NBseq__def) ).
fof(fact_lemma__NBseq__def2,axiom,
! [V_X_2,T_b] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_lemma__NBseq__def2) ).
fof(fact_lessI,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_lessI) ).
fof(fact_Suc__mono,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_Suc__mono) ).
fof(fact_zero__less__Suc,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(fact_less__iff__Suc__add,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)) ),
file('theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__add__Suc2,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
file('theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_less__add__Suc1,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
file('theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_Suc__le__lessD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_le__less__Suc__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
<=> V_n_2 = V_ma_2 ) ),
file('theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
file('theBenchmark.p',fact_Suc__leI) ).
fof(fact_le__imp__less__Suc,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_Suc__le__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__Suc__eq__le,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__eq__Suc__le,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) ),
file('theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_One__nat__def) ).
fof(fact_diff__less__Suc,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
file('theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_mult__Suc__right,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = 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),c_Nat_OSuc(V_m)),V_n) = 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_Suc__mult__le__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_one__is__add,axiom,
! [V_n_2,V_ma_2] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [V_n_2,V_ma_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_add__is__1) ).
fof(fact_diff__Suc__1,axiom,
! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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__Suc__eq__diff__pred,axiom,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
file('theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_Suc__diff__diff,axiom,
! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_add__Suc__right,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_add__Suc__right) ).
fof(fact_add__Suc,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_Suc__n__not__le__n,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
file('theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_not__less__eq__eq,axiom,
! [V_n_2,V_ma_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_le__Suc__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> ( V_ma_2 = c_Nat_OSuc(V_n_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__le__mono,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__SucI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_le__SucI) ).
fof(fact_le__SucE,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> V_m = c_Nat_OSuc(V_n) ) ),
file('theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__leD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__leD) ).
fof(fact_Suc__eq__plus1,axiom,
! [V_n] : c_Nat_OSuc(V_n) = 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_Suc__eq__plus1__left,axiom,
! [V_n] : c_Nat_OSuc(V_n) = 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__diff__le,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
file('theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_Suc__inject,axiom,
! [V_y,V_x] :
( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
=> V_x = V_y ),
file('theBenchmark.p',fact_Suc__inject) ).
fof(fact_nat_Oinject,axiom,
! [V_nat_H_2,V_nat_2] :
( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
<=> V_nat_2 = V_nat_H_2 ),
file('theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__n__not__n,axiom,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
file('theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [V_n] : V_n != c_Nat_OSuc(V_n),
file('theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_Suc__mult__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
<=> V_ma_2 = V_n_2 ),
file('theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_Suc__neq__Zero,axiom,
! [V_m] : 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) != c_Nat_OSuc(V_m),
file('theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__not__Zero,axiom,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H),
file('theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__not__Suc,axiom,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
file('theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_not__less__eq,axiom,
! [V_n_2,V_ma_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) ),
file('theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__Suc__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__less__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [V_ma_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
<=> V_n_2 = V_ma_2 ) ),
file('theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [V_m,V_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_less__SucI) ).
fof(fact_Suc__lessI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Nat_OSuc(V_m) != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ),
file('theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_less__SucE,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
=> ( ~ 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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> 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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> ( ? [B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
& V_ma_2 = c_Nat_OSuc(B_j) )
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_less__Suc0,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_less__Suc0) ).
fof(fact_gr0__conv__Suc,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
<=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ),
file('theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_mult__eq__1__iff,axiom,
! [V_n_2,V_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)),
file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).
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),c_Nat_OSuc(V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_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),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_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),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_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),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),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ),
file('theBenchmark.p',fact_power__Suc2) ).
fof(fact_power__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)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_power__0__Suc) ).
fof(fact_power__Suc__0,axiom,
! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = 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_ma_2,V_x_2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_power__le__imp__le__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_power__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( 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__gt1,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> 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),c_Nat_OSuc(V_n))) ) ),
file('theBenchmark.p',fact_power__gt1) ).
fof(fact_realpow__two__disj,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_realpow__two__disj) ).
fof(fact_one__less__mult,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,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] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> 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_n__less__m__mult__n,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> 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_diff__Suc__less,axiom,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n) ),
file('theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_Suc__pred,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
file('theBenchmark.p',fact_Suc__pred) ).
fof(fact_one__le__mult__iff,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ma_2) ) ),
file('theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_real__of__nat__Suc__gt__zero,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
file('theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [V_m,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [V_m,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_real__of__nat__one,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__one) ).
fof(fact_real__of__nat__Suc,axiom,
! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_nat__one__le__power,axiom,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_realpow__Suc__le__self,axiom,
! [V_n,V_r,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r) ) ) ),
file('theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_power__Suc__less__one,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ),
file('theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_lemma__realpow__diff,axiom,
! [V_y,V_n,V_p,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ),
file('theBenchmark.p',fact_lemma__realpow__diff) ).
fof(fact_Suc__pred_H,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_n = c_Nat_OSuc(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_Suc__diff__1,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Nat_OSuc(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_add__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n ) ),
file('theBenchmark.p',fact_add__eq__if) ).
fof(fact_Bseq__iff,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_Bseq__iff) ).
fof(fact_Bseq__iff1a,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_Bseq__iff1a) ).
fof(fact_realpow__two__diff,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ),
file('theBenchmark.p',fact_realpow__two__diff) ).
fof(fact_reals__Archimedean4,axiom,
! [V_x,V_y] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y),V_x) ) ) ),
file('theBenchmark.p',fact_reals__Archimedean4) ).
fof(fact_int__power__div__base,axiom,
! [V_k,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
=> 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('theBenchmark.p',fact_int__power__div__base) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_div__self,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> 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_zdiv__self,axiom,
! [V_a] :
( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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_zdiv__zminus__zminus,axiom,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),
file('theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(fact_zdiv__zminus2,axiom,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b),
file('theBenchmark.p',fact_zdiv__zminus2) ).
fof(fact_div__by__1,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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_pos__imp__zdiv__neg__iff,axiom,
! [V_a_2,V_b_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> 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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> 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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,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_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)
=> 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_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)
=> 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)) = 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)
=> 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)
=> 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)
=> 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_Divides_Odiv__class_Odiv(T_a,V_a,V_b) )
& ( V_c = c_Groups_Ozero__class_Ozero(T_a)
=> 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_zdiv__zero,axiom,
! [V_b] : 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_div__by__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_div__by__0) ).
fof(fact_div__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> 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_zdiv__eq__0__iff,axiom,
! [V_k_2,V_i_2] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
& 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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
<=> 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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
<=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
& 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
=> 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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
<=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
=> 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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),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] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,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] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,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)
=> c_Divides_Odiv__class_Odiv(T_a,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_Groups_Oplus__class_Oplus(T_a,V_c,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)
=> c_Divides_Odiv__class_Odiv(T_a,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_Groups_Oplus__class_Oplus(T_a,V_c,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)
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,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)
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,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_split__zdiv,axiom,
! [V_k_2,V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [B_i] :
( ? [B_j] :
( V_n_2 = 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)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) )
=> hBOOL(hAPP(V_P_2,B_i)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
=> ! [B_i] :
( ? [B_j] :
( V_n_2 = 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)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
& 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 = 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)
=> ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)
& 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)
=> 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_z3div__def,axiom,
! [V_k,V_l] :
( ( ~ 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) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))) )
& ( 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) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l) ) ),
file('theBenchmark.p',fact_z3div__def) ).
fof(fact_reals__Archimedean6a,axiom,
! [V_r] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
=> ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r) ) ),
file('theBenchmark.p',fact_reals__Archimedean6a) ).
fof(fact_div__1,axiom,
! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
file('theBenchmark.p',fact_div__1) ).
fof(fact_div__le__dividend,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),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] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,V_b),V_c),
file('theBenchmark.p',fact_div__mult2__eq) ).
fof(fact_div__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> 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)
=> 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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) )
& ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> 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_poly__div__mult__right,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z) ),
file('theBenchmark.p',fact_poly__div__mult__right) ).
fof(fact_poly__div__minus__left,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ),
file('theBenchmark.p',fact_poly__div__minus__left) ).
fof(fact_poly__div__minus__right,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ),
file('theBenchmark.p',fact_poly__div__minus__right) ).
fof(fact_div__le__mono2,axiom,
! [V_k,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)) ) ),
file('theBenchmark.p',fact_div__le__mono2) ).
fof(fact_nat__mult__div__cancel1,axiom,
! [V_n,V_m,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> 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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_nat__mult__div__cancel1) ).
fof(fact_div__mult__self__is__m,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m ),
file('theBenchmark.p',fact_div__mult__self__is__m) ).
fof(fact_div__mult__self1__is__m,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> 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__less__dividend,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ) ),
file('theBenchmark.p',fact_div__less__dividend) ).
fof(fact_div__if,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> 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_div__geq,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ),
file('theBenchmark.p',fact_div__geq) ).
fof(fact_split__div,axiom,
! [V_k_2,V_n_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
<=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [B_i,B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
=> ( V_n_2 = 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(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
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__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_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__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_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__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__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__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
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__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__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
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__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__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__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
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__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__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__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
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__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__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
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__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__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
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__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
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__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_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).
fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
! [T_1] :
( class_Fields_Ofield(T_1)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [T_1] :
( class_Groups_Ozero(T_1)
=> class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
file('theBenchmark.p',conj_0) ).
fof(f_1_1,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
inference(fof_nnf,[status(thm)],[fact_ext]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = U_2
| ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
fof(f_1_4,plain,
! [U_1,U_2] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,plain,
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(fof_nnf,[status(thm)],[fact__0960_A_060_061_Acmod_Ac_096]) ).
fof(f_2_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
inference(fof_nnf,[status(thm)],[fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096]) ).
fof(f_3_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
inference(definitional_conversion,[status(esa)],[f_3_1]) ).
cnf(f_3_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))),
inference(fof_nnf,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(f_4_2,plain,
! [U_3] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_3))),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_3] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_3))),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_3))),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x),
inference(fof_nnf,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(f_5_2,plain,
! [U_4] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_4),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_4] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_4),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_4),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [V_s,V_y,V_r,V_x,T_a] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__add__less]) ).
fof(f_6_2,plain,
! [U_9,U_8,U_7,U_6,U_5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,c_Groups_Oplus__class_Oplus(U_5,U_6,U_8)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_7,U_9))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,U_8),U_9)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,U_6),U_7)
| ~ class_RealVector_Oreal__normed__vector(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_5,U_6,U_7,U_8,U_9] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,c_Groups_Oplus__class_Oplus(U_5,U_6,U_8)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_7,U_9))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,U_8),U_9)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,U_6),U_7)
| ~ class_RealVector_Oreal__normed__vector(U_5) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,c_Groups_Oplus__class_Oplus(U_5,U_6,U_8)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_7,U_9))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,U_8),U_9)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_5,U_6),U_7)
| ~ class_RealVector_Oreal__normed__vector(U_5) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [V_s,V_y,V_r,V_x,T_a] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__mult__less]) ).
fof(f_7_2,plain,
! [U_14,U_13,U_12,U_11,U_10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_12),U_14))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_13),U_14)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_11),U_12)
| ~ class_RealVector_Oreal__normed__algebra(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_10,U_11,U_12,U_13,U_14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_12),U_14))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_13),U_14)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_11),U_12)
| ~ class_RealVector_Oreal__normed__algebra(U_10) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_12),U_14))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_13),U_14)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_11),U_12)
| ~ class_RealVector_Oreal__normed__algebra(U_10) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
| V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff]) ).
fof(f_8_2,plain,
! [U_16,U_15] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_15,U_16))
| U_16 = c_Groups_Ozero__class_Ozero(U_15) )
& ( U_16 != c_Groups_Ozero__class_Ozero(U_15)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_15,U_16)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_15) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_15,U_16] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_15,U_16))
| U_16 = c_Groups_Ozero__class_Ozero(U_15)
| ~ sP0(U_15,U_16) )
& ! [U_15,U_16] :
( U_16 != c_Groups_Ozero__class_Ozero(U_15)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_15,U_16))
| ~ sP0(U_15,U_16) )
& ! [U_15,U_16] :
( sP0(U_15,U_16)
| ~ class_RealVector_Oreal__normed__vector(U_15) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP0(U_15,U_16)
| ~ class_RealVector_Oreal__normed__vector(U_15) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( U_16 != c_Groups_Ozero__class_Ozero(U_15)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_15,U_16))
| ~ sP0(U_15,U_16) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_15,U_16))
| U_16 = c_Groups_Ozero__class_Ozero(U_15)
| ~ sP0(U_15,U_16) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),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_9_2,plain,
! [U_17] :
( c_Orderings_Oord__class_Oless(U_17,c_Groups_Ozero__class_Ozero(U_17),c_Groups_Oplus__class_Oplus(U_17,c_Groups_Oone__class_Oone(U_17),c_Groups_Oone__class_Oone(U_17)))
| ~ class_Rings_Olinordered__semidom(U_17) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_17] :
( c_Orderings_Oord__class_Oless(U_17,c_Groups_Ozero__class_Ozero(U_17),c_Groups_Oplus__class_Oplus(U_17,c_Groups_Oone__class_Oone(U_17),c_Groups_Oone__class_Oone(U_17)))
| ~ class_Rings_Olinordered__semidom(U_17) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( c_Orderings_Oord__class_Oless(U_17,c_Groups_Ozero__class_Ozero(U_17),c_Groups_Oplus__class_Oplus(U_17,c_Groups_Oone__class_Oone(U_17),c_Groups_Oone__class_Oone(U_17)))
| ~ class_Rings_Olinordered__semidom(U_17) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,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_10_2,plain,
! [U_20,U_19,U_18] :
( ~ c_Orderings_Oord__class_Oless(U_18,c_Groups_Oplus__class_Oplus(U_18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18),U_19),U_19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18),U_20),U_20)),c_Groups_Ozero__class_Ozero(U_18))
| ~ class_Rings_Olinordered__ring(U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_18,U_19,U_20] :
( ~ c_Orderings_Oord__class_Oless(U_18,c_Groups_Oplus__class_Oplus(U_18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18),U_19),U_19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18),U_20),U_20)),c_Groups_Ozero__class_Ozero(U_18))
| ~ class_Rings_Olinordered__ring(U_18) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_18,c_Groups_Oplus__class_Oplus(U_18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18),U_19),U_19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18),U_20),U_20)),c_Groups_Ozero__class_Ozero(U_18))
| ~ class_Rings_Olinordered__ring(U_18) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).
fof(f_11_2,plain,
! [U_23,U_22,U_21] :
( ( ( c_Orderings_Oord__class_Oless(U_21,c_Groups_Ozero__class_Ozero(U_21),c_Groups_Oplus__class_Oplus(U_21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_22),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_23),U_23)))
| ( U_23 = c_Groups_Ozero__class_Ozero(U_21)
& U_22 = c_Groups_Ozero__class_Ozero(U_21) ) )
& ( U_23 != c_Groups_Ozero__class_Ozero(U_21)
| U_22 != c_Groups_Ozero__class_Ozero(U_21)
| ~ c_Orderings_Oord__class_Oless(U_21,c_Groups_Ozero__class_Ozero(U_21),c_Groups_Oplus__class_Oplus(U_21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_22),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_23),U_23))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_21) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_22,U_23,U_21] :
( U_23 = c_Groups_Ozero__class_Ozero(U_21)
| ~ sP1(U_22,U_23,U_21) )
& ! [U_22,U_23,U_21] :
( U_22 = c_Groups_Ozero__class_Ozero(U_21)
| ~ sP1(U_22,U_23,U_21) )
& ! [U_22,U_23,U_21] :
( c_Orderings_Oord__class_Oless(U_21,c_Groups_Ozero__class_Ozero(U_21),c_Groups_Oplus__class_Oplus(U_21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_22),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_23),U_23)))
| sP1(U_22,U_23,U_21)
| ~ sP2(U_22,U_23,U_21) )
& ! [U_22,U_23,U_21] :
( U_23 != c_Groups_Ozero__class_Ozero(U_21)
| U_22 != c_Groups_Ozero__class_Ozero(U_21)
| ~ c_Orderings_Oord__class_Oless(U_21,c_Groups_Ozero__class_Ozero(U_21),c_Groups_Oplus__class_Oplus(U_21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_22),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_23),U_23)))
| ~ sP2(U_22,U_23,U_21) )
& ! [U_22,U_23,U_21] :
( sP2(U_22,U_23,U_21)
| ~ class_Rings_Olinordered__ring__strict(U_21) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP2(U_22,U_23,U_21)
| ~ class_Rings_Olinordered__ring__strict(U_21) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( U_23 != c_Groups_Ozero__class_Ozero(U_21)
| U_22 != c_Groups_Ozero__class_Ozero(U_21)
| ~ c_Orderings_Oord__class_Oless(U_21,c_Groups_Ozero__class_Ozero(U_21),c_Groups_Oplus__class_Oplus(U_21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_22),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_23),U_23)))
| ~ sP2(U_22,U_23,U_21) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( c_Orderings_Oord__class_Oless(U_21,c_Groups_Ozero__class_Ozero(U_21),c_Groups_Oplus__class_Oplus(U_21,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_22),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_21),U_23),U_23)))
| sP1(U_22,U_23,U_21)
| ~ sP2(U_22,U_23,U_21) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( U_22 = c_Groups_Ozero__class_Ozero(U_21)
| ~ sP1(U_22,U_23,U_21) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_8,plain,
( U_23 = c_Groups_Ozero__class_Ozero(U_21)
| ~ sP1(U_22,U_23,U_21) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff]) ).
fof(f_12_2,plain,
! [U_25,U_24] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_24),U_24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_25),U_25)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_25 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_24 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_25 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_24 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_24),U_24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_25),U_25)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_29,U_27] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_27),U_27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_29),U_29)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_29 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_27 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_28,U_26] :
( ( U_28 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_26 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_26),U_26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_28),U_28)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_26,U_28] :
( U_28 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP3(U_26,U_28) )
& ! [U_26,U_28] :
( U_26 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP3(U_26,U_28) )
& ! [U_29,U_27] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_27),U_27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_29),U_29)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_29 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_27 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_26,U_28] :
( sP3(U_26,U_28)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_26),U_26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_28),U_28)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_12_3]) ).
cnf(f_12_5,plain,
( sP3(U_26,U_28)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_26),U_26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_28),U_28)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_27),U_27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_29),U_29)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_29 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_27 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_7,plain,
( U_26 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP3(U_26,U_28) ),
inference(clausify,[status(thm)],[f_12_4]) ).
cnf(f_12_8,plain,
( U_28 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP3(U_26,U_28) ),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__one]) ).
fof(f_13_2,plain,
! [U_30] :
( c_RealVector_Onorm__class_Onorm(U_30,c_Groups_Oone__class_Oone(U_30)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_30) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_30] :
( c_RealVector_Onorm__class_Onorm(U_30,c_Groups_Oone__class_Oone(U_30)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_30) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( c_RealVector_Onorm__class_Onorm(U_30,c_Groups_Oone__class_Oone(U_30)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_30) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__not__less__zero]) ).
fof(f_14_2,plain,
! [U_32,U_31] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_31,U_32),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_31) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_31,U_32] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_31,U_32),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_31) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_31,U_32),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_31) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [V_x_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(f_15_2,plain,
! [U_33] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_33),U_33))
| U_33 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_33 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_33),U_33)) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_35] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_35),U_35))
| U_35 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_34] :
( U_34 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_34),U_34)) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_35] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_35),U_35))
| U_35 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_34] :
( U_34 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_34),U_34)) ) ),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
( U_34 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_34),U_34)) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_35),U_35))
| U_35 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
inference(fof_nnf,[status(thm)],[fact_real__le__refl]) ).
fof(f_16_2,plain,
! [U_36] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_36,U_36),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_36] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_36,U_36),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_36,U_36),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_real__le__linear]) ).
fof(f_17_2,plain,
! [U_38,U_37] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_38,U_37)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_37,U_38) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_37,U_38] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_38,U_37)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_37,U_38) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_38,U_37)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_37,U_38) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_real__le__trans]) ).
fof(f_18_2,plain,
! [U_41,U_40,U_39] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_39,U_41)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_40,U_41)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_39,U_40) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_39,U_40,U_41] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_39,U_41)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_40,U_41)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_39,U_40) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_39,U_41)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_40,U_41)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_39,U_40) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_real__le__antisym]) ).
fof(f_19_2,plain,
! [U_43,U_42] :
( U_42 = U_43
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_43,U_42)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_42,U_43) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_43,U_42] :
( U_42 = U_43
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_43,U_42)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_42,U_43) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( U_42 = U_43
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_43,U_42)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_42,U_43) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__real__def]) ).
fof(f_20_2,plain,
! [U_45,U_44] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_44,U_45)
| ( U_44 != U_45
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_44,U_45) ) )
& ( U_44 = U_45
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_44,U_45)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_44,U_45) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_49,U_47] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_47,U_49)
| ( U_47 != U_49
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_47,U_49) ) )
& ! [U_48,U_46] :
( U_46 = U_48
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_46,U_48)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_46,U_48) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_49,U_47] :
( U_47 != U_49
| ~ sP4(U_49,U_47) )
& ! [U_49,U_47] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_47,U_49)
| ~ sP4(U_49,U_47) )
& ! [U_49,U_47] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_47,U_49)
| sP4(U_49,U_47) )
& ! [U_46,U_48] :
( U_46 = U_48
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_46,U_48)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_46,U_48) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_20_3]) ).
cnf(f_20_5,plain,
( U_46 = U_48
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_46,U_48)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_46,U_48) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_47,U_49)
| sP4(U_49,U_47) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_47,U_49)
| ~ sP4(U_49,U_47) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_8,plain,
( U_47 != U_49
| ~ sP4(U_49,U_47) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__less__def]) ).
fof(f_21_2,plain,
! [U_51,U_50] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_50,U_51)
| U_50 = U_51
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_50,U_51) )
& ( ( U_50 != U_51
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_50,U_51) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_50,U_51) ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_55,U_53] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_53,U_55)
| U_53 = U_55
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_53,U_55) )
& ! [U_54,U_52] :
( ( U_52 != U_54
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_52,U_54) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_52,U_54) ) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_52,U_54] :
( U_52 != U_54
| ~ sP5(U_52,U_54) )
& ! [U_52,U_54] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_52,U_54)
| ~ sP5(U_52,U_54) )
& ! [U_53,U_55] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_53,U_55)
| U_53 = U_55
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_53,U_55) )
& ! [U_52,U_54] :
( sP5(U_52,U_54)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_52,U_54) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_21_3]) ).
cnf(f_21_5,plain,
( sP5(U_52,U_54)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_52,U_54) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_53,U_55)
| U_53 = U_55
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_53,U_55) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_52,U_54)
| ~ sP5(U_52,U_54) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_8,plain,
( U_52 != U_54
| ~ sP5(U_52,U_54) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
inference(fof_nnf,[status(thm)],[fact_real__norm__def]) ).
fof(f_22_2,plain,
! [U_56] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_56) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_56),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_56] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_56) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_56),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_56) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_56),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__add__left__mono]) ).
fof(f_23_2,plain,
! [U_59,U_58,U_57] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_59,U_57),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_59,U_58))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_57,U_58) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_57,U_58,U_59] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_59,U_57),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_59,U_58))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_57,U_58) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_59,U_57),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_59,U_58))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_57,U_58) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))),
inference(fof_nnf,[status(thm)],[fact_complex__mod__triangle__sub]) ).
fof(f_24_2,plain,
! [U_61,U_60] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_60),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_60,U_61)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_61))),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_60,U_61] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_60),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_60,U_61)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_61))),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_60),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_60,U_61)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_61))),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_25_2,plain,
! [U_64,U_63,U_62] :
( c_Orderings_Oord__class_Oless__eq(U_62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_62),U_63),U_64),c_Groups_Ozero__class_Ozero(U_62))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_62,c_Groups_Ozero__class_Ozero(U_62),U_64)
| ~ c_Orderings_Oord__class_Oless__eq(U_62,U_63,c_Groups_Ozero__class_Ozero(U_62)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_62,U_64,c_Groups_Ozero__class_Ozero(U_62))
| ~ c_Orderings_Oord__class_Oless__eq(U_62,c_Groups_Ozero__class_Ozero(U_62),U_63) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_62) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_62,U_63,U_64] :
( ~ c_Orderings_Oord__class_Oless__eq(U_62,c_Groups_Ozero__class_Ozero(U_62),U_64)
| ~ c_Orderings_Oord__class_Oless__eq(U_62,U_63,c_Groups_Ozero__class_Ozero(U_62))
| ~ sP6(U_62,U_63,U_64) )
& ! [U_62,U_63,U_64] :
( ~ c_Orderings_Oord__class_Oless__eq(U_62,U_64,c_Groups_Ozero__class_Ozero(U_62))
| ~ c_Orderings_Oord__class_Oless__eq(U_62,c_Groups_Ozero__class_Ozero(U_62),U_63)
| ~ sP6(U_62,U_63,U_64) )
& ! [U_62,U_63,U_64] :
( c_Orderings_Oord__class_Oless__eq(U_62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_62),U_63),U_64),c_Groups_Ozero__class_Ozero(U_62))
| sP6(U_62,U_63,U_64)
| ~ class_Rings_Oordered__cancel__semiring(U_62) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_25_2]) ).
cnf(f_25_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_62,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_62),U_63),U_64),c_Groups_Ozero__class_Ozero(U_62))
| sP6(U_62,U_63,U_64)
| ~ class_Rings_Oordered__cancel__semiring(U_62) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_62,U_64,c_Groups_Ozero__class_Ozero(U_62))
| ~ c_Orderings_Oord__class_Oless__eq(U_62,c_Groups_Ozero__class_Ozero(U_62),U_63)
| ~ sP6(U_62,U_63,U_64) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_62,c_Groups_Ozero__class_Ozero(U_62),U_64)
| ~ c_Orderings_Oord__class_Oless__eq(U_62,U_63,c_Groups_Ozero__class_Ozero(U_62))
| ~ sP6(U_62,U_63,U_64) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_26_2,plain,
! [U_67,U_66,U_65] :
( c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_65),U_66),U_67))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_65,U_67,c_Groups_Ozero__class_Ozero(U_65))
| ~ c_Orderings_Oord__class_Oless__eq(U_65,U_66,c_Groups_Ozero__class_Ozero(U_65)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),U_67)
| ~ c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),U_66) ) )
| ~ class_Rings_Oordered__ring(U_65) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_66,U_65,U_67] :
( ~ c_Orderings_Oord__class_Oless__eq(U_65,U_67,c_Groups_Ozero__class_Ozero(U_65))
| ~ c_Orderings_Oord__class_Oless__eq(U_65,U_66,c_Groups_Ozero__class_Ozero(U_65))
| ~ sP7(U_66,U_65,U_67) )
& ! [U_66,U_65,U_67] :
( ~ c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),U_67)
| ~ c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),U_66)
| ~ sP7(U_66,U_65,U_67) )
& ! [U_66,U_65,U_67] :
( c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_65),U_66),U_67))
| sP7(U_66,U_65,U_67)
| ~ class_Rings_Oordered__ring(U_65) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_26_2]) ).
cnf(f_26_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_65),U_66),U_67))
| sP7(U_66,U_65,U_67)
| ~ class_Rings_Oordered__ring(U_65) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),U_67)
| ~ c_Orderings_Oord__class_Oless__eq(U_65,c_Groups_Ozero__class_Ozero(U_65),U_66)
| ~ sP7(U_66,U_65,U_67) ),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_65,U_67,c_Groups_Ozero__class_Ozero(U_65))
| ~ c_Orderings_Oord__class_Oless__eq(U_65,U_66,c_Groups_Ozero__class_Ozero(U_65))
| ~ sP7(U_66,U_65,U_67) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ 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_27_2,plain,
! [U_72,U_71,U_70,U_69,U_68] :
( c_Orderings_Oord__class_Oless__eq(U_68,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_68),U_69),U_71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_68),U_70),U_72))
| ~ c_Orderings_Oord__class_Oless__eq(U_68,c_Groups_Ozero__class_Ozero(U_68),U_71)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,c_Groups_Ozero__class_Ozero(U_68),U_70)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,U_71,U_72)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,U_69,U_70)
| ~ class_Rings_Oordered__semiring(U_68) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_70,U_69,U_68,U_71,U_72] :
( c_Orderings_Oord__class_Oless__eq(U_68,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_68),U_69),U_71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_68),U_70),U_72))
| ~ c_Orderings_Oord__class_Oless__eq(U_68,c_Groups_Ozero__class_Ozero(U_68),U_71)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,c_Groups_Ozero__class_Ozero(U_68),U_70)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,U_71,U_72)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,U_69,U_70)
| ~ class_Rings_Oordered__semiring(U_68) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_68,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_68),U_69),U_71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_68),U_70),U_72))
| ~ c_Orderings_Oord__class_Oless__eq(U_68,c_Groups_Ozero__class_Ozero(U_68),U_71)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,c_Groups_Ozero__class_Ozero(U_68),U_70)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,U_71,U_72)
| ~ c_Orderings_Oord__class_Oless__eq(U_68,U_69,U_70)
| ~ class_Rings_Oordered__semiring(U_68) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ 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_28_2,plain,
! [U_77,U_76,U_75,U_74,U_73] :
( c_Orderings_Oord__class_Oless__eq(U_73,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_73),U_74),U_76),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_73),U_75),U_77))
| ~ c_Orderings_Oord__class_Oless__eq(U_73,c_Groups_Ozero__class_Ozero(U_73),U_76)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,c_Groups_Ozero__class_Ozero(U_73),U_74)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_76,U_77)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_74,U_75)
| ~ class_Rings_Oordered__semiring(U_73) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_73,U_74,U_75,U_76,U_77] :
( c_Orderings_Oord__class_Oless__eq(U_73,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_73),U_74),U_76),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_73),U_75),U_77))
| ~ c_Orderings_Oord__class_Oless__eq(U_73,c_Groups_Ozero__class_Ozero(U_73),U_76)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,c_Groups_Ozero__class_Ozero(U_73),U_74)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_76,U_77)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_74,U_75)
| ~ class_Rings_Oordered__semiring(U_73) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_73,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_73),U_74),U_76),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_73),U_75),U_77))
| ~ c_Orderings_Oord__class_Oless__eq(U_73,c_Groups_Ozero__class_Ozero(U_73),U_76)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,c_Groups_Ozero__class_Ozero(U_73),U_74)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_76,U_77)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_74,U_75)
| ~ class_Rings_Oordered__semiring(U_73) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_29_2,plain,
! [U_81,U_80,U_79,U_78] :
( c_Orderings_Oord__class_Oless__eq(U_78,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_78),U_81),U_80),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_78),U_81),U_79))
| ~ c_Orderings_Oord__class_Oless__eq(U_78,U_81,c_Groups_Ozero__class_Ozero(U_78))
| ~ c_Orderings_Oord__class_Oless__eq(U_78,U_79,U_80)
| ~ class_Rings_Oordered__ring(U_78) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_78,U_79,U_80,U_81] :
( c_Orderings_Oord__class_Oless__eq(U_78,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_78),U_81),U_80),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_78),U_81),U_79))
| ~ c_Orderings_Oord__class_Oless__eq(U_78,U_81,c_Groups_Ozero__class_Ozero(U_78))
| ~ c_Orderings_Oord__class_Oless__eq(U_78,U_79,U_80)
| ~ class_Rings_Oordered__ring(U_78) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_78,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_78),U_81),U_80),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_78),U_81),U_79))
| ~ c_Orderings_Oord__class_Oless__eq(U_78,U_81,c_Groups_Ozero__class_Ozero(U_78))
| ~ c_Orderings_Oord__class_Oless__eq(U_78,U_79,U_80)
| ~ class_Rings_Oordered__ring(U_78) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_30_2,plain,
! [U_85,U_84,U_83,U_82] :
( c_Orderings_Oord__class_Oless__eq(U_82,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_82),U_84),U_85),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_82),U_83),U_85))
| ~ c_Orderings_Oord__class_Oless__eq(U_82,U_85,c_Groups_Ozero__class_Ozero(U_82))
| ~ c_Orderings_Oord__class_Oless__eq(U_82,U_83,U_84)
| ~ class_Rings_Oordered__ring(U_82) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_85,U_82,U_83,U_84] :
( c_Orderings_Oord__class_Oless__eq(U_82,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_82),U_84),U_85),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_82),U_83),U_85))
| ~ c_Orderings_Oord__class_Oless__eq(U_82,U_85,c_Groups_Ozero__class_Ozero(U_82))
| ~ c_Orderings_Oord__class_Oless__eq(U_82,U_83,U_84)
| ~ class_Rings_Oordered__ring(U_82) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_82,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_82),U_84),U_85),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_82),U_83),U_85))
| ~ c_Orderings_Oord__class_Oless__eq(U_82,U_85,c_Groups_Ozero__class_Ozero(U_82))
| ~ c_Orderings_Oord__class_Oless__eq(U_82,U_83,U_84)
| ~ class_Rings_Oordered__ring(U_82) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_31_2,plain,
! [U_89,U_88,U_87,U_86] :
( c_Orderings_Oord__class_Oless__eq(U_86,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_86),U_89),U_87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_86),U_89),U_88))
| ~ c_Orderings_Oord__class_Oless__eq(U_86,c_Groups_Ozero__class_Ozero(U_86),U_89)
| ~ c_Orderings_Oord__class_Oless__eq(U_86,U_87,U_88)
| ~ class_Rings_Oordered__comm__semiring(U_86) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_86,U_87,U_88,U_89] :
( c_Orderings_Oord__class_Oless__eq(U_86,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_86),U_89),U_87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_86),U_89),U_88))
| ~ c_Orderings_Oord__class_Oless__eq(U_86,c_Groups_Ozero__class_Ozero(U_86),U_89)
| ~ c_Orderings_Oord__class_Oless__eq(U_86,U_87,U_88)
| ~ class_Rings_Oordered__comm__semiring(U_86) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_86,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_86),U_89),U_87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_86),U_89),U_88))
| ~ c_Orderings_Oord__class_Oless__eq(U_86,c_Groups_Ozero__class_Ozero(U_86),U_89)
| ~ c_Orderings_Oord__class_Oless__eq(U_86,U_87,U_88)
| ~ class_Rings_Oordered__comm__semiring(U_86) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_32_2,plain,
! [U_93,U_92,U_91,U_90] :
( c_Orderings_Oord__class_Oless__eq(U_90,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_90),U_93),U_91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_90),U_93),U_92))
| ~ c_Orderings_Oord__class_Oless__eq(U_90,c_Groups_Ozero__class_Ozero(U_90),U_93)
| ~ c_Orderings_Oord__class_Oless__eq(U_90,U_91,U_92)
| ~ class_Rings_Oordered__semiring(U_90) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_90,U_91,U_92,U_93] :
( c_Orderings_Oord__class_Oless__eq(U_90,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_90),U_93),U_91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_90),U_93),U_92))
| ~ c_Orderings_Oord__class_Oless__eq(U_90,c_Groups_Ozero__class_Ozero(U_90),U_93)
| ~ c_Orderings_Oord__class_Oless__eq(U_90,U_91,U_92)
| ~ class_Rings_Oordered__semiring(U_90) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_90,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_90),U_93),U_91),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_90),U_93),U_92))
| ~ c_Orderings_Oord__class_Oless__eq(U_90,c_Groups_Ozero__class_Ozero(U_90),U_93)
| ~ c_Orderings_Oord__class_Oless__eq(U_90,U_91,U_92)
| ~ class_Rings_Oordered__semiring(U_90) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_33_2,plain,
! [U_97,U_96,U_95,U_94] :
( c_Orderings_Oord__class_Oless__eq(U_94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_94),U_95),U_97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_94),U_96),U_97))
| ~ c_Orderings_Oord__class_Oless__eq(U_94,c_Groups_Ozero__class_Ozero(U_94),U_97)
| ~ c_Orderings_Oord__class_Oless__eq(U_94,U_95,U_96)
| ~ class_Rings_Oordered__semiring(U_94) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_96,U_94,U_95,U_97] :
( c_Orderings_Oord__class_Oless__eq(U_94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_94),U_95),U_97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_94),U_96),U_97))
| ~ c_Orderings_Oord__class_Oless__eq(U_94,c_Groups_Ozero__class_Ozero(U_94),U_97)
| ~ c_Orderings_Oord__class_Oless__eq(U_94,U_95,U_96)
| ~ class_Rings_Oordered__semiring(U_94) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_94,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_94),U_95),U_97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_94),U_96),U_97))
| ~ c_Orderings_Oord__class_Oless__eq(U_94,c_Groups_Ozero__class_Ozero(U_94),U_97)
| ~ c_Orderings_Oord__class_Oless__eq(U_94,U_95,U_96)
| ~ class_Rings_Oordered__semiring(U_94) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_34_2,plain,
! [U_100,U_99,U_98] :
( c_Orderings_Oord__class_Oless__eq(U_98,c_Groups_Ozero__class_Ozero(U_98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_98),U_99),U_100))
| ~ c_Orderings_Oord__class_Oless__eq(U_98,U_100,c_Groups_Ozero__class_Ozero(U_98))
| ~ c_Orderings_Oord__class_Oless__eq(U_98,U_99,c_Groups_Ozero__class_Ozero(U_98))
| ~ class_Rings_Oordered__ring(U_98) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_99,U_100,U_98] :
( c_Orderings_Oord__class_Oless__eq(U_98,c_Groups_Ozero__class_Ozero(U_98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_98),U_99),U_100))
| ~ c_Orderings_Oord__class_Oless__eq(U_98,U_100,c_Groups_Ozero__class_Ozero(U_98))
| ~ c_Orderings_Oord__class_Oless__eq(U_98,U_99,c_Groups_Ozero__class_Ozero(U_98))
| ~ class_Rings_Oordered__ring(U_98) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_98,c_Groups_Ozero__class_Ozero(U_98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_98),U_99),U_100))
| ~ c_Orderings_Oord__class_Oless__eq(U_98,U_100,c_Groups_Ozero__class_Ozero(U_98))
| ~ c_Orderings_Oord__class_Oless__eq(U_98,U_99,c_Groups_Ozero__class_Ozero(U_98))
| ~ class_Rings_Oordered__ring(U_98) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_35_2,plain,
! [U_103,U_102,U_101] :
( c_Orderings_Oord__class_Oless__eq(U_101,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_101),U_102),U_103),c_Groups_Ozero__class_Ozero(U_101))
| ~ c_Orderings_Oord__class_Oless__eq(U_101,c_Groups_Ozero__class_Ozero(U_101),U_103)
| ~ c_Orderings_Oord__class_Oless__eq(U_101,U_102,c_Groups_Ozero__class_Ozero(U_101))
| ~ class_Rings_Oordered__cancel__semiring(U_101) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_102,U_101,U_103] :
( c_Orderings_Oord__class_Oless__eq(U_101,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_101),U_102),U_103),c_Groups_Ozero__class_Ozero(U_101))
| ~ c_Orderings_Oord__class_Oless__eq(U_101,c_Groups_Ozero__class_Ozero(U_101),U_103)
| ~ c_Orderings_Oord__class_Oless__eq(U_101,U_102,c_Groups_Ozero__class_Ozero(U_101))
| ~ class_Rings_Oordered__cancel__semiring(U_101) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_101,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_101),U_102),U_103),c_Groups_Ozero__class_Ozero(U_101))
| ~ c_Orderings_Oord__class_Oless__eq(U_101,c_Groups_Ozero__class_Ozero(U_101),U_103)
| ~ c_Orderings_Oord__class_Oless__eq(U_101,U_102,c_Groups_Ozero__class_Ozero(U_101))
| ~ class_Rings_Oordered__cancel__semiring(U_101) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_36_2,plain,
! [U_106,U_105,U_104] :
( c_Orderings_Oord__class_Oless__eq(U_104,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_104),U_106),U_105),c_Groups_Ozero__class_Ozero(U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_104,U_106,c_Groups_Ozero__class_Ozero(U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_104,c_Groups_Ozero__class_Ozero(U_104),U_105)
| ~ class_Rings_Oordered__cancel__semiring(U_104) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_104,U_106,U_105] :
( c_Orderings_Oord__class_Oless__eq(U_104,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_104),U_106),U_105),c_Groups_Ozero__class_Ozero(U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_104,U_106,c_Groups_Ozero__class_Ozero(U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_104,c_Groups_Ozero__class_Ozero(U_104),U_105)
| ~ class_Rings_Oordered__cancel__semiring(U_104) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_104,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_104),U_106),U_105),c_Groups_Ozero__class_Ozero(U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_104,U_106,c_Groups_Ozero__class_Ozero(U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_104,c_Groups_Ozero__class_Ozero(U_104),U_105)
| ~ class_Rings_Oordered__cancel__semiring(U_104) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_37_2,plain,
! [U_109,U_108,U_107] :
( c_Orderings_Oord__class_Oless__eq(U_107,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_107),U_108),U_109),c_Groups_Ozero__class_Ozero(U_107))
| ~ c_Orderings_Oord__class_Oless__eq(U_107,U_109,c_Groups_Ozero__class_Ozero(U_107))
| ~ c_Orderings_Oord__class_Oless__eq(U_107,c_Groups_Ozero__class_Ozero(U_107),U_108)
| ~ class_Rings_Oordered__cancel__semiring(U_107) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_109,U_108,U_107] :
( c_Orderings_Oord__class_Oless__eq(U_107,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_107),U_108),U_109),c_Groups_Ozero__class_Ozero(U_107))
| ~ c_Orderings_Oord__class_Oless__eq(U_107,U_109,c_Groups_Ozero__class_Ozero(U_107))
| ~ c_Orderings_Oord__class_Oless__eq(U_107,c_Groups_Ozero__class_Ozero(U_107),U_108)
| ~ class_Rings_Oordered__cancel__semiring(U_107) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_107,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_107),U_108),U_109),c_Groups_Ozero__class_Ozero(U_107))
| ~ c_Orderings_Oord__class_Oless__eq(U_107,U_109,c_Groups_Ozero__class_Ozero(U_107))
| ~ c_Orderings_Oord__class_Oless__eq(U_107,c_Groups_Ozero__class_Ozero(U_107),U_108)
| ~ class_Rings_Oordered__cancel__semiring(U_107) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_38_2,plain,
! [U_112,U_111,U_110] :
( c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_111),U_112))
| ~ c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),U_112)
| ~ c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),U_111)
| ~ class_Rings_Oordered__cancel__semiring(U_110) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_110,U_112,U_111] :
( c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_111),U_112))
| ~ c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),U_112)
| ~ c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),U_111)
| ~ class_Rings_Oordered__cancel__semiring(U_110) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_111),U_112))
| ~ c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),U_112)
| ~ c_Orderings_Oord__class_Oless__eq(U_110,c_Groups_Ozero__class_Ozero(U_110),U_111)
| ~ class_Rings_Oordered__cancel__semiring(U_110) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).
fof(f_39_2,plain,
! [U_115,U_114,U_113] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_113),U_114),U_115),c_Groups_Ozero__class_Ozero(U_113))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_115)
| ~ c_Orderings_Oord__class_Oless__eq(U_113,U_114,c_Groups_Ozero__class_Ozero(U_113)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_113,U_115,c_Groups_Ozero__class_Ozero(U_113))
| ~ c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_114) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_115)
& c_Orderings_Oord__class_Oless__eq(U_113,U_114,c_Groups_Ozero__class_Ozero(U_113)) )
| ( c_Orderings_Oord__class_Oless__eq(U_113,U_115,c_Groups_Ozero__class_Ozero(U_113))
& c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_114) )
| ~ c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_113),U_114),U_115),c_Groups_Ozero__class_Ozero(U_113)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_113) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ! [U_114,U_113,U_115] :
( ~ c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_115)
| ~ c_Orderings_Oord__class_Oless__eq(U_113,U_114,c_Groups_Ozero__class_Ozero(U_113))
| ~ sP10(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( ~ c_Orderings_Oord__class_Oless__eq(U_113,U_115,c_Groups_Ozero__class_Ozero(U_113))
| ~ c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_114)
| ~ sP10(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_115)
| ~ sP9(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( c_Orderings_Oord__class_Oless__eq(U_113,U_114,c_Groups_Ozero__class_Ozero(U_113))
| ~ sP9(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( c_Orderings_Oord__class_Oless__eq(U_113,U_115,c_Groups_Ozero__class_Ozero(U_113))
| ~ sP8(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_114)
| ~ sP8(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_113),U_114),U_115),c_Groups_Ozero__class_Ozero(U_113))
| sP10(U_114,U_113,U_115)
| ~ sP11(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( sP9(U_114,U_113,U_115)
| sP8(U_114,U_113,U_115)
| ~ c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_113),U_114),U_115),c_Groups_Ozero__class_Ozero(U_113))
| ~ sP11(U_114,U_113,U_115) )
& ! [U_114,U_113,U_115] :
( sP11(U_114,U_113,U_115)
| ~ class_Rings_Olinordered__ring__strict(U_113) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9,sP10,sP11])],[f_39_2]) ).
cnf(f_39_4,plain,
( sP11(U_114,U_113,U_115)
| ~ class_Rings_Olinordered__ring__strict(U_113) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
( sP9(U_114,U_113,U_115)
| sP8(U_114,U_113,U_115)
| ~ c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_113),U_114),U_115),c_Groups_Ozero__class_Ozero(U_113))
| ~ sP11(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_113),U_114),U_115),c_Groups_Ozero__class_Ozero(U_113))
| sP10(U_114,U_113,U_115)
| ~ sP11(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_114)
| ~ sP8(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_113,U_115,c_Groups_Ozero__class_Ozero(U_113))
| ~ sP8(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_113,U_114,c_Groups_Ozero__class_Ozero(U_113))
| ~ sP9(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_115)
| ~ sP9(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_113,U_115,c_Groups_Ozero__class_Ozero(U_113))
| ~ c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_114)
| ~ sP10(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_113,c_Groups_Ozero__class_Ozero(U_113),U_115)
| ~ c_Orderings_Oord__class_Oless__eq(U_113,U_114,c_Groups_Ozero__class_Ozero(U_113))
| ~ sP10(U_114,U_113,U_115) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( 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_2),V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ 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_2),V_b_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).
fof(f_40_2,plain,
! [U_118,U_117,U_116] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_116),U_117),U_118))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_116,U_118,c_Groups_Ozero__class_Ozero(U_116))
| ~ c_Orderings_Oord__class_Oless__eq(U_116,U_117,c_Groups_Ozero__class_Ozero(U_116)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_118)
| ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_117) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_116,U_118,c_Groups_Ozero__class_Ozero(U_116))
& c_Orderings_Oord__class_Oless__eq(U_116,U_117,c_Groups_Ozero__class_Ozero(U_116)) )
| ( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_118)
& c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_117) )
| ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_116),U_117),U_118)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_116) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ! [U_116,U_117,U_118] :
( ~ c_Orderings_Oord__class_Oless__eq(U_116,U_118,c_Groups_Ozero__class_Ozero(U_116))
| ~ c_Orderings_Oord__class_Oless__eq(U_116,U_117,c_Groups_Ozero__class_Ozero(U_116))
| ~ sP14(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_118)
| ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_117)
| ~ sP14(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( c_Orderings_Oord__class_Oless__eq(U_116,U_118,c_Groups_Ozero__class_Ozero(U_116))
| ~ sP13(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( c_Orderings_Oord__class_Oless__eq(U_116,U_117,c_Groups_Ozero__class_Ozero(U_116))
| ~ sP13(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_118)
| ~ sP12(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_117)
| ~ sP12(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_116),U_117),U_118))
| sP14(U_116,U_117,U_118)
| ~ sP15(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( sP13(U_116,U_117,U_118)
| sP12(U_116,U_117,U_118)
| ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_116),U_117),U_118))
| ~ sP15(U_116,U_117,U_118) )
& ! [U_116,U_117,U_118] :
( sP15(U_116,U_117,U_118)
| ~ class_Rings_Olinordered__ring__strict(U_116) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12,sP13,sP14,sP15])],[f_40_2]) ).
cnf(f_40_4,plain,
( sP15(U_116,U_117,U_118)
| ~ class_Rings_Olinordered__ring__strict(U_116) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
( sP13(U_116,U_117,U_118)
| sP12(U_116,U_117,U_118)
| ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_116),U_117),U_118))
| ~ sP15(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_116),U_117),U_118))
| sP14(U_116,U_117,U_118)
| ~ sP15(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_117)
| ~ sP12(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_118)
| ~ sP12(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_116,U_117,c_Groups_Ozero__class_Ozero(U_116))
| ~ sP13(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_116,U_118,c_Groups_Ozero__class_Ozero(U_116))
| ~ sP13(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_118)
| ~ c_Orderings_Oord__class_Oless__eq(U_116,c_Groups_Ozero__class_Ozero(U_116),U_117)
| ~ sP14(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_116,U_118,c_Groups_Ozero__class_Ozero(U_116))
| ~ c_Orderings_Oord__class_Oless__eq(U_116,U_117,c_Groups_Ozero__class_Ozero(U_116))
| ~ sP14(U_116,U_117,U_118) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [V_a,T_a] :
( 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_41_2,plain,
! [U_120,U_119] :
( c_Orderings_Oord__class_Oless__eq(U_119,c_Groups_Ozero__class_Ozero(U_119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_119),U_120),U_120))
| ~ class_Rings_Olinordered__ring(U_119) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_119,U_120] :
( c_Orderings_Oord__class_Oless__eq(U_119,c_Groups_Ozero__class_Ozero(U_119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_119),U_120),U_120))
| ~ class_Rings_Olinordered__ring(U_119) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_119,c_Groups_Ozero__class_Ozero(U_119),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_119),U_120),U_120))
| ~ class_Rings_Olinordered__ring(U_119) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [T_a] :
( 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_42_2,plain,
! [U_121] :
( c_Orderings_Oord__class_Oless__eq(U_121,c_Groups_Ozero__class_Ozero(U_121),c_Groups_Oone__class_Oone(U_121))
| ~ class_Rings_Olinordered__semidom(U_121) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_121] :
( c_Orderings_Oord__class_Oless__eq(U_121,c_Groups_Ozero__class_Ozero(U_121),c_Groups_Oone__class_Oone(U_121))
| ~ class_Rings_Olinordered__semidom(U_121) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_121,c_Groups_Ozero__class_Ozero(U_121),c_Groups_Oone__class_Oone(U_121))
| ~ class_Rings_Olinordered__semidom(U_121) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [T_a] :
( ~ 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_43_2,plain,
! [U_122] :
( ~ c_Orderings_Oord__class_Oless__eq(U_122,c_Groups_Oone__class_Oone(U_122),c_Groups_Ozero__class_Ozero(U_122))
| ~ class_Rings_Olinordered__semidom(U_122) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_122] :
( ~ c_Orderings_Oord__class_Oless__eq(U_122,c_Groups_Oone__class_Oone(U_122),c_Groups_Ozero__class_Ozero(U_122))
| ~ class_Rings_Olinordered__semidom(U_122) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_122,c_Groups_Oone__class_Oone(U_122),c_Groups_Ozero__class_Ozero(U_122))
| ~ class_Rings_Olinordered__semidom(U_122) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__ge__zero]) ).
fof(f_44_2,plain,
! [U_124,U_123] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_123,U_124))
| ~ class_RealVector_Oreal__normed__vector(U_123) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_124,U_123] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_123,U_124))
| ~ class_RealVector_Oreal__normed__vector(U_123) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_123,U_124))
| ~ class_RealVector_Oreal__normed__vector(U_123) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_45_2,plain,
! [U_128,U_127,U_126,U_125] :
( c_Orderings_Oord__class_Oless__eq(U_125,U_127,U_128)
| ~ c_Orderings_Oord__class_Oless(U_125,c_Groups_Ozero__class_Ozero(U_125),U_126)
| ~ c_Orderings_Oord__class_Oless__eq(U_125,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_125),U_126),U_127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_125),U_126),U_128))
| ~ class_Rings_Olinordered__semiring__strict(U_125) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_128,U_125,U_127,U_126] :
( c_Orderings_Oord__class_Oless__eq(U_125,U_127,U_128)
| ~ c_Orderings_Oord__class_Oless(U_125,c_Groups_Ozero__class_Ozero(U_125),U_126)
| ~ c_Orderings_Oord__class_Oless__eq(U_125,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_125),U_126),U_127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_125),U_126),U_128))
| ~ class_Rings_Olinordered__semiring__strict(U_125) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_125,U_127,U_128)
| ~ c_Orderings_Oord__class_Oless(U_125,c_Groups_Ozero__class_Ozero(U_125),U_126)
| ~ c_Orderings_Oord__class_Oless__eq(U_125,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_125),U_126),U_127),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_125),U_126),U_128))
| ~ class_Rings_Olinordered__semiring__strict(U_125) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_46_2,plain,
! [U_132,U_131,U_130,U_129] :
( c_Orderings_Oord__class_Oless__eq(U_129,U_130,U_132)
| ~ c_Orderings_Oord__class_Oless(U_129,c_Groups_Ozero__class_Ozero(U_129),U_131)
| ~ c_Orderings_Oord__class_Oless__eq(U_129,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_130),U_131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_132),U_131))
| ~ class_Rings_Olinordered__semiring__strict(U_129) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_131,U_129,U_130,U_132] :
( c_Orderings_Oord__class_Oless__eq(U_129,U_130,U_132)
| ~ c_Orderings_Oord__class_Oless(U_129,c_Groups_Ozero__class_Ozero(U_129),U_131)
| ~ c_Orderings_Oord__class_Oless__eq(U_129,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_130),U_131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_132),U_131))
| ~ class_Rings_Olinordered__semiring__strict(U_129) ),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_129,U_130,U_132)
| ~ c_Orderings_Oord__class_Oless(U_129,c_Groups_Ozero__class_Ozero(U_129),U_131)
| ~ c_Orderings_Oord__class_Oless__eq(U_129,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_130),U_131),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_132),U_131))
| ~ class_Rings_Olinordered__semiring__strict(U_129) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_47_2,plain,
! [U_136,U_135,U_134,U_133] :
( c_Orderings_Oord__class_Oless(U_133,U_135,U_136)
| ~ c_Orderings_Oord__class_Oless__eq(U_133,c_Groups_Ozero__class_Ozero(U_133),U_134)
| ~ c_Orderings_Oord__class_Oless(U_133,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_133),U_134),U_135),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_133),U_134),U_136))
| ~ class_Rings_Olinordered__semiring__strict(U_133) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_136,U_134,U_135,U_133] :
( c_Orderings_Oord__class_Oless(U_133,U_135,U_136)
| ~ c_Orderings_Oord__class_Oless__eq(U_133,c_Groups_Ozero__class_Ozero(U_133),U_134)
| ~ c_Orderings_Oord__class_Oless(U_133,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_133),U_134),U_135),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_133),U_134),U_136))
| ~ class_Rings_Olinordered__semiring__strict(U_133) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( c_Orderings_Oord__class_Oless(U_133,U_135,U_136)
| ~ c_Orderings_Oord__class_Oless__eq(U_133,c_Groups_Ozero__class_Ozero(U_133),U_134)
| ~ c_Orderings_Oord__class_Oless(U_133,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_133),U_134),U_135),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_133),U_134),U_136))
| ~ class_Rings_Olinordered__semiring__strict(U_133) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_48_2,plain,
! [U_140,U_139,U_138,U_137] :
( c_Orderings_Oord__class_Oless(U_137,U_139,U_140)
| ~ c_Orderings_Oord__class_Oless__eq(U_137,c_Groups_Ozero__class_Ozero(U_137),U_138)
| ~ c_Orderings_Oord__class_Oless(U_137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),U_139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),U_140))
| ~ class_Rings_Olinordered__semiring(U_137) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_140,U_138,U_139,U_137] :
( c_Orderings_Oord__class_Oless(U_137,U_139,U_140)
| ~ c_Orderings_Oord__class_Oless__eq(U_137,c_Groups_Ozero__class_Ozero(U_137),U_138)
| ~ c_Orderings_Oord__class_Oless(U_137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),U_139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),U_140))
| ~ class_Rings_Olinordered__semiring(U_137) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( c_Orderings_Oord__class_Oless(U_137,U_139,U_140)
| ~ c_Orderings_Oord__class_Oless__eq(U_137,c_Groups_Ozero__class_Ozero(U_137),U_138)
| ~ c_Orderings_Oord__class_Oless(U_137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),U_139),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),U_140))
| ~ class_Rings_Olinordered__semiring(U_137) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_49_2,plain,
! [U_144,U_143,U_142,U_141] :
( c_Orderings_Oord__class_Oless(U_141,U_142,U_144)
| ~ c_Orderings_Oord__class_Oless__eq(U_141,c_Groups_Ozero__class_Ozero(U_141),U_143)
| ~ c_Orderings_Oord__class_Oless(U_141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),U_142),U_143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),U_144),U_143))
| ~ class_Rings_Olinordered__semiring__strict(U_141) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_143,U_142,U_141,U_144] :
( c_Orderings_Oord__class_Oless(U_141,U_142,U_144)
| ~ c_Orderings_Oord__class_Oless__eq(U_141,c_Groups_Ozero__class_Ozero(U_141),U_143)
| ~ c_Orderings_Oord__class_Oless(U_141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),U_142),U_143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),U_144),U_143))
| ~ class_Rings_Olinordered__semiring__strict(U_141) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( c_Orderings_Oord__class_Oless(U_141,U_142,U_144)
| ~ c_Orderings_Oord__class_Oless__eq(U_141,c_Groups_Ozero__class_Ozero(U_141),U_143)
| ~ c_Orderings_Oord__class_Oless(U_141,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),U_142),U_143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),U_144),U_143))
| ~ class_Rings_Olinordered__semiring__strict(U_141) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_50_2,plain,
! [U_148,U_147,U_146,U_145] :
( c_Orderings_Oord__class_Oless(U_145,U_146,U_148)
| ~ c_Orderings_Oord__class_Oless__eq(U_145,c_Groups_Ozero__class_Ozero(U_145),U_147)
| ~ c_Orderings_Oord__class_Oless(U_145,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_146),U_147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_148),U_147))
| ~ class_Rings_Olinordered__semiring(U_145) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_147,U_145,U_146,U_148] :
( c_Orderings_Oord__class_Oless(U_145,U_146,U_148)
| ~ c_Orderings_Oord__class_Oless__eq(U_145,c_Groups_Ozero__class_Ozero(U_145),U_147)
| ~ c_Orderings_Oord__class_Oless(U_145,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_146),U_147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_148),U_147))
| ~ class_Rings_Olinordered__semiring(U_145) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( c_Orderings_Oord__class_Oless(U_145,U_146,U_148)
| ~ c_Orderings_Oord__class_Oless__eq(U_145,c_Groups_Ozero__class_Ozero(U_145),U_147)
| ~ c_Orderings_Oord__class_Oless(U_145,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_146),U_147),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_148),U_147))
| ~ class_Rings_Olinordered__semiring(U_145) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ 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_51_2,plain,
! [U_153,U_152,U_151,U_150,U_149] :
( c_Orderings_Oord__class_Oless(U_149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_153))
| ~ c_Orderings_Oord__class_Oless__eq(U_149,c_Groups_Ozero__class_Ozero(U_149),U_152)
| ~ c_Orderings_Oord__class_Oless(U_149,c_Groups_Ozero__class_Ozero(U_149),U_150)
| ~ c_Orderings_Oord__class_Oless(U_149,U_152,U_153)
| ~ c_Orderings_Oord__class_Oless__eq(U_149,U_150,U_151)
| ~ class_Rings_Olinordered__semiring__strict(U_149) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_151,U_150,U_149,U_152,U_153] :
( c_Orderings_Oord__class_Oless(U_149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_153))
| ~ c_Orderings_Oord__class_Oless__eq(U_149,c_Groups_Ozero__class_Ozero(U_149),U_152)
| ~ c_Orderings_Oord__class_Oless(U_149,c_Groups_Ozero__class_Ozero(U_149),U_150)
| ~ c_Orderings_Oord__class_Oless(U_149,U_152,U_153)
| ~ c_Orderings_Oord__class_Oless__eq(U_149,U_150,U_151)
| ~ class_Rings_Olinordered__semiring__strict(U_149) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( c_Orderings_Oord__class_Oless(U_149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_153))
| ~ c_Orderings_Oord__class_Oless__eq(U_149,c_Groups_Ozero__class_Ozero(U_149),U_152)
| ~ c_Orderings_Oord__class_Oless(U_149,c_Groups_Ozero__class_Ozero(U_149),U_150)
| ~ c_Orderings_Oord__class_Oless(U_149,U_152,U_153)
| ~ c_Orderings_Oord__class_Oless__eq(U_149,U_150,U_151)
| ~ class_Rings_Olinordered__semiring__strict(U_149) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ 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_52_2,plain,
! [U_158,U_157,U_156,U_155,U_154] :
( c_Orderings_Oord__class_Oless(U_154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_154),U_155),U_157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_154),U_156),U_158))
| ~ c_Orderings_Oord__class_Oless(U_154,c_Groups_Ozero__class_Ozero(U_154),U_157)
| ~ c_Orderings_Oord__class_Oless__eq(U_154,c_Groups_Ozero__class_Ozero(U_154),U_155)
| ~ c_Orderings_Oord__class_Oless__eq(U_154,U_157,U_158)
| ~ c_Orderings_Oord__class_Oless(U_154,U_155,U_156)
| ~ class_Rings_Olinordered__semiring__strict(U_154) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_155,U_154,U_158,U_157,U_156] :
( c_Orderings_Oord__class_Oless(U_154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_154),U_155),U_157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_154),U_156),U_158))
| ~ c_Orderings_Oord__class_Oless(U_154,c_Groups_Ozero__class_Ozero(U_154),U_157)
| ~ c_Orderings_Oord__class_Oless__eq(U_154,c_Groups_Ozero__class_Ozero(U_154),U_155)
| ~ c_Orderings_Oord__class_Oless__eq(U_154,U_157,U_158)
| ~ c_Orderings_Oord__class_Oless(U_154,U_155,U_156)
| ~ class_Rings_Olinordered__semiring__strict(U_154) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( c_Orderings_Oord__class_Oless(U_154,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_154),U_155),U_157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_154),U_156),U_158))
| ~ c_Orderings_Oord__class_Oless(U_154,c_Groups_Ozero__class_Ozero(U_154),U_157)
| ~ c_Orderings_Oord__class_Oless__eq(U_154,c_Groups_Ozero__class_Ozero(U_154),U_155)
| ~ c_Orderings_Oord__class_Oless__eq(U_154,U_157,U_158)
| ~ c_Orderings_Oord__class_Oless(U_154,U_155,U_156)
| ~ class_Rings_Olinordered__semiring__strict(U_154) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ 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_53_2,plain,
! [U_163,U_162,U_161,U_160,U_159] :
( c_Orderings_Oord__class_Oless(U_159,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_159),U_160),U_162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_159),U_161),U_163))
| ~ c_Orderings_Oord__class_Oless__eq(U_159,c_Groups_Ozero__class_Ozero(U_159),U_162)
| ~ c_Orderings_Oord__class_Oless__eq(U_159,c_Groups_Ozero__class_Ozero(U_159),U_160)
| ~ c_Orderings_Oord__class_Oless(U_159,U_162,U_163)
| ~ c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| ~ class_Rings_Olinordered__semiring__strict(U_159) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_159,U_163,U_162,U_160,U_161] :
( c_Orderings_Oord__class_Oless(U_159,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_159),U_160),U_162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_159),U_161),U_163))
| ~ c_Orderings_Oord__class_Oless__eq(U_159,c_Groups_Ozero__class_Ozero(U_159),U_162)
| ~ c_Orderings_Oord__class_Oless__eq(U_159,c_Groups_Ozero__class_Ozero(U_159),U_160)
| ~ c_Orderings_Oord__class_Oless(U_159,U_162,U_163)
| ~ c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| ~ class_Rings_Olinordered__semiring__strict(U_159) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( c_Orderings_Oord__class_Oless(U_159,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_159),U_160),U_162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_159),U_161),U_163))
| ~ c_Orderings_Oord__class_Oless__eq(U_159,c_Groups_Ozero__class_Ozero(U_159),U_162)
| ~ c_Orderings_Oord__class_Oless__eq(U_159,c_Groups_Ozero__class_Ozero(U_159),U_160)
| ~ c_Orderings_Oord__class_Oless(U_159,U_162,U_163)
| ~ c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| ~ class_Rings_Olinordered__semiring__strict(U_159) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ 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_54_2,plain,
! [U_168,U_167,U_166,U_165,U_164] :
( c_Orderings_Oord__class_Oless(U_164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_165),U_167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_166),U_168))
| ~ c_Orderings_Oord__class_Oless__eq(U_164,c_Groups_Ozero__class_Ozero(U_164),U_167)
| ~ c_Orderings_Oord__class_Oless(U_164,c_Groups_Ozero__class_Ozero(U_164),U_166)
| ~ c_Orderings_Oord__class_Oless(U_164,U_167,U_168)
| ~ c_Orderings_Oord__class_Oless(U_164,U_165,U_166)
| ~ class_Rings_Olinordered__semiring__strict(U_164) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_164,U_165,U_168,U_166,U_167] :
( c_Orderings_Oord__class_Oless(U_164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_165),U_167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_166),U_168))
| ~ c_Orderings_Oord__class_Oless__eq(U_164,c_Groups_Ozero__class_Ozero(U_164),U_167)
| ~ c_Orderings_Oord__class_Oless(U_164,c_Groups_Ozero__class_Ozero(U_164),U_166)
| ~ c_Orderings_Oord__class_Oless(U_164,U_167,U_168)
| ~ c_Orderings_Oord__class_Oless(U_164,U_165,U_166)
| ~ class_Rings_Olinordered__semiring__strict(U_164) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( c_Orderings_Oord__class_Oless(U_164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_165),U_167),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_166),U_168))
| ~ c_Orderings_Oord__class_Oless__eq(U_164,c_Groups_Ozero__class_Ozero(U_164),U_167)
| ~ c_Orderings_Oord__class_Oless(U_164,c_Groups_Ozero__class_Ozero(U_164),U_166)
| ~ c_Orderings_Oord__class_Oless(U_164,U_167,U_168)
| ~ c_Orderings_Oord__class_Oless(U_164,U_165,U_166)
| ~ class_Rings_Olinordered__semiring__strict(U_164) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).
fof(f_55_2,plain,
! [U_172,U_171,U_170,U_169] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_172))
| ~ c_Orderings_Oord__class_Oless__eq(U_169,U_172,U_171) )
& ( c_Orderings_Oord__class_Oless__eq(U_169,U_172,U_171)
| ~ c_Orderings_Oord__class_Oless__eq(U_169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_172)) ) )
| ~ c_Orderings_Oord__class_Oless(U_169,U_170,c_Groups_Ozero__class_Ozero(U_169))
| ~ class_Rings_Olinordered__ring__strict(U_169) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ! [U_169,U_170,U_172,U_171] :
( c_Orderings_Oord__class_Oless__eq(U_169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_172))
| ~ c_Orderings_Oord__class_Oless__eq(U_169,U_172,U_171)
| ~ sP16(U_169,U_170,U_172,U_171) )
& ! [U_169,U_170,U_172,U_171] :
( c_Orderings_Oord__class_Oless__eq(U_169,U_172,U_171)
| ~ c_Orderings_Oord__class_Oless__eq(U_169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_172))
| ~ sP16(U_169,U_170,U_172,U_171) )
& ! [U_169,U_170,U_172,U_171] :
( sP16(U_169,U_170,U_172,U_171)
| ~ c_Orderings_Oord__class_Oless(U_169,U_170,c_Groups_Ozero__class_Ozero(U_169))
| ~ class_Rings_Olinordered__ring__strict(U_169) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_55_2]) ).
cnf(f_55_4,plain,
( sP16(U_169,U_170,U_172,U_171)
| ~ c_Orderings_Oord__class_Oless(U_169,U_170,c_Groups_Ozero__class_Ozero(U_169))
| ~ class_Rings_Olinordered__ring__strict(U_169) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_169,U_172,U_171)
| ~ c_Orderings_Oord__class_Oless__eq(U_169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_172))
| ~ sP16(U_169,U_170,U_172,U_171) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_169,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_169),U_170),U_172))
| ~ c_Orderings_Oord__class_Oless__eq(U_169,U_172,U_171)
| ~ sP16(U_169,U_170,U_172,U_171) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).
fof(f_56_2,plain,
! [U_176,U_175,U_174,U_173] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_176))
| ~ c_Orderings_Oord__class_Oless__eq(U_173,U_175,U_176) )
& ( c_Orderings_Oord__class_Oless__eq(U_173,U_175,U_176)
| ~ c_Orderings_Oord__class_Oless__eq(U_173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_176)) ) )
| ~ c_Orderings_Oord__class_Oless(U_173,c_Groups_Ozero__class_Ozero(U_173),U_174)
| ~ class_Rings_Olinordered__ring__strict(U_173) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_173,U_175,U_174,U_176] :
( c_Orderings_Oord__class_Oless__eq(U_173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_176))
| ~ c_Orderings_Oord__class_Oless__eq(U_173,U_175,U_176)
| ~ sP17(U_173,U_175,U_174,U_176) )
& ! [U_173,U_175,U_174,U_176] :
( c_Orderings_Oord__class_Oless__eq(U_173,U_175,U_176)
| ~ c_Orderings_Oord__class_Oless__eq(U_173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_176))
| ~ sP17(U_173,U_175,U_174,U_176) )
& ! [U_173,U_175,U_174,U_176] :
( sP17(U_173,U_175,U_174,U_176)
| ~ c_Orderings_Oord__class_Oless(U_173,c_Groups_Ozero__class_Ozero(U_173),U_174)
| ~ class_Rings_Olinordered__ring__strict(U_173) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_56_2]) ).
cnf(f_56_4,plain,
( sP17(U_173,U_175,U_174,U_176)
| ~ c_Orderings_Oord__class_Oless(U_173,c_Groups_Ozero__class_Ozero(U_173),U_174)
| ~ class_Rings_Olinordered__ring__strict(U_173) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_173,U_175,U_176)
| ~ c_Orderings_Oord__class_Oless__eq(U_173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_176))
| ~ sP17(U_173,U_175,U_174,U_176) ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_173),U_174),U_176))
| ~ c_Orderings_Oord__class_Oless__eq(U_173,U_175,U_176)
| ~ sP17(U_173,U_175,U_174,U_176) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).
fof(f_57_2,plain,
! [U_179,U_178,U_177] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_177,c_Groups_Oplus__class_Oplus(U_177,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_178),U_178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_179),U_179)),c_Groups_Ozero__class_Ozero(U_177))
| U_179 != c_Groups_Ozero__class_Ozero(U_177)
| U_178 != c_Groups_Ozero__class_Ozero(U_177) )
& ( ( U_179 = c_Groups_Ozero__class_Ozero(U_177)
& U_178 = c_Groups_Ozero__class_Ozero(U_177) )
| ~ c_Orderings_Oord__class_Oless__eq(U_177,c_Groups_Oplus__class_Oplus(U_177,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_178),U_178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_179),U_179)),c_Groups_Ozero__class_Ozero(U_177)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_177) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ! [U_178,U_177,U_179] :
( U_179 = c_Groups_Ozero__class_Ozero(U_177)
| ~ sP18(U_178,U_177,U_179) )
& ! [U_178,U_177,U_179] :
( U_178 = c_Groups_Ozero__class_Ozero(U_177)
| ~ sP18(U_178,U_177,U_179) )
& ! [U_178,U_177,U_179] :
( c_Orderings_Oord__class_Oless__eq(U_177,c_Groups_Oplus__class_Oplus(U_177,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_178),U_178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_179),U_179)),c_Groups_Ozero__class_Ozero(U_177))
| U_179 != c_Groups_Ozero__class_Ozero(U_177)
| U_178 != c_Groups_Ozero__class_Ozero(U_177)
| ~ sP19(U_178,U_177,U_179) )
& ! [U_178,U_177,U_179] :
( sP18(U_178,U_177,U_179)
| ~ c_Orderings_Oord__class_Oless__eq(U_177,c_Groups_Oplus__class_Oplus(U_177,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_178),U_178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_179),U_179)),c_Groups_Ozero__class_Ozero(U_177))
| ~ sP19(U_178,U_177,U_179) )
& ! [U_178,U_177,U_179] :
( sP19(U_178,U_177,U_179)
| ~ class_Rings_Olinordered__ring__strict(U_177) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18,sP19])],[f_57_2]) ).
cnf(f_57_4,plain,
( sP19(U_178,U_177,U_179)
| ~ class_Rings_Olinordered__ring__strict(U_177) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( sP18(U_178,U_177,U_179)
| ~ c_Orderings_Oord__class_Oless__eq(U_177,c_Groups_Oplus__class_Oplus(U_177,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_178),U_178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_179),U_179)),c_Groups_Ozero__class_Ozero(U_177))
| ~ sP19(U_178,U_177,U_179) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_177,c_Groups_Oplus__class_Oplus(U_177,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_178),U_178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_177),U_179),U_179)),c_Groups_Ozero__class_Ozero(U_177))
| U_179 != c_Groups_Ozero__class_Ozero(U_177)
| U_178 != c_Groups_Ozero__class_Ozero(U_177)
| ~ sP19(U_178,U_177,U_179) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_7,plain,
( U_178 = c_Groups_Ozero__class_Ozero(U_177)
| ~ sP18(U_178,U_177,U_179) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_8,plain,
( U_179 = c_Groups_Ozero__class_Ozero(U_177)
| ~ sP18(U_178,U_177,U_179) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_58_2,plain,
! [U_182,U_181,U_180] :
( c_Orderings_Oord__class_Oless__eq(U_180,c_Groups_Ozero__class_Ozero(U_180),c_Groups_Oplus__class_Oplus(U_180,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_180),U_181),U_181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_180),U_182),U_182)))
| ~ class_Rings_Olinordered__ring(U_180) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_181,U_182,U_180] :
( c_Orderings_Oord__class_Oless__eq(U_180,c_Groups_Ozero__class_Ozero(U_180),c_Groups_Oplus__class_Oplus(U_180,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_180),U_181),U_181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_180),U_182),U_182)))
| ~ class_Rings_Olinordered__ring(U_180) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_180,c_Groups_Ozero__class_Ozero(U_180),c_Groups_Oplus__class_Oplus(U_180,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_180),U_181),U_181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_180),U_182),U_182)))
| ~ class_Rings_Olinordered__ring(U_180) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ 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_59_2,plain,
! [U_185,U_184,U_183] :
( c_Orderings_Oord__class_Oless__eq(U_183,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_183),U_185),U_184),U_184)
| ~ c_Orderings_Oord__class_Oless__eq(U_183,U_185,c_Groups_Oone__class_Oone(U_183))
| ~ c_Orderings_Oord__class_Oless__eq(U_183,c_Groups_Ozero__class_Ozero(U_183),U_185)
| ~ c_Orderings_Oord__class_Oless__eq(U_183,c_Groups_Ozero__class_Ozero(U_183),U_184)
| ~ class_Rings_Olinordered__idom(U_183) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_184,U_183,U_185] :
( c_Orderings_Oord__class_Oless__eq(U_183,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_183),U_185),U_184),U_184)
| ~ c_Orderings_Oord__class_Oless__eq(U_183,U_185,c_Groups_Oone__class_Oone(U_183))
| ~ c_Orderings_Oord__class_Oless__eq(U_183,c_Groups_Ozero__class_Ozero(U_183),U_185)
| ~ c_Orderings_Oord__class_Oless__eq(U_183,c_Groups_Ozero__class_Ozero(U_183),U_184)
| ~ class_Rings_Olinordered__idom(U_183) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_183,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_183),U_185),U_184),U_184)
| ~ c_Orderings_Oord__class_Oless__eq(U_183,U_185,c_Groups_Oone__class_Oone(U_183))
| ~ c_Orderings_Oord__class_Oless__eq(U_183,c_Groups_Ozero__class_Ozero(U_183),U_185)
| ~ c_Orderings_Oord__class_Oless__eq(U_183,c_Groups_Ozero__class_Ozero(U_183),U_184)
| ~ class_Rings_Olinordered__idom(U_183) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ 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_60_2,plain,
! [U_188,U_187,U_186] :
( c_Orderings_Oord__class_Oless__eq(U_186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_186),U_187),U_188),U_187)
| ~ c_Orderings_Oord__class_Oless__eq(U_186,U_188,c_Groups_Oone__class_Oone(U_186))
| ~ c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186),U_188)
| ~ c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186),U_187)
| ~ class_Rings_Olinordered__idom(U_186) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_188,U_187,U_186] :
( c_Orderings_Oord__class_Oless__eq(U_186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_186),U_187),U_188),U_187)
| ~ c_Orderings_Oord__class_Oless__eq(U_186,U_188,c_Groups_Oone__class_Oone(U_186))
| ~ c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186),U_188)
| ~ c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186),U_187)
| ~ class_Rings_Olinordered__idom(U_186) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_186,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_186),U_187),U_188),U_187)
| ~ c_Orderings_Oord__class_Oless__eq(U_186,U_188,c_Groups_Oone__class_Oone(U_186))
| ~ c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186),U_188)
| ~ c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186),U_187)
| ~ class_Rings_Olinordered__idom(U_186) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [V_b,V_a,T_a] :
( 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b))
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
& ~ 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_61_2,plain,
! [U_191,U_190,U_189] :
( c_Groups_Oabs__class_Oabs(U_189,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_189),U_190),U_191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_189),c_Groups_Oabs__class_Oabs(U_189,U_190)),c_Groups_Oabs__class_Oabs(U_189,U_191))
| ( ~ c_Orderings_Oord__class_Oless__eq(U_189,U_191,c_Groups_Ozero__class_Ozero(U_189))
& ~ c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189),U_191) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_189,U_190,c_Groups_Ozero__class_Ozero(U_189))
& ~ c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189),U_190) )
| ~ class_Rings_Oordered__ring__abs(U_189) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ! [U_189,U_191] :
( ~ c_Orderings_Oord__class_Oless__eq(U_189,U_191,c_Groups_Ozero__class_Ozero(U_189))
| ~ sP21(U_189,U_191) )
& ! [U_189,U_191] :
( ~ c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189),U_191)
| ~ sP21(U_189,U_191) )
& ! [U_189,U_190] :
( ~ c_Orderings_Oord__class_Oless__eq(U_189,U_190,c_Groups_Ozero__class_Ozero(U_189))
| ~ sP20(U_189,U_190) )
& ! [U_189,U_190] :
( ~ c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189),U_190)
| ~ sP20(U_189,U_190) )
& ! [U_189,U_190,U_191] :
( c_Groups_Oabs__class_Oabs(U_189,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_189),U_190),U_191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_189),c_Groups_Oabs__class_Oabs(U_189,U_190)),c_Groups_Oabs__class_Oabs(U_189,U_191))
| sP21(U_189,U_191)
| sP20(U_189,U_190)
| ~ class_Rings_Oordered__ring__abs(U_189) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20,sP21])],[f_61_2]) ).
cnf(f_61_4,plain,
( c_Groups_Oabs__class_Oabs(U_189,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_189),U_190),U_191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_189),c_Groups_Oabs__class_Oabs(U_189,U_190)),c_Groups_Oabs__class_Oabs(U_189,U_191))
| sP21(U_189,U_191)
| sP20(U_189,U_190)
| ~ class_Rings_Oordered__ring__abs(U_189) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189),U_190)
| ~ sP20(U_189,U_190) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_189,U_190,c_Groups_Ozero__class_Ozero(U_189))
| ~ sP20(U_189,U_190) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189),U_191)
| ~ sP21(U_189,U_191) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_189,U_191,c_Groups_Ozero__class_Ozero(U_189))
| ~ sP21(U_189,U_191) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))
| ~ 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_62_2,plain,
! [U_194,U_193,U_192] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_192),c_Groups_Oabs__class_Oabs(U_192,U_194)),U_193) = c_Groups_Oabs__class_Oabs(U_192,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_192),U_194),U_193))
| ~ c_Orderings_Oord__class_Oless__eq(U_192,c_Groups_Ozero__class_Ozero(U_192),U_193)
| ~ class_Rings_Olinordered__idom(U_192) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_193,U_194,U_192] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_192),c_Groups_Oabs__class_Oabs(U_192,U_194)),U_193) = c_Groups_Oabs__class_Oabs(U_192,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_192),U_194),U_193))
| ~ c_Orderings_Oord__class_Oless__eq(U_192,c_Groups_Ozero__class_Ozero(U_192),U_193)
| ~ class_Rings_Olinordered__idom(U_192) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_192),c_Groups_Oabs__class_Oabs(U_192,U_194)),U_193) = c_Groups_Oabs__class_Oabs(U_192,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_192),U_194),U_193))
| ~ c_Orderings_Oord__class_Oless__eq(U_192,c_Groups_Ozero__class_Ozero(U_192),U_193)
| ~ class_Rings_Olinordered__idom(U_192) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff]) ).
fof(f_63_2,plain,
! [U_196,U_195] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_195,U_196),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_196 != c_Groups_Ozero__class_Ozero(U_195) )
& ( U_196 = c_Groups_Ozero__class_Ozero(U_195)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_195,U_196),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_195) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ! [U_195,U_196] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_195,U_196),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_196 != c_Groups_Ozero__class_Ozero(U_195)
| ~ sP22(U_195,U_196) )
& ! [U_195,U_196] :
( U_196 = c_Groups_Ozero__class_Ozero(U_195)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_195,U_196),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP22(U_195,U_196) )
& ! [U_195,U_196] :
( sP22(U_195,U_196)
| ~ class_RealVector_Oreal__normed__vector(U_195) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_63_2]) ).
cnf(f_63_4,plain,
( sP22(U_195,U_196)
| ~ class_RealVector_Oreal__normed__vector(U_195) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_5,plain,
( U_196 = c_Groups_Ozero__class_Ozero(U_195)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_195,U_196),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP22(U_195,U_196) ),
inference(clausify,[status(thm)],[f_63_3]) ).
cnf(f_63_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_195,U_196),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_196 != c_Groups_Ozero__class_Ozero(U_195)
| ~ sP22(U_195,U_196) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq]) ).
fof(f_64_2,plain,
! [U_199,U_198,U_197] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_197,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_197),U_198),U_199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_197,U_198)),c_RealVector_Onorm__class_Onorm(U_197,U_199)))
| ~ class_RealVector_Oreal__normed__algebra(U_197) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_197,U_198,U_199] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_197,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_197),U_198),U_199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_197,U_198)),c_RealVector_Onorm__class_Onorm(U_197,U_199)))
| ~ class_RealVector_Oreal__normed__algebra(U_197) ),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_197,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_197),U_198),U_199)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_197,U_198)),c_RealVector_Onorm__class_Onorm(U_197,U_199)))
| ~ class_RealVector_Oreal__normed__algebra(U_197) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2]) ).
fof(f_65_2,plain,
! [U_202,U_201,U_200] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_202))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_201,U_202) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_201,U_202)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_202)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_200) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
( ! [U_200,U_201,U_202] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_202))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_201,U_202)
| ~ sP23(U_200,U_201,U_202) )
& ! [U_200,U_201,U_202] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_201,U_202)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_202))
| ~ sP23(U_200,U_201,U_202) )
& ! [U_200,U_201,U_202] :
( sP23(U_200,U_201,U_202)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_200) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_65_2]) ).
cnf(f_65_4,plain,
( sP23(U_200,U_201,U_202)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_200) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_201,U_202)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_202))
| ~ sP23(U_200,U_201,U_202) ),
inference(clausify,[status(thm)],[f_65_3]) ).
cnf(f_65_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_200),U_202))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_201,U_202)
| ~ sP23(U_200,U_201,U_202) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1]) ).
fof(f_66_2,plain,
! [U_205,U_204,U_203] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_204),U_203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_205),U_203))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_204,U_205) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_204,U_205)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_204),U_203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_205),U_203)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_203) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ! [U_205,U_204,U_203] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_204),U_203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_205),U_203))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_204,U_205)
| ~ sP24(U_205,U_204,U_203) )
& ! [U_205,U_204,U_203] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_204,U_205)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_204),U_203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_205),U_203))
| ~ sP24(U_205,U_204,U_203) )
& ! [U_205,U_204,U_203] :
( sP24(U_205,U_204,U_203)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_203) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_66_2]) ).
cnf(f_66_4,plain,
( sP24(U_205,U_204,U_203)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_203) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_204,U_205)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_204),U_203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_205),U_203))
| ~ sP24(U_205,U_204,U_203) ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_204),U_203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_205),U_203))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_204,U_205)
| ~ sP24(U_205,U_204,U_203) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq]) ).
fof(f_67_2,plain,
! [U_208,U_207,U_206] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_206,c_Groups_Oplus__class_Oplus(U_206,U_207,U_208)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_206,U_207),c_RealVector_Onorm__class_Onorm(U_206,U_208)))
| ~ class_RealVector_Oreal__normed__vector(U_206) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_207,U_206,U_208] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_206,c_Groups_Oplus__class_Oplus(U_206,U_207,U_208)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_206,U_207),c_RealVector_Onorm__class_Onorm(U_206,U_208)))
| ~ class_RealVector_Oreal__normed__vector(U_206) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_206,c_Groups_Oplus__class_Oplus(U_206,U_207,U_208)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_206,U_207),c_RealVector_Onorm__class_Onorm(U_206,U_208)))
| ~ class_RealVector_Oreal__normed__vector(U_206) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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)
| c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
| ~ 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_68_2,plain,
! [U_214,U_213,U_212,U_211,U_210,U_209] :
( c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Oplus__class_Oplus(U_209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),U_213),U_210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),U_214),U_212)),U_211)
| c_Groups_Oplus__class_Oplus(U_209,U_213,U_214) != c_Groups_Oone__class_Oone(U_209)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Ozero__class_Ozero(U_209),U_214)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Ozero__class_Ozero(U_209),U_213)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,U_212,U_211)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,U_210,U_211)
| ~ class_Rings_Olinordered__semiring__1(U_209) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_209,U_210,U_211,U_212,U_213,U_214] :
( c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Oplus__class_Oplus(U_209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),U_213),U_210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),U_214),U_212)),U_211)
| c_Groups_Oplus__class_Oplus(U_209,U_213,U_214) != c_Groups_Oone__class_Oone(U_209)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Ozero__class_Ozero(U_209),U_214)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Ozero__class_Ozero(U_209),U_213)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,U_212,U_211)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,U_210,U_211)
| ~ class_Rings_Olinordered__semiring__1(U_209) ),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Oplus__class_Oplus(U_209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),U_213),U_210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),U_214),U_212)),U_211)
| c_Groups_Oplus__class_Oplus(U_209,U_213,U_214) != c_Groups_Oone__class_Oone(U_209)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Ozero__class_Ozero(U_209),U_214)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,c_Groups_Ozero__class_Ozero(U_209),U_213)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,U_212,U_211)
| ~ c_Orderings_Oord__class_Oless__eq(U_209,U_210,U_211)
| ~ class_Rings_Olinordered__semiring__1(U_209) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| 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_69_2,plain,
! [U_217,U_216,U_215] :
( c_Orderings_Oord__class_Oless(U_215,U_217,U_216)
| c_Orderings_Oord__class_Oless(U_215,U_216,U_217)
| U_216 = U_217
| ~ class_Rings_Olinordered__idom(U_215) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_216,U_217,U_215] :
( c_Orderings_Oord__class_Oless(U_215,U_217,U_216)
| c_Orderings_Oord__class_Oless(U_215,U_216,U_217)
| U_216 = U_217
| ~ class_Rings_Olinordered__idom(U_215) ),
inference(definitional_conversion,[status(esa)],[f_69_2]) ).
cnf(f_69_4,plain,
( c_Orderings_Oord__class_Oless(U_215,U_217,U_216)
| c_Orderings_Oord__class_Oless(U_215,U_216,U_217)
| U_216 = U_217
| ~ class_Rings_Olinordered__idom(U_215) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_1,plain,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)),
inference(fof_nnf,[status(thm)],[fact_real__mult__assoc]) ).
fof(f_70_2,plain,
! [U_220,U_219,U_218] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_218),U_219)),U_220) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_219),U_220)),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_220,U_218,U_219] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_218),U_219)),U_220) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_219),U_220)),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_218),U_219)),U_220) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_218),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_219),U_220)),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_1,plain,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z),
inference(fof_nnf,[status(thm)],[fact_real__mult__commute]) ).
fof(f_71_2,plain,
! [U_222,U_221] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_221),U_222) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_222),U_221),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_222,U_221] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_221),U_222) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_222),U_221),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_221),U_222) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_222),U_221),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,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)
| c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
| ~ 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_72_2,plain,
! [U_228,U_227,U_226,U_225,U_224,U_223] :
( c_Orderings_Oord__class_Oless(U_223,c_Groups_Oplus__class_Oplus(U_223,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_223),U_227),U_224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_223),U_228),U_226)),U_225)
| c_Groups_Oplus__class_Oplus(U_223,U_227,U_228) != c_Groups_Oone__class_Oone(U_223)
| ~ c_Orderings_Oord__class_Oless__eq(U_223,c_Groups_Ozero__class_Ozero(U_223),U_228)
| ~ c_Orderings_Oord__class_Oless__eq(U_223,c_Groups_Ozero__class_Ozero(U_223),U_227)
| ~ c_Orderings_Oord__class_Oless(U_223,U_226,U_225)
| ~ c_Orderings_Oord__class_Oless(U_223,U_224,U_225)
| ~ class_Rings_Olinordered__semiring__1__strict(U_223) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_223,U_224,U_225,U_226,U_227,U_228] :
( c_Orderings_Oord__class_Oless(U_223,c_Groups_Oplus__class_Oplus(U_223,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_223),U_227),U_224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_223),U_228),U_226)),U_225)
| c_Groups_Oplus__class_Oplus(U_223,U_227,U_228) != c_Groups_Oone__class_Oone(U_223)
| ~ c_Orderings_Oord__class_Oless__eq(U_223,c_Groups_Ozero__class_Ozero(U_223),U_228)
| ~ c_Orderings_Oord__class_Oless__eq(U_223,c_Groups_Ozero__class_Ozero(U_223),U_227)
| ~ c_Orderings_Oord__class_Oless(U_223,U_226,U_225)
| ~ c_Orderings_Oord__class_Oless(U_223,U_224,U_225)
| ~ class_Rings_Olinordered__semiring__1__strict(U_223) ),
inference(definitional_conversion,[status(esa)],[f_72_2]) ).
cnf(f_72_4,plain,
( c_Orderings_Oord__class_Oless(U_223,c_Groups_Oplus__class_Oplus(U_223,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_223),U_227),U_224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_223),U_228),U_226)),U_225)
| c_Groups_Oplus__class_Oplus(U_223,U_227,U_228) != c_Groups_Oone__class_Oone(U_223)
| ~ c_Orderings_Oord__class_Oless__eq(U_223,c_Groups_Ozero__class_Ozero(U_223),U_228)
| ~ c_Orderings_Oord__class_Oless__eq(U_223,c_Groups_Ozero__class_Ozero(U_223),U_227)
| ~ c_Orderings_Oord__class_Oless(U_223,U_226,U_225)
| ~ c_Orderings_Oord__class_Oless(U_223,U_224,U_225)
| ~ class_Rings_Olinordered__semiring__1__strict(U_223) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_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_73_2,plain,
! [U_231,U_230,U_229] :
( U_231 = c_Groups_Ozero__class_Ozero(U_229)
| U_230 = c_Groups_Ozero__class_Ozero(U_229)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_229),U_230),U_231) != c_Groups_Ozero__class_Ozero(U_229)
| ~ class_Rings_Ono__zero__divisors(U_229) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_231,U_230,U_229] :
( U_231 = c_Groups_Ozero__class_Ozero(U_229)
| U_230 = c_Groups_Ozero__class_Ozero(U_229)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_229),U_230),U_231) != c_Groups_Ozero__class_Ozero(U_229)
| ~ class_Rings_Ono__zero__divisors(U_229) ),
inference(definitional_conversion,[status(esa)],[f_73_2]) ).
cnf(f_73_4,plain,
( U_231 = c_Groups_Ozero__class_Ozero(U_229)
| U_230 = c_Groups_Ozero__class_Ozero(U_229)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_229),U_230),U_231) != c_Groups_Ozero__class_Ozero(U_229)
| ~ class_Rings_Ono__zero__divisors(U_229) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_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_74_2,plain,
! [U_234,U_233,U_232] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_232),U_233),U_234) != c_Groups_Ozero__class_Ozero(U_232)
| U_234 = c_Groups_Ozero__class_Ozero(U_232)
| U_233 = c_Groups_Ozero__class_Ozero(U_232)
| ~ class_Rings_Ono__zero__divisors(U_232) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_234,U_233,U_232] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_232),U_233),U_234) != c_Groups_Ozero__class_Ozero(U_232)
| U_234 = c_Groups_Ozero__class_Ozero(U_232)
| U_233 = c_Groups_Ozero__class_Ozero(U_232)
| ~ class_Rings_Ono__zero__divisors(U_232) ),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_232),U_233),U_234) != c_Groups_Ozero__class_Ozero(U_232)
| U_234 = c_Groups_Ozero__class_Ozero(U_232)
| U_233 = c_Groups_Ozero__class_Ozero(U_232)
| ~ class_Rings_Ono__zero__divisors(U_232) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
& V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oring__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).
fof(f_75_2,plain,
! [U_237,U_236,U_235] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_235),U_236),U_237) = c_Groups_Ozero__class_Ozero(U_235)
| ( U_237 != c_Groups_Ozero__class_Ozero(U_235)
& U_236 != c_Groups_Ozero__class_Ozero(U_235) ) )
& ( U_237 = c_Groups_Ozero__class_Ozero(U_235)
| U_236 = c_Groups_Ozero__class_Ozero(U_235)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_235),U_236),U_237) != c_Groups_Ozero__class_Ozero(U_235) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_235) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
( ! [U_235,U_236,U_237] :
( U_237 != c_Groups_Ozero__class_Ozero(U_235)
| ~ sP25(U_235,U_236,U_237) )
& ! [U_235,U_236,U_237] :
( U_236 != c_Groups_Ozero__class_Ozero(U_235)
| ~ sP25(U_235,U_236,U_237) )
& ! [U_235,U_236,U_237] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_235),U_236),U_237) = c_Groups_Ozero__class_Ozero(U_235)
| sP25(U_235,U_236,U_237)
| ~ sP26(U_235,U_236,U_237) )
& ! [U_235,U_236,U_237] :
( U_237 = c_Groups_Ozero__class_Ozero(U_235)
| U_236 = c_Groups_Ozero__class_Ozero(U_235)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_235),U_236),U_237) != c_Groups_Ozero__class_Ozero(U_235)
| ~ sP26(U_235,U_236,U_237) )
& ! [U_235,U_236,U_237] :
( sP26(U_235,U_236,U_237)
| ~ class_Rings_Oring__no__zero__divisors(U_235) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26])],[f_75_2]) ).
cnf(f_75_4,plain,
( sP26(U_235,U_236,U_237)
| ~ class_Rings_Oring__no__zero__divisors(U_235) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_5,plain,
( U_237 = c_Groups_Ozero__class_Ozero(U_235)
| U_236 = c_Groups_Ozero__class_Ozero(U_235)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_235),U_236),U_237) != c_Groups_Ozero__class_Ozero(U_235)
| ~ sP26(U_235,U_236,U_237) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_235),U_236),U_237) = c_Groups_Ozero__class_Ozero(U_235)
| sP25(U_235,U_236,U_237)
| ~ sP26(U_235,U_236,U_237) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_7,plain,
( U_236 != c_Groups_Ozero__class_Ozero(U_235)
| ~ sP25(U_235,U_236,U_237) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_8,plain,
( U_237 != c_Groups_Ozero__class_Ozero(U_235)
| ~ sP25(U_235,U_236,U_237) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero]) ).
fof(f_76_2,plain,
! [U_239,U_238] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_238),U_239),c_Groups_Ozero__class_Ozero(U_238)) = c_Groups_Ozero__class_Ozero(U_238)
| ~ class_RealVector_Oreal__normed__algebra(U_238) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
! [U_238,U_239] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_238),U_239),c_Groups_Ozero__class_Ozero(U_238)) = c_Groups_Ozero__class_Ozero(U_238)
| ~ class_RealVector_Oreal__normed__algebra(U_238) ),
inference(definitional_conversion,[status(esa)],[f_76_2]) ).
cnf(f_76_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_238),U_239),c_Groups_Ozero__class_Ozero(U_238)) = c_Groups_Ozero__class_Ozero(U_238)
| ~ class_RealVector_Oreal__normed__algebra(U_238) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_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_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right]) ).
fof(f_77_2,plain,
! [U_241,U_240] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_240),U_241),c_Groups_Ozero__class_Ozero(U_240)) = c_Groups_Ozero__class_Ozero(U_240)
| ~ class_RealVector_Oreal__normed__algebra(U_240) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
! [U_241,U_240] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_240),U_241),c_Groups_Ozero__class_Ozero(U_240)) = c_Groups_Ozero__class_Ozero(U_240)
| ~ class_RealVector_Oreal__normed__algebra(U_240) ),
inference(definitional_conversion,[status(esa)],[f_77_2]) ).
cnf(f_77_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_240),U_241),c_Groups_Ozero__class_Ozero(U_240)) = c_Groups_Ozero__class_Ozero(U_240)
| ~ class_RealVector_Oreal__normed__algebra(U_240) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_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_78_2,plain,
! [U_243,U_242] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_242),U_243),c_Groups_Ozero__class_Ozero(U_242)) = c_Groups_Ozero__class_Ozero(U_242)
| ~ class_Rings_Omult__zero(U_242) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_242,U_243] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_242),U_243),c_Groups_Ozero__class_Ozero(U_242)) = c_Groups_Ozero__class_Ozero(U_242)
| ~ class_Rings_Omult__zero(U_242) ),
inference(definitional_conversion,[status(esa)],[f_78_2]) ).
cnf(f_78_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_242),U_243),c_Groups_Ozero__class_Ozero(U_242)) = c_Groups_Ozero__class_Ozero(U_242)
| ~ class_Rings_Omult__zero(U_242) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [V_y,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero]) ).
fof(f_79_2,plain,
! [U_245,U_244] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_244),c_Groups_Ozero__class_Ozero(U_244)),U_245) = c_Groups_Ozero__class_Ozero(U_244)
| ~ class_RealVector_Oreal__normed__algebra(U_244) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
! [U_244,U_245] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_244),c_Groups_Ozero__class_Ozero(U_244)),U_245) = c_Groups_Ozero__class_Ozero(U_244)
| ~ class_RealVector_Oreal__normed__algebra(U_244) ),
inference(definitional_conversion,[status(esa)],[f_79_2]) ).
cnf(f_79_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_244),c_Groups_Ozero__class_Ozero(U_244)),U_245) = c_Groups_Ozero__class_Ozero(U_244)
| ~ class_RealVector_Oreal__normed__algebra(U_244) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [V_b,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left]) ).
fof(f_80_2,plain,
! [U_247,U_246] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_246),c_Groups_Ozero__class_Ozero(U_246)),U_247) = c_Groups_Ozero__class_Ozero(U_246)
| ~ class_RealVector_Oreal__normed__algebra(U_246) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_246,U_247] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_246),c_Groups_Ozero__class_Ozero(U_246)),U_247) = c_Groups_Ozero__class_Ozero(U_246)
| ~ class_RealVector_Oreal__normed__algebra(U_246) ),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_246),c_Groups_Ozero__class_Ozero(U_246)),U_247) = c_Groups_Ozero__class_Ozero(U_246)
| ~ class_RealVector_Oreal__normed__algebra(U_246) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_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_81_2,plain,
! [U_249,U_248] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_248),c_Groups_Ozero__class_Ozero(U_248)),U_249) = c_Groups_Ozero__class_Ozero(U_248)
| ~ class_Rings_Omult__zero(U_248) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
! [U_248,U_249] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_248),c_Groups_Ozero__class_Ozero(U_248)),U_249) = c_Groups_Ozero__class_Ozero(U_248)
| ~ class_Rings_Omult__zero(U_248) ),
inference(definitional_conversion,[status(esa)],[f_81_2]) ).
cnf(f_81_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_248),c_Groups_Ozero__class_Ozero(U_248)),U_249) = c_Groups_Ozero__class_Ozero(U_248)
| ~ class_Rings_Omult__zero(U_248) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_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_82_2,plain,
! [U_250] :
( c_Groups_Ozero__class_Ozero(U_250) != c_Groups_Oone__class_Oone(U_250)
| ~ class_Rings_Ozero__neq__one(U_250) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_250] :
( c_Groups_Ozero__class_Ozero(U_250) != c_Groups_Oone__class_Oone(U_250)
| ~ class_Rings_Ozero__neq__one(U_250) ),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
( c_Groups_Ozero__class_Ozero(U_250) != c_Groups_Oone__class_Oone(U_250)
| ~ class_Rings_Ozero__neq__one(U_250) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_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_83_2,plain,
! [U_251] :
( c_Groups_Oone__class_Oone(U_251) != c_Groups_Ozero__class_Ozero(U_251)
| ~ class_Rings_Ozero__neq__one(U_251) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_251] :
( c_Groups_Oone__class_Oone(U_251) != c_Groups_Ozero__class_Ozero(U_251)
| ~ class_Rings_Ozero__neq__one(U_251) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( c_Groups_Oone__class_Oone(U_251) != c_Groups_Ozero__class_Ozero(U_251)
| ~ class_Rings_Ozero__neq__one(U_251) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [V_c,V_b,V_e,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_84_2,plain,
! [U_256,U_255,U_254,U_253,U_252] :
( c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),U_253),U_254),c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),U_255),U_254),U_256)) = c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),c_Groups_Oplus__class_Oplus(U_252,U_253,U_255)),U_254),U_256)
| ~ class_Rings_Osemiring(U_252) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
! [U_252,U_253,U_254,U_255,U_256] :
( c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),U_253),U_254),c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),U_255),U_254),U_256)) = c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),c_Groups_Oplus__class_Oplus(U_252,U_253,U_255)),U_254),U_256)
| ~ class_Rings_Osemiring(U_252) ),
inference(definitional_conversion,[status(esa)],[f_84_2]) ).
cnf(f_84_4,plain,
( c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),U_253),U_254),c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),U_255),U_254),U_256)) = c_Groups_Oplus__class_Oplus(U_252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_252),c_Groups_Oplus__class_Oplus(U_252,U_253,U_255)),U_254),U_256)
| ~ class_Rings_Osemiring(U_252) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd]) ).
fof(f_85_2,plain,
! [U_260,U_259,U_258,U_257] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),c_Groups_Oplus__class_Oplus(U_257,U_258,U_259)),U_260) = c_Groups_Oplus__class_Oplus(U_257,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),U_258),U_260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),U_259),U_260))
| ~ class_RealVector_Oreal__normed__algebra(U_257) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_257,U_258,U_259,U_260] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),c_Groups_Oplus__class_Oplus(U_257,U_258,U_259)),U_260) = c_Groups_Oplus__class_Oplus(U_257,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),U_258),U_260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),U_259),U_260))
| ~ class_RealVector_Oreal__normed__algebra(U_257) ),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),c_Groups_Oplus__class_Oplus(U_257,U_258,U_259)),U_260) = c_Groups_Oplus__class_Oplus(U_257,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),U_258),U_260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_257),U_259),U_260))
| ~ class_RealVector_Oreal__normed__algebra(U_257) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(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_H),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left]) ).
fof(f_86_2,plain,
! [U_264,U_263,U_262,U_261] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),c_Groups_Oplus__class_Oplus(U_261,U_262,U_263)),U_264) = c_Groups_Oplus__class_Oplus(U_261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),U_262),U_264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),U_263),U_264))
| ~ class_RealVector_Oreal__normed__algebra(U_261) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_264,U_263,U_261,U_262] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),c_Groups_Oplus__class_Oplus(U_261,U_262,U_263)),U_264) = c_Groups_Oplus__class_Oplus(U_261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),U_262),U_264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),U_263),U_264))
| ~ class_RealVector_Oreal__normed__algebra(U_261) ),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),c_Groups_Oplus__class_Oplus(U_261,U_262,U_263)),U_264) = c_Groups_Oplus__class_Oplus(U_261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),U_262),U_264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_261),U_263),U_264))
| ~ class_RealVector_Oreal__normed__algebra(U_261) ),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = 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_87_2,plain,
! [U_268,U_267,U_266,U_265] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),c_Groups_Oplus__class_Oplus(U_265,U_266,U_267)),U_268) = c_Groups_Oplus__class_Oplus(U_265,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),U_266),U_268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),U_267),U_268))
| ~ class_Rings_Ocomm__semiring(U_265) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_265,U_266,U_267,U_268] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),c_Groups_Oplus__class_Oplus(U_265,U_266,U_267)),U_268) = c_Groups_Oplus__class_Oplus(U_265,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),U_266),U_268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),U_267),U_268))
| ~ class_Rings_Ocomm__semiring(U_265) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),c_Groups_Oplus__class_Oplus(U_265,U_266,U_267)),U_268) = c_Groups_Oplus__class_Oplus(U_265,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),U_266),U_268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_265),U_267),U_268))
| ~ class_Rings_Ocomm__semiring(U_265) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [V_y,V_x,V_xa,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd]) ).
fof(f_88_2,plain,
! [U_272,U_271,U_270,U_269] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),c_Groups_Oplus__class_Oplus(U_269,U_271,U_272)) = c_Groups_Oplus__class_Oplus(U_269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),U_271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),U_272))
| ~ class_RealVector_Oreal__normed__algebra(U_269) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_269,U_270,U_271,U_272] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),c_Groups_Oplus__class_Oplus(U_269,U_271,U_272)) = c_Groups_Oplus__class_Oplus(U_269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),U_271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),U_272))
| ~ class_RealVector_Oreal__normed__algebra(U_269) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),c_Groups_Oplus__class_Oplus(U_269,U_271,U_272)) = c_Groups_Oplus__class_Oplus(U_269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),U_271),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_269),U_270),U_272))
| ~ class_RealVector_Oreal__normed__algebra(U_269) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(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),V_b_H))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right]) ).
fof(f_89_2,plain,
! [U_276,U_275,U_274,U_273] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),c_Groups_Oplus__class_Oplus(U_273,U_275,U_276)) = c_Groups_Oplus__class_Oplus(U_273,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),U_275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),U_276))
| ~ class_RealVector_Oreal__normed__algebra(U_273) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_273,U_274,U_275,U_276] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),c_Groups_Oplus__class_Oplus(U_273,U_275,U_276)) = c_Groups_Oplus__class_Oplus(U_273,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),U_275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),U_276))
| ~ class_RealVector_Oreal__normed__algebra(U_273) ),
inference(definitional_conversion,[status(esa)],[f_89_2]) ).
cnf(f_89_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),c_Groups_Oplus__class_Oplus(U_273,U_275,U_276)) = c_Groups_Oplus__class_Oplus(U_273,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),U_275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_273),U_274),U_276))
| ~ class_RealVector_Oreal__normed__algebra(U_273) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),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_90_2,plain,
! [U_278,U_277] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_277),c_Groups_Oabs__class_Oabs(U_277,U_278)),c_Groups_Oabs__class_Oabs(U_277,U_278)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_277),U_278),U_278)
| ~ class_Rings_Olinordered__idom(U_277) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_277,U_278] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_277),c_Groups_Oabs__class_Oabs(U_277,U_278)),c_Groups_Oabs__class_Oabs(U_277,U_278)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_277),U_278),U_278)
| ~ class_Rings_Olinordered__idom(U_277) ),
inference(definitional_conversion,[status(esa)],[f_90_2]) ).
cnf(f_90_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_277),c_Groups_Oabs__class_Oabs(U_277,U_278)),c_Groups_Oabs__class_Oabs(U_277,U_278)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_277),U_278),U_278)
| ~ class_Rings_Olinordered__idom(U_277) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_1,plain,
! [V_b,V_a,T_a] :
( 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),c_Groups_Oabs__class_Oabs(T_a,V_a)),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_91_2,plain,
! [U_281,U_280,U_279] :
( c_Groups_Oabs__class_Oabs(U_279,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_279),U_280),U_281)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_279),c_Groups_Oabs__class_Oabs(U_279,U_280)),c_Groups_Oabs__class_Oabs(U_279,U_281))
| ~ class_Rings_Olinordered__idom(U_279) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_279,U_280,U_281] :
( c_Groups_Oabs__class_Oabs(U_279,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_279),U_280),U_281)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_279),c_Groups_Oabs__class_Oabs(U_279,U_280)),c_Groups_Oabs__class_Oabs(U_279,U_281))
| ~ class_Rings_Olinordered__idom(U_279) ),
inference(definitional_conversion,[status(esa)],[f_91_2]) ).
cnf(f_91_4,plain,
( c_Groups_Oabs__class_Oabs(U_279,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_279),U_280),U_281)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_279),c_Groups_Oabs__class_Oabs(U_279,U_280)),c_Groups_Oabs__class_Oabs(U_279,U_281))
| ~ class_Rings_Olinordered__idom(U_279) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [T_a] :
( 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_92_2,plain,
! [U_282] :
( c_Groups_Oabs__class_Oabs(U_282,c_Groups_Oone__class_Oone(U_282)) = c_Groups_Oone__class_Oone(U_282)
| ~ class_Rings_Olinordered__idom(U_282) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
! [U_282] :
( c_Groups_Oabs__class_Oabs(U_282,c_Groups_Oone__class_Oone(U_282)) = c_Groups_Oone__class_Oone(U_282)
| ~ class_Rings_Olinordered__idom(U_282) ),
inference(definitional_conversion,[status(esa)],[f_92_2]) ).
cnf(f_92_4,plain,
( c_Groups_Oabs__class_Oabs(U_282,c_Groups_Oone__class_Oone(U_282)) = c_Groups_Oone__class_Oone(U_282)
| ~ class_Rings_Olinordered__idom(U_282) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_1,plain,
! [V_b_2,V_a_2,V_ca_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2) ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel]) ).
fof(f_93_2,plain,
! [U_285,U_284,U_283] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_284) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_285)
| U_284 != U_285 )
& ( U_284 = U_285
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_284) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_285) ) )
| U_283 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_283,U_284,U_285] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_284) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_285)
| U_284 != U_285
| ~ sP27(U_283,U_284,U_285) )
& ! [U_283,U_284,U_285] :
( U_284 = U_285
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_284) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_285)
| ~ sP27(U_283,U_284,U_285) )
& ! [U_283,U_284,U_285] :
( sP27(U_283,U_284,U_285)
| U_283 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_93_2]) ).
cnf(f_93_4,plain,
( sP27(U_283,U_284,U_285)
| U_283 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_5,plain,
( U_284 = U_285
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_284) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_285)
| ~ sP27(U_283,U_284,U_285) ),
inference(clausify,[status(thm)],[f_93_3]) ).
cnf(f_93_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_284) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_283),U_285)
| U_284 != U_285
| ~ sP27(U_283,U_284,U_285) ),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_1,plain,
! [V_b_2,V_a_2,V_ca_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2) ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel]) ).
fof(f_94_2,plain,
! [U_288,U_287,U_286] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_287),U_286) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_288),U_286)
| U_287 != U_288 )
& ( U_287 = U_288
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_287),U_286) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_288),U_286) ) )
| U_286 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
( ! [U_288,U_287,U_286] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_287),U_286) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_288),U_286)
| U_287 != U_288
| ~ sP28(U_288,U_287,U_286) )
& ! [U_288,U_287,U_286] :
( U_287 = U_288
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_287),U_286) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_288),U_286)
| ~ sP28(U_288,U_287,U_286) )
& ! [U_288,U_287,U_286] :
( sP28(U_288,U_287,U_286)
| U_286 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_94_2]) ).
cnf(f_94_4,plain,
( sP28(U_288,U_287,U_286)
| U_286 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_5,plain,
( U_287 = U_288
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_287),U_286) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_288),U_286)
| ~ sP28(U_288,U_287,U_286) ),
inference(clausify,[status(thm)],[f_94_3]) ).
cnf(f_94_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_287),U_286) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_288),U_286)
| U_287 != U_288
| ~ sP28(U_288,U_287,U_286) ),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_1,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__zero__not__eq__one]) ).
fof(f_95_2,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_95_1]) ).
cnf(f_95_3,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_real__mult__1]) ).
fof(f_96_2,plain,
! [U_289] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_289) = U_289,
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_289] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_289) = U_289,
inference(definitional_conversion,[status(esa)],[f_96_2]) ).
cnf(f_96_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_289) = U_289,
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)),
inference(fof_nnf,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(f_97_2,plain,
! [U_292,U_291,U_290] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_290,U_291)),U_292) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_290),U_292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_291),U_292)),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_290,U_291,U_292] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_290,U_291)),U_292) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_290),U_292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_291),U_292)),
inference(definitional_conversion,[status(esa)],[f_97_2]) ).
cnf(f_97_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_290,U_291)),U_292) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_290),U_292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_291),U_292)),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel]) ).
fof(f_98_2,plain,
! [U_294,U_293] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_293,U_294)) = c_RealVector_Onorm__class_Onorm(U_293,U_294)
| ~ class_RealVector_Oreal__normed__vector(U_293) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
! [U_293,U_294] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_293,U_294)) = c_RealVector_Onorm__class_Onorm(U_293,U_294)
| ~ class_RealVector_Oreal__normed__vector(U_293) ),
inference(definitional_conversion,[status(esa)],[f_98_2]) ).
cnf(f_98_4,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_293,U_294)) = c_RealVector_Onorm__class_Onorm(U_293,U_294)
| ~ class_RealVector_Oreal__normed__vector(U_293) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_99_2,plain,
! [U_298,U_297,U_296,U_295] :
( c_Orderings_Oord__class_Oless(U_295,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_295),U_298),U_297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_295),U_298),U_296))
| ~ c_Orderings_Oord__class_Oless(U_295,U_298,c_Groups_Ozero__class_Ozero(U_295))
| ~ c_Orderings_Oord__class_Oless(U_295,U_296,U_297)
| ~ class_Rings_Olinordered__ring__strict(U_295) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_295,U_296,U_297,U_298] :
( c_Orderings_Oord__class_Oless(U_295,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_295),U_298),U_297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_295),U_298),U_296))
| ~ c_Orderings_Oord__class_Oless(U_295,U_298,c_Groups_Ozero__class_Ozero(U_295))
| ~ c_Orderings_Oord__class_Oless(U_295,U_296,U_297)
| ~ class_Rings_Olinordered__ring__strict(U_295) ),
inference(definitional_conversion,[status(esa)],[f_99_2]) ).
cnf(f_99_4,plain,
( c_Orderings_Oord__class_Oless(U_295,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_295),U_298),U_297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_295),U_298),U_296))
| ~ c_Orderings_Oord__class_Oless(U_295,U_298,c_Groups_Ozero__class_Ozero(U_295))
| ~ c_Orderings_Oord__class_Oless(U_295,U_296,U_297)
| ~ class_Rings_Olinordered__ring__strict(U_295) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_1,plain,
! [V_c,V_a,V_b,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_100_2,plain,
! [U_302,U_301,U_300,U_299] :
( c_Orderings_Oord__class_Oless(U_299,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_299),U_301),U_302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_299),U_300),U_302))
| ~ c_Orderings_Oord__class_Oless(U_299,U_302,c_Groups_Ozero__class_Ozero(U_299))
| ~ c_Orderings_Oord__class_Oless(U_299,U_300,U_301)
| ~ class_Rings_Olinordered__ring__strict(U_299) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_302,U_299,U_300,U_301] :
( c_Orderings_Oord__class_Oless(U_299,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_299),U_301),U_302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_299),U_300),U_302))
| ~ c_Orderings_Oord__class_Oless(U_299,U_302,c_Groups_Ozero__class_Ozero(U_299))
| ~ c_Orderings_Oord__class_Oless(U_299,U_300,U_301)
| ~ class_Rings_Olinordered__ring__strict(U_299) ),
inference(definitional_conversion,[status(esa)],[f_100_2]) ).
cnf(f_100_4,plain,
( c_Orderings_Oord__class_Oless(U_299,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_299),U_301),U_302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_299),U_300),U_302))
| ~ c_Orderings_Oord__class_Oless(U_299,U_302,c_Groups_Ozero__class_Ozero(U_299))
| ~ c_Orderings_Oord__class_Oless(U_299,U_300,U_301)
| ~ class_Rings_Olinordered__ring__strict(U_299) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_101_2,plain,
! [U_306,U_305,U_304,U_303] :
( c_Orderings_Oord__class_Oless(U_303,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_306),U_304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_306),U_305))
| ~ c_Orderings_Oord__class_Oless(U_303,c_Groups_Ozero__class_Ozero(U_303),U_306)
| ~ c_Orderings_Oord__class_Oless(U_303,U_304,U_305)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_303) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_304,U_306,U_303,U_305] :
( c_Orderings_Oord__class_Oless(U_303,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_306),U_304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_306),U_305))
| ~ c_Orderings_Oord__class_Oless(U_303,c_Groups_Ozero__class_Ozero(U_303),U_306)
| ~ c_Orderings_Oord__class_Oless(U_303,U_304,U_305)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_303) ),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
( c_Orderings_Oord__class_Oless(U_303,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_306),U_304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_306),U_305))
| ~ c_Orderings_Oord__class_Oless(U_303,c_Groups_Ozero__class_Ozero(U_303),U_306)
| ~ c_Orderings_Oord__class_Oless(U_303,U_304,U_305)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_303) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_102_2,plain,
! [U_310,U_309,U_308,U_307] :
( c_Orderings_Oord__class_Oless(U_307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_310),U_308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_310),U_309))
| ~ c_Orderings_Oord__class_Oless(U_307,c_Groups_Ozero__class_Ozero(U_307),U_310)
| ~ c_Orderings_Oord__class_Oless(U_307,U_308,U_309)
| ~ class_Rings_Olinordered__semiring__strict(U_307) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_310,U_308,U_309,U_307] :
( c_Orderings_Oord__class_Oless(U_307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_310),U_308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_310),U_309))
| ~ c_Orderings_Oord__class_Oless(U_307,c_Groups_Ozero__class_Ozero(U_307),U_310)
| ~ c_Orderings_Oord__class_Oless(U_307,U_308,U_309)
| ~ class_Rings_Olinordered__semiring__strict(U_307) ),
inference(definitional_conversion,[status(esa)],[f_102_2]) ).
cnf(f_102_4,plain,
( c_Orderings_Oord__class_Oless(U_307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_310),U_308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_310),U_309))
| ~ c_Orderings_Oord__class_Oless(U_307,c_Groups_Ozero__class_Ozero(U_307),U_310)
| ~ c_Orderings_Oord__class_Oless(U_307,U_308,U_309)
| ~ class_Rings_Olinordered__semiring__strict(U_307) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ 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_103_2,plain,
! [U_314,U_313,U_312,U_311] :
( c_Orderings_Oord__class_Oless(U_311,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_311),U_312),U_314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_311),U_313),U_314))
| ~ c_Orderings_Oord__class_Oless(U_311,c_Groups_Ozero__class_Ozero(U_311),U_314)
| ~ c_Orderings_Oord__class_Oless(U_311,U_312,U_313)
| ~ class_Rings_Olinordered__semiring__strict(U_311) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_313,U_311,U_312,U_314] :
( c_Orderings_Oord__class_Oless(U_311,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_311),U_312),U_314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_311),U_313),U_314))
| ~ c_Orderings_Oord__class_Oless(U_311,c_Groups_Ozero__class_Ozero(U_311),U_314)
| ~ c_Orderings_Oord__class_Oless(U_311,U_312,U_313)
| ~ class_Rings_Olinordered__semiring__strict(U_311) ),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
( c_Orderings_Oord__class_Oless(U_311,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_311),U_312),U_314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_311),U_313),U_314))
| ~ c_Orderings_Oord__class_Oless(U_311,c_Groups_Ozero__class_Ozero(U_311),U_314)
| ~ c_Orderings_Oord__class_Oless(U_311,U_312,U_313)
| ~ class_Rings_Olinordered__semiring__strict(U_311) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_104_2,plain,
! [U_317,U_316,U_315] :
( c_Orderings_Oord__class_Oless(U_315,c_Groups_Ozero__class_Ozero(U_315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_315),U_316),U_317))
| ~ c_Orderings_Oord__class_Oless(U_315,U_317,c_Groups_Ozero__class_Ozero(U_315))
| ~ c_Orderings_Oord__class_Oless(U_315,U_316,c_Groups_Ozero__class_Ozero(U_315))
| ~ class_Rings_Olinordered__ring__strict(U_315) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_316,U_315,U_317] :
( c_Orderings_Oord__class_Oless(U_315,c_Groups_Ozero__class_Ozero(U_315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_315),U_316),U_317))
| ~ c_Orderings_Oord__class_Oless(U_315,U_317,c_Groups_Ozero__class_Ozero(U_315))
| ~ c_Orderings_Oord__class_Oless(U_315,U_316,c_Groups_Ozero__class_Ozero(U_315))
| ~ class_Rings_Olinordered__ring__strict(U_315) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( c_Orderings_Oord__class_Oless(U_315,c_Groups_Ozero__class_Ozero(U_315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_315),U_316),U_317))
| ~ c_Orderings_Oord__class_Oless(U_315,U_317,c_Groups_Ozero__class_Ozero(U_315))
| ~ c_Orderings_Oord__class_Oless(U_315,U_316,c_Groups_Ozero__class_Ozero(U_315))
| ~ class_Rings_Olinordered__ring__strict(U_315) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_105_2,plain,
! [U_320,U_319,U_318] :
( c_Orderings_Oord__class_Oless(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_319),U_320),c_Groups_Ozero__class_Ozero(U_318))
| ~ c_Orderings_Oord__class_Oless(U_318,c_Groups_Ozero__class_Ozero(U_318),U_320)
| ~ c_Orderings_Oord__class_Oless(U_318,U_319,c_Groups_Ozero__class_Ozero(U_318))
| ~ class_Rings_Olinordered__semiring__strict(U_318) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_318,U_319,U_320] :
( c_Orderings_Oord__class_Oless(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_319),U_320),c_Groups_Ozero__class_Ozero(U_318))
| ~ c_Orderings_Oord__class_Oless(U_318,c_Groups_Ozero__class_Ozero(U_318),U_320)
| ~ c_Orderings_Oord__class_Oless(U_318,U_319,c_Groups_Ozero__class_Ozero(U_318))
| ~ class_Rings_Olinordered__semiring__strict(U_318) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( c_Orderings_Oord__class_Oless(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_319),U_320),c_Groups_Ozero__class_Ozero(U_318))
| ~ c_Orderings_Oord__class_Oless(U_318,c_Groups_Ozero__class_Ozero(U_318),U_320)
| ~ c_Orderings_Oord__class_Oless(U_318,U_319,c_Groups_Ozero__class_Ozero(U_318))
| ~ class_Rings_Olinordered__semiring__strict(U_318) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).
fof(f_106_2,plain,
! [U_324,U_323,U_322,U_321] :
( ( ( c_Orderings_Oord__class_Oless(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_324))
| ~ c_Orderings_Oord__class_Oless(U_321,U_324,U_323) )
& ( c_Orderings_Oord__class_Oless(U_321,U_324,U_323)
| ~ c_Orderings_Oord__class_Oless(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_324)) ) )
| ~ c_Orderings_Oord__class_Oless(U_321,U_322,c_Groups_Ozero__class_Ozero(U_321))
| ~ class_Rings_Olinordered__ring__strict(U_321) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
( ! [U_322,U_323,U_321,U_324] :
( c_Orderings_Oord__class_Oless(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_324))
| ~ c_Orderings_Oord__class_Oless(U_321,U_324,U_323)
| ~ sP29(U_322,U_323,U_321,U_324) )
& ! [U_322,U_323,U_321,U_324] :
( c_Orderings_Oord__class_Oless(U_321,U_324,U_323)
| ~ c_Orderings_Oord__class_Oless(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_324))
| ~ sP29(U_322,U_323,U_321,U_324) )
& ! [U_322,U_323,U_321,U_324] :
( sP29(U_322,U_323,U_321,U_324)
| ~ c_Orderings_Oord__class_Oless(U_321,U_322,c_Groups_Ozero__class_Ozero(U_321))
| ~ class_Rings_Olinordered__ring__strict(U_321) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_106_2]) ).
cnf(f_106_4,plain,
( sP29(U_322,U_323,U_321,U_324)
| ~ c_Orderings_Oord__class_Oless(U_321,U_322,c_Groups_Ozero__class_Ozero(U_321))
| ~ class_Rings_Olinordered__ring__strict(U_321) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_5,plain,
( c_Orderings_Oord__class_Oless(U_321,U_324,U_323)
| ~ c_Orderings_Oord__class_Oless(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_324))
| ~ sP29(U_322,U_323,U_321,U_324) ),
inference(clausify,[status(thm)],[f_106_3]) ).
cnf(f_106_6,plain,
( c_Orderings_Oord__class_Oless(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_323),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),U_322),U_324))
| ~ c_Orderings_Oord__class_Oless(U_321,U_324,U_323)
| ~ sP29(U_322,U_323,U_321,U_324) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ 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_107_2,plain,
! [U_327,U_326,U_325] :
( c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),U_326)
| ~ c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),U_327)
| ~ c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_326),U_327))
| ~ class_Rings_Olinordered__semiring__strict(U_325) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_325,U_327,U_326] :
( c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),U_326)
| ~ c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),U_327)
| ~ c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_326),U_327))
| ~ class_Rings_Olinordered__semiring__strict(U_325) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),U_326)
| ~ c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),U_327)
| ~ c_Orderings_Oord__class_Oless(U_325,c_Groups_Ozero__class_Ozero(U_325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_326),U_327))
| ~ class_Rings_Olinordered__semiring__strict(U_325) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ 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_108_2,plain,
! [U_330,U_329,U_328] :
( c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),U_330)
| ~ c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),U_329)
| ~ c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),U_329),U_330))
| ~ class_Rings_Olinordered__semiring__strict(U_328) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_330,U_329,U_328] :
( c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),U_330)
| ~ c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),U_329)
| ~ c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),U_329),U_330))
| ~ class_Rings_Olinordered__semiring__strict(U_328) ),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
( c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),U_330)
| ~ c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),U_329)
| ~ c_Orderings_Oord__class_Oless(U_328,c_Groups_Ozero__class_Ozero(U_328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),U_329),U_330))
| ~ class_Rings_Olinordered__semiring__strict(U_328) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_109_2,plain,
! [U_333,U_332,U_331] :
( c_Orderings_Oord__class_Oless(U_331,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),U_333),U_332),c_Groups_Ozero__class_Ozero(U_331))
| ~ c_Orderings_Oord__class_Oless(U_331,U_333,c_Groups_Ozero__class_Ozero(U_331))
| ~ c_Orderings_Oord__class_Oless(U_331,c_Groups_Ozero__class_Ozero(U_331),U_332)
| ~ class_Rings_Olinordered__semiring__strict(U_331) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_333,U_332,U_331] :
( c_Orderings_Oord__class_Oless(U_331,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),U_333),U_332),c_Groups_Ozero__class_Ozero(U_331))
| ~ c_Orderings_Oord__class_Oless(U_331,U_333,c_Groups_Ozero__class_Ozero(U_331))
| ~ c_Orderings_Oord__class_Oless(U_331,c_Groups_Ozero__class_Ozero(U_331),U_332)
| ~ class_Rings_Olinordered__semiring__strict(U_331) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( c_Orderings_Oord__class_Oless(U_331,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),U_333),U_332),c_Groups_Ozero__class_Ozero(U_331))
| ~ c_Orderings_Oord__class_Oless(U_331,U_333,c_Groups_Ozero__class_Ozero(U_331))
| ~ c_Orderings_Oord__class_Oless(U_331,c_Groups_Ozero__class_Ozero(U_331),U_332)
| ~ class_Rings_Olinordered__semiring__strict(U_331) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_110_2,plain,
! [U_336,U_335,U_334] :
( c_Orderings_Oord__class_Oless(U_334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_334),U_335),U_336),c_Groups_Ozero__class_Ozero(U_334))
| ~ c_Orderings_Oord__class_Oless(U_334,U_336,c_Groups_Ozero__class_Ozero(U_334))
| ~ c_Orderings_Oord__class_Oless(U_334,c_Groups_Ozero__class_Ozero(U_334),U_335)
| ~ class_Rings_Olinordered__semiring__strict(U_334) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_334,U_336,U_335] :
( c_Orderings_Oord__class_Oless(U_334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_334),U_335),U_336),c_Groups_Ozero__class_Ozero(U_334))
| ~ c_Orderings_Oord__class_Oless(U_334,U_336,c_Groups_Ozero__class_Ozero(U_334))
| ~ c_Orderings_Oord__class_Oless(U_334,c_Groups_Ozero__class_Ozero(U_334),U_335)
| ~ class_Rings_Olinordered__semiring__strict(U_334) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( c_Orderings_Oord__class_Oless(U_334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_334),U_335),U_336),c_Groups_Ozero__class_Ozero(U_334))
| ~ c_Orderings_Oord__class_Oless(U_334,U_336,c_Groups_Ozero__class_Ozero(U_334))
| ~ c_Orderings_Oord__class_Oless(U_334,c_Groups_Ozero__class_Ozero(U_334),U_335)
| ~ class_Rings_Olinordered__semiring__strict(U_334) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_1,plain,
! [V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_111_2,plain,
! [U_339,U_338,U_337] :
( c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),U_338),U_339))
| ~ c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),U_339)
| ~ c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),U_338)
| ~ class_Rings_Olinordered__semiring__strict(U_337) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_339,U_337,U_338] :
( c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),U_338),U_339))
| ~ c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),U_339)
| ~ c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),U_338)
| ~ class_Rings_Olinordered__semiring__strict(U_337) ),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
( c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),U_338),U_339))
| ~ c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),U_339)
| ~ c_Orderings_Oord__class_Oless(U_337,c_Groups_Ozero__class_Ozero(U_337),U_338)
| ~ class_Rings_Olinordered__semiring__strict(U_337) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_112_2,plain,
! [U_343,U_342,U_341,U_340] :
( ( ( c_Orderings_Oord__class_Oless(U_340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_343))
| ~ c_Orderings_Oord__class_Oless(U_340,U_342,U_343) )
& ( c_Orderings_Oord__class_Oless(U_340,U_342,U_343)
| ~ c_Orderings_Oord__class_Oless(U_340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_343)) ) )
| ~ c_Orderings_Oord__class_Oless(U_340,c_Groups_Ozero__class_Ozero(U_340),U_341)
| ~ class_Rings_Olinordered__ring__strict(U_340) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
( ! [U_343,U_342,U_341,U_340] :
( c_Orderings_Oord__class_Oless(U_340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_343))
| ~ c_Orderings_Oord__class_Oless(U_340,U_342,U_343)
| ~ sP30(U_343,U_342,U_341,U_340) )
& ! [U_343,U_342,U_341,U_340] :
( c_Orderings_Oord__class_Oless(U_340,U_342,U_343)
| ~ c_Orderings_Oord__class_Oless(U_340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_343))
| ~ sP30(U_343,U_342,U_341,U_340) )
& ! [U_343,U_342,U_341,U_340] :
( sP30(U_343,U_342,U_341,U_340)
| ~ c_Orderings_Oord__class_Oless(U_340,c_Groups_Ozero__class_Ozero(U_340),U_341)
| ~ class_Rings_Olinordered__ring__strict(U_340) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_112_2]) ).
cnf(f_112_4,plain,
( sP30(U_343,U_342,U_341,U_340)
| ~ c_Orderings_Oord__class_Oless(U_340,c_Groups_Ozero__class_Ozero(U_340),U_341)
| ~ class_Rings_Olinordered__ring__strict(U_340) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_5,plain,
( c_Orderings_Oord__class_Oless(U_340,U_342,U_343)
| ~ c_Orderings_Oord__class_Oless(U_340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_343))
| ~ sP30(U_343,U_342,U_341,U_340) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_6,plain,
( c_Orderings_Oord__class_Oless(U_340,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_340),U_341),U_343))
| ~ c_Orderings_Oord__class_Oless(U_340,U_342,U_343)
| ~ sP30(U_343,U_342,U_341,U_340) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_113_2,plain,
! [U_347,U_346,U_345,U_344] :
( ( ( c_Orderings_Oord__class_Oless(U_344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_347))
| ( ( ~ c_Orderings_Oord__class_Oless(U_344,U_347,U_346)
| ~ c_Orderings_Oord__class_Oless(U_344,U_345,c_Groups_Ozero__class_Ozero(U_344)) )
& ( ~ c_Orderings_Oord__class_Oless(U_344,U_346,U_347)
| ~ c_Orderings_Oord__class_Oless(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_344,U_347,U_346)
& c_Orderings_Oord__class_Oless(U_344,U_345,c_Groups_Ozero__class_Ozero(U_344)) )
| ( c_Orderings_Oord__class_Oless(U_344,U_346,U_347)
& c_Orderings_Oord__class_Oless(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345) )
| ~ c_Orderings_Oord__class_Oless(U_344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_347)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_344) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_344,U_345,U_347,U_346] :
( ~ c_Orderings_Oord__class_Oless(U_344,U_347,U_346)
| ~ c_Orderings_Oord__class_Oless(U_344,U_345,c_Groups_Ozero__class_Ozero(U_344))
| ~ sP33(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( ~ c_Orderings_Oord__class_Oless(U_344,U_346,U_347)
| ~ c_Orderings_Oord__class_Oless(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345)
| ~ sP33(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( c_Orderings_Oord__class_Oless(U_344,U_347,U_346)
| ~ sP32(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( c_Orderings_Oord__class_Oless(U_344,U_345,c_Groups_Ozero__class_Ozero(U_344))
| ~ sP32(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( c_Orderings_Oord__class_Oless(U_344,U_346,U_347)
| ~ sP31(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( c_Orderings_Oord__class_Oless(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345)
| ~ sP31(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( c_Orderings_Oord__class_Oless(U_344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_347))
| sP33(U_344,U_345,U_347,U_346)
| ~ sP34(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( sP32(U_344,U_345,U_347,U_346)
| sP31(U_344,U_345,U_347,U_346)
| ~ c_Orderings_Oord__class_Oless(U_344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_347))
| ~ sP34(U_344,U_345,U_347,U_346) )
& ! [U_344,U_345,U_347,U_346] :
( sP34(U_344,U_345,U_347,U_346)
| ~ class_Rings_Olinordered__ring__strict(U_344) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31,sP32,sP33,sP34])],[f_113_2]) ).
cnf(f_113_4,plain,
( sP34(U_344,U_345,U_347,U_346)
| ~ class_Rings_Olinordered__ring__strict(U_344) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
( sP32(U_344,U_345,U_347,U_346)
| sP31(U_344,U_345,U_347,U_346)
| ~ c_Orderings_Oord__class_Oless(U_344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_347))
| ~ sP34(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_6,plain,
( c_Orderings_Oord__class_Oless(U_344,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_346),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_344),U_345),U_347))
| sP33(U_344,U_345,U_347,U_346)
| ~ sP34(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_7,plain,
( c_Orderings_Oord__class_Oless(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345)
| ~ sP31(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_8,plain,
( c_Orderings_Oord__class_Oless(U_344,U_346,U_347)
| ~ sP31(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_9,plain,
( c_Orderings_Oord__class_Oless(U_344,U_345,c_Groups_Ozero__class_Ozero(U_344))
| ~ sP32(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_10,plain,
( c_Orderings_Oord__class_Oless(U_344,U_347,U_346)
| ~ sP32(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_344,U_346,U_347)
| ~ c_Orderings_Oord__class_Oless(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345)
| ~ sP33(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_344,U_347,U_346)
| ~ c_Orderings_Oord__class_Oless(U_344,U_345,c_Groups_Ozero__class_Ozero(U_344))
| ~ sP33(U_344,U_345,U_347,U_346) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_114_2,plain,
! [U_351,U_350,U_349,U_348] :
( ( ( c_Orderings_Oord__class_Oless(U_348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_351),U_350))
| ( ( ~ c_Orderings_Oord__class_Oless(U_348,U_351,U_349)
| ~ c_Orderings_Oord__class_Oless(U_348,U_350,c_Groups_Ozero__class_Ozero(U_348)) )
& ( ~ c_Orderings_Oord__class_Oless(U_348,U_349,U_351)
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Ozero__class_Ozero(U_348),U_350) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_348,U_351,U_349)
& c_Orderings_Oord__class_Oless(U_348,U_350,c_Groups_Ozero__class_Ozero(U_348)) )
| ( c_Orderings_Oord__class_Oless(U_348,U_349,U_351)
& c_Orderings_Oord__class_Oless(U_348,c_Groups_Ozero__class_Ozero(U_348),U_350) )
| ~ c_Orderings_Oord__class_Oless(U_348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_351),U_350)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_348) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
( ! [U_351,U_348,U_350,U_349] :
( ~ c_Orderings_Oord__class_Oless(U_348,U_351,U_349)
| ~ c_Orderings_Oord__class_Oless(U_348,U_350,c_Groups_Ozero__class_Ozero(U_348))
| ~ sP37(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( ~ c_Orderings_Oord__class_Oless(U_348,U_349,U_351)
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Ozero__class_Ozero(U_348),U_350)
| ~ sP37(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( c_Orderings_Oord__class_Oless(U_348,U_351,U_349)
| ~ sP36(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( c_Orderings_Oord__class_Oless(U_348,U_350,c_Groups_Ozero__class_Ozero(U_348))
| ~ sP36(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( c_Orderings_Oord__class_Oless(U_348,U_349,U_351)
| ~ sP35(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( c_Orderings_Oord__class_Oless(U_348,c_Groups_Ozero__class_Ozero(U_348),U_350)
| ~ sP35(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( c_Orderings_Oord__class_Oless(U_348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_351),U_350))
| sP37(U_351,U_348,U_350,U_349)
| ~ sP38(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( sP36(U_351,U_348,U_350,U_349)
| sP35(U_351,U_348,U_350,U_349)
| ~ c_Orderings_Oord__class_Oless(U_348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_351),U_350))
| ~ sP38(U_351,U_348,U_350,U_349) )
& ! [U_351,U_348,U_350,U_349] :
( sP38(U_351,U_348,U_350,U_349)
| ~ class_Rings_Olinordered__ring__strict(U_348) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35,sP36,sP37,sP38])],[f_114_2]) ).
cnf(f_114_4,plain,
( sP38(U_351,U_348,U_350,U_349)
| ~ class_Rings_Olinordered__ring__strict(U_348) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_5,plain,
( sP36(U_351,U_348,U_350,U_349)
| sP35(U_351,U_348,U_350,U_349)
| ~ c_Orderings_Oord__class_Oless(U_348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_351),U_350))
| ~ sP38(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_6,plain,
( c_Orderings_Oord__class_Oless(U_348,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_351),U_350))
| sP37(U_351,U_348,U_350,U_349)
| ~ sP38(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_7,plain,
( c_Orderings_Oord__class_Oless(U_348,c_Groups_Ozero__class_Ozero(U_348),U_350)
| ~ sP35(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_8,plain,
( c_Orderings_Oord__class_Oless(U_348,U_349,U_351)
| ~ sP35(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_9,plain,
( c_Orderings_Oord__class_Oless(U_348,U_350,c_Groups_Ozero__class_Ozero(U_348))
| ~ sP36(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_10,plain,
( c_Orderings_Oord__class_Oless(U_348,U_351,U_349)
| ~ sP36(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_348,U_349,U_351)
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Ozero__class_Ozero(U_348),U_350)
| ~ sP37(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
cnf(f_114_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_348,U_351,U_349)
| ~ c_Orderings_Oord__class_Oless(U_348,U_350,c_Groups_Ozero__class_Ozero(U_348))
| ~ sP37(U_351,U_348,U_350,U_349) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [V_a,T_a] :
( ~ 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_115_2,plain,
! [U_353,U_352] :
( ~ c_Orderings_Oord__class_Oless(U_352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_352),U_353),U_353),c_Groups_Ozero__class_Ozero(U_352))
| ~ class_Rings_Olinordered__ring(U_352) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_352,U_353] :
( ~ c_Orderings_Oord__class_Oless(U_352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_352),U_353),U_353),c_Groups_Ozero__class_Ozero(U_352))
| ~ class_Rings_Olinordered__ring(U_352) ),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_352),U_353),U_353),c_Groups_Ozero__class_Ozero(U_352))
| ~ class_Rings_Olinordered__ring(U_352) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| ~ 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_116_2,plain,
! [U_357,U_356,U_355,U_354] :
( c_Orderings_Oord__class_Oless(U_354,U_356,c_Groups_Oplus__class_Oplus(U_354,U_355,U_357))
| ~ c_Orderings_Oord__class_Oless(U_354,U_356,U_357)
| ~ c_Orderings_Oord__class_Oless(U_354,c_Groups_Ozero__class_Ozero(U_354),U_355)
| ~ class_Rings_Olinordered__semidom(U_354) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_354,U_355,U_357,U_356] :
( c_Orderings_Oord__class_Oless(U_354,U_356,c_Groups_Oplus__class_Oplus(U_354,U_355,U_357))
| ~ c_Orderings_Oord__class_Oless(U_354,U_356,U_357)
| ~ c_Orderings_Oord__class_Oless(U_354,c_Groups_Ozero__class_Ozero(U_354),U_355)
| ~ class_Rings_Olinordered__semidom(U_354) ),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
( c_Orderings_Oord__class_Oless(U_354,U_356,c_Groups_Oplus__class_Oplus(U_354,U_355,U_357))
| ~ c_Orderings_Oord__class_Oless(U_354,U_356,U_357)
| ~ c_Orderings_Oord__class_Oless(U_354,c_Groups_Ozero__class_Ozero(U_354),U_355)
| ~ class_Rings_Olinordered__semidom(U_354) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).
fof(f_117_2,plain,
! [U_360,U_359,U_358] :
( ( ( c_Groups_Oplus__class_Oplus(U_358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_359),U_359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_360),U_360)) = c_Groups_Ozero__class_Ozero(U_358)
| U_360 != c_Groups_Ozero__class_Ozero(U_358)
| U_359 != c_Groups_Ozero__class_Ozero(U_358) )
& ( ( U_360 = c_Groups_Ozero__class_Ozero(U_358)
& U_359 = c_Groups_Ozero__class_Ozero(U_358) )
| c_Groups_Oplus__class_Oplus(U_358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_359),U_359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_360),U_360)) != c_Groups_Ozero__class_Ozero(U_358) ) )
| ~ class_Rings_Olinordered__ring__strict(U_358) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_359,U_358,U_360] :
( U_360 = c_Groups_Ozero__class_Ozero(U_358)
| ~ sP39(U_359,U_358,U_360) )
& ! [U_359,U_358,U_360] :
( U_359 = c_Groups_Ozero__class_Ozero(U_358)
| ~ sP39(U_359,U_358,U_360) )
& ! [U_359,U_358,U_360] :
( c_Groups_Oplus__class_Oplus(U_358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_359),U_359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_360),U_360)) = c_Groups_Ozero__class_Ozero(U_358)
| U_360 != c_Groups_Ozero__class_Ozero(U_358)
| U_359 != c_Groups_Ozero__class_Ozero(U_358)
| ~ sP40(U_359,U_358,U_360) )
& ! [U_359,U_358,U_360] :
( sP39(U_359,U_358,U_360)
| c_Groups_Oplus__class_Oplus(U_358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_359),U_359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_360),U_360)) != c_Groups_Ozero__class_Ozero(U_358)
| ~ sP40(U_359,U_358,U_360) )
& ! [U_359,U_358,U_360] :
( sP40(U_359,U_358,U_360)
| ~ class_Rings_Olinordered__ring__strict(U_358) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39,sP40])],[f_117_2]) ).
cnf(f_117_4,plain,
( sP40(U_359,U_358,U_360)
| ~ class_Rings_Olinordered__ring__strict(U_358) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_5,plain,
( sP39(U_359,U_358,U_360)
| c_Groups_Oplus__class_Oplus(U_358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_359),U_359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_360),U_360)) != c_Groups_Ozero__class_Ozero(U_358)
| ~ sP40(U_359,U_358,U_360) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_6,plain,
( c_Groups_Oplus__class_Oplus(U_358,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_359),U_359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_358),U_360),U_360)) = c_Groups_Ozero__class_Ozero(U_358)
| U_360 != c_Groups_Ozero__class_Ozero(U_358)
| U_359 != c_Groups_Ozero__class_Ozero(U_358)
| ~ sP40(U_359,U_358,U_360) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_7,plain,
( U_359 = c_Groups_Ozero__class_Ozero(U_358)
| ~ sP39(U_359,U_358,U_360) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_8,plain,
( U_360 = c_Groups_Ozero__class_Ozero(U_358)
| ~ sP39(U_359,U_358,U_360) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [T_a] :
( 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_118_2,plain,
! [U_361] :
( c_Orderings_Oord__class_Oless(U_361,c_Groups_Ozero__class_Ozero(U_361),c_Groups_Oone__class_Oone(U_361))
| ~ class_Rings_Olinordered__semidom(U_361) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_361] :
( c_Orderings_Oord__class_Oless(U_361,c_Groups_Ozero__class_Ozero(U_361),c_Groups_Oone__class_Oone(U_361))
| ~ class_Rings_Olinordered__semidom(U_361) ),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
( c_Orderings_Oord__class_Oless(U_361,c_Groups_Ozero__class_Ozero(U_361),c_Groups_Oone__class_Oone(U_361))
| ~ class_Rings_Olinordered__semidom(U_361) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_1,plain,
! [T_a] :
( ~ 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_119_2,plain,
! [U_362] :
( ~ c_Orderings_Oord__class_Oless(U_362,c_Groups_Oone__class_Oone(U_362),c_Groups_Ozero__class_Ozero(U_362))
| ~ class_Rings_Olinordered__semidom(U_362) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_362] :
( ~ c_Orderings_Oord__class_Oless(U_362,c_Groups_Oone__class_Oone(U_362),c_Groups_Ozero__class_Ozero(U_362))
| ~ class_Rings_Olinordered__semidom(U_362) ),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_362,c_Groups_Oone__class_Oone(U_362),c_Groups_Ozero__class_Ozero(U_362))
| ~ class_Rings_Olinordered__semidom(U_362) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [V_n,V_m,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
| ~ 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_120_2,plain,
! [U_365,U_364,U_363] :
( c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_363),U_364),U_365))
| ~ c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),U_365)
| ~ c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),U_364)
| ~ class_Rings_Olinordered__semidom(U_363) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
! [U_363,U_364,U_365] :
( c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_363),U_364),U_365))
| ~ c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),U_365)
| ~ c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),U_364)
| ~ class_Rings_Olinordered__semidom(U_363) ),
inference(definitional_conversion,[status(esa)],[f_120_2]) ).
cnf(f_120_4,plain,
( c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_363),U_364),U_365))
| ~ c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),U_365)
| ~ c_Orderings_Oord__class_Oless(U_363,c_Groups_Oone__class_Oone(U_363),U_364)
| ~ class_Rings_Olinordered__semidom(U_363) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,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_121_2,plain,
! [U_367,U_366] :
( c_Orderings_Oord__class_Oless(U_366,U_367,c_Groups_Oplus__class_Oplus(U_366,U_367,c_Groups_Oone__class_Oone(U_366)))
| ~ class_Rings_Olinordered__semidom(U_366) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_367,U_366] :
( c_Orderings_Oord__class_Oless(U_366,U_367,c_Groups_Oplus__class_Oplus(U_366,U_367,c_Groups_Oone__class_Oone(U_366)))
| ~ class_Rings_Olinordered__semidom(U_366) ),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
( c_Orderings_Oord__class_Oless(U_366,U_367,c_Groups_Oplus__class_Oplus(U_366,U_367,c_Groups_Oone__class_Oone(U_366)))
| ~ class_Rings_Olinordered__semidom(U_366) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,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_122_2,plain,
! [U_372,U_371,U_370,U_369,U_368] :
( c_Orderings_Oord__class_Oless(U_368,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),c_Groups_Oabs__class_Oabs(U_368,U_369)),c_Groups_Oabs__class_Oabs(U_368,U_371)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_370),U_372))
| ~ c_Orderings_Oord__class_Oless(U_368,c_Groups_Oabs__class_Oabs(U_368,U_371),U_372)
| ~ c_Orderings_Oord__class_Oless(U_368,c_Groups_Oabs__class_Oabs(U_368,U_369),U_370)
| ~ class_Rings_Olinordered__idom(U_368) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_368,U_369,U_370,U_371,U_372] :
( c_Orderings_Oord__class_Oless(U_368,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),c_Groups_Oabs__class_Oabs(U_368,U_369)),c_Groups_Oabs__class_Oabs(U_368,U_371)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_370),U_372))
| ~ c_Orderings_Oord__class_Oless(U_368,c_Groups_Oabs__class_Oabs(U_368,U_371),U_372)
| ~ c_Orderings_Oord__class_Oless(U_368,c_Groups_Oabs__class_Oabs(U_368,U_369),U_370)
| ~ class_Rings_Olinordered__idom(U_368) ),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
( c_Orderings_Oord__class_Oless(U_368,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),c_Groups_Oabs__class_Oabs(U_368,U_369)),c_Groups_Oabs__class_Oabs(U_368,U_371)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_370),U_372))
| ~ c_Orderings_Oord__class_Oless(U_368,c_Groups_Oabs__class_Oabs(U_368,U_371),U_372)
| ~ c_Orderings_Oord__class_Oless(U_368,c_Groups_Oabs__class_Oabs(U_368,U_369),U_370)
| ~ class_Rings_Olinordered__idom(U_368) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [V_x_2,T_a] :
( ( ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_RealVector_Onorm__class_Onorm(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__eq__zero]) ).
fof(f_123_2,plain,
! [U_374,U_373] :
( ( ( c_RealVector_Onorm__class_Onorm(U_373,U_374) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_374 != c_Groups_Ozero__class_Ozero(U_373) )
& ( U_374 = c_Groups_Ozero__class_Ozero(U_373)
| c_RealVector_Onorm__class_Onorm(U_373,U_374) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(U_373) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_374,U_373] :
( c_RealVector_Onorm__class_Onorm(U_373,U_374) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_374 != c_Groups_Ozero__class_Ozero(U_373)
| ~ sP41(U_374,U_373) )
& ! [U_374,U_373] :
( U_374 = c_Groups_Ozero__class_Ozero(U_373)
| c_RealVector_Onorm__class_Onorm(U_373,U_374) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP41(U_374,U_373) )
& ! [U_374,U_373] :
( sP41(U_374,U_373)
| ~ class_RealVector_Oreal__normed__vector(U_373) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_123_2]) ).
cnf(f_123_4,plain,
( sP41(U_374,U_373)
| ~ class_RealVector_Oreal__normed__vector(U_373) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_5,plain,
( U_374 = c_Groups_Ozero__class_Ozero(U_373)
| c_RealVector_Onorm__class_Onorm(U_373,U_374) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP41(U_374,U_373) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_6,plain,
( c_RealVector_Onorm__class_Onorm(U_373,U_374) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_374 != c_Groups_Ozero__class_Ozero(U_373)
| ~ sP41(U_374,U_373) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__zero]) ).
fof(f_124_2,plain,
! [U_375] :
( c_RealVector_Onorm__class_Onorm(U_375,c_Groups_Ozero__class_Ozero(U_375)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_375) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_375] :
( c_RealVector_Onorm__class_Onorm(U_375,c_Groups_Ozero__class_Ozero(U_375)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_375) ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( c_RealVector_Onorm__class_Onorm(U_375,c_Groups_Ozero__class_Ozero(U_375)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_375) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [V_y,V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))
| ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__mult]) ).
fof(f_125_2,plain,
! [U_378,U_377,U_376] :
( c_RealVector_Onorm__class_Onorm(U_376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),U_377),U_378)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_376,U_377)),c_RealVector_Onorm__class_Onorm(U_376,U_378))
| ~ class_RealVector_Oreal__normed__div__algebra(U_376) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_376,U_377,U_378] :
( c_RealVector_Onorm__class_Onorm(U_376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),U_377),U_378)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_376,U_377)),c_RealVector_Onorm__class_Onorm(U_376,U_378))
| ~ class_RealVector_Oreal__normed__div__algebra(U_376) ),
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
( c_RealVector_Onorm__class_Onorm(U_376,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),U_377),U_378)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_376,U_377)),c_RealVector_Onorm__class_Onorm(U_376,U_378))
| ~ class_RealVector_Oreal__normed__div__algebra(U_376) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [V_y,V_x,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2]) ).
fof(f_126_2,plain,
! [U_381,U_380,U_379] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_379),U_380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_379),U_381))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_380,U_381)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_379) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_379,U_380,U_381] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_379),U_380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_379),U_381))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_380,U_381)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_379) ),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_379),U_380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_379),U_381))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_380,U_381)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_379) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__order]) ).
fof(f_127_2,plain,
! [U_383,U_382] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_382),U_383))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_383)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_382) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_383,U_382] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_382),U_383))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_383)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_382) ),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_382),U_383))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_383)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_382) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1]) ).
fof(f_128_2,plain,
! [U_386,U_385,U_384] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_385),U_384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_386),U_384))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_385,U_386) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_385,U_386)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_385),U_384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_386),U_384)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_384) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
( ! [U_385,U_386,U_384] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_385),U_384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_386),U_384))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_385,U_386)
| ~ sP42(U_385,U_386,U_384) )
& ! [U_385,U_386,U_384] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_385,U_386)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_385),U_384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_386),U_384))
| ~ sP42(U_385,U_386,U_384) )
& ! [U_385,U_386,U_384] :
( sP42(U_385,U_386,U_384)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_384) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42])],[f_128_2]) ).
cnf(f_128_4,plain,
( sP42(U_385,U_386,U_384)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_384) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_385,U_386)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_385),U_384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_386),U_384))
| ~ sP42(U_385,U_386,U_384) ),
inference(clausify,[status(thm)],[f_128_3]) ).
cnf(f_128_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_385),U_384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_386),U_384))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_385,U_386)
| ~ sP42(U_385,U_386,U_384) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact_m]) ).
fof(f_129_2,plain,
! [U_387] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_387)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_387),v_r) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_387] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_387)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_387),v_r) ),
inference(definitional_conversion,[status(esa)],[f_129_2]) ).
cnf(f_129_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_387)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_387),v_r) ),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [V_y,V_x,V_c,T_a] :
( V_x = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma]) ).
fof(f_130_2,plain,
! [U_391,U_390,U_389,U_388] :
( U_390 = c_Groups_Ozero__class_Ozero(U_388)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_388,U_390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_389),c_RealVector_Onorm__class_Onorm(U_388,U_391)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_389,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_388) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_389,U_390,U_391,U_388] :
( U_390 = c_Groups_Ozero__class_Ozero(U_388)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_388,U_390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_389),c_RealVector_Onorm__class_Onorm(U_388,U_391)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_389,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_388) ),
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
( U_390 = c_Groups_Ozero__class_Ozero(U_388)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_388,U_390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_389),c_RealVector_Onorm__class_Onorm(U_388,U_391)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_389,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_388) ),
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_1,plain,
! [V_y,V_x,V_c] :
( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[fact_rabs__ratiotest__lemma]) ).
fof(f_131_2,plain,
! [U_394,U_393,U_392] :
( U_393 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_392),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_394)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_392,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_392,U_393,U_394] :
( U_393 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_392),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_394)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_392,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
( U_393 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_392),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_394)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_392,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_132_2,plain,
! [U_397,U_396,U_395] :
( c_Orderings_Oord__class_Oless(U_395,c_Groups_Oplus__class_Oplus(U_395,U_396,U_397),c_Groups_Ozero__class_Ozero(U_395))
| ~ c_Orderings_Oord__class_Oless(U_395,U_397,c_Groups_Ozero__class_Ozero(U_395))
| ~ c_Orderings_Oord__class_Oless__eq(U_395,U_396,c_Groups_Ozero__class_Ozero(U_395))
| ~ class_Groups_Oordered__comm__monoid__add(U_395) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_397,U_395,U_396] :
( c_Orderings_Oord__class_Oless(U_395,c_Groups_Oplus__class_Oplus(U_395,U_396,U_397),c_Groups_Ozero__class_Ozero(U_395))
| ~ c_Orderings_Oord__class_Oless(U_395,U_397,c_Groups_Ozero__class_Ozero(U_395))
| ~ c_Orderings_Oord__class_Oless__eq(U_395,U_396,c_Groups_Ozero__class_Ozero(U_395))
| ~ class_Groups_Oordered__comm__monoid__add(U_395) ),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
( c_Orderings_Oord__class_Oless(U_395,c_Groups_Oplus__class_Oplus(U_395,U_396,U_397),c_Groups_Ozero__class_Ozero(U_395))
| ~ c_Orderings_Oord__class_Oless(U_395,U_397,c_Groups_Ozero__class_Ozero(U_395))
| ~ c_Orderings_Oord__class_Oless__eq(U_395,U_396,c_Groups_Ozero__class_Ozero(U_395))
| ~ class_Groups_Oordered__comm__monoid__add(U_395) ),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_133_2,plain,
! [U_400,U_399,U_398] :
( c_Orderings_Oord__class_Oless(U_398,c_Groups_Oplus__class_Oplus(U_398,U_399,U_400),c_Groups_Ozero__class_Ozero(U_398))
| ~ c_Orderings_Oord__class_Oless__eq(U_398,U_400,c_Groups_Ozero__class_Ozero(U_398))
| ~ c_Orderings_Oord__class_Oless(U_398,U_399,c_Groups_Ozero__class_Ozero(U_398))
| ~ class_Groups_Oordered__comm__monoid__add(U_398) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_399,U_400,U_398] :
( c_Orderings_Oord__class_Oless(U_398,c_Groups_Oplus__class_Oplus(U_398,U_399,U_400),c_Groups_Ozero__class_Ozero(U_398))
| ~ c_Orderings_Oord__class_Oless__eq(U_398,U_400,c_Groups_Ozero__class_Ozero(U_398))
| ~ c_Orderings_Oord__class_Oless(U_398,U_399,c_Groups_Ozero__class_Ozero(U_398))
| ~ class_Groups_Oordered__comm__monoid__add(U_398) ),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
( c_Orderings_Oord__class_Oless(U_398,c_Groups_Oplus__class_Oplus(U_398,U_399,U_400),c_Groups_Ozero__class_Ozero(U_398))
| ~ c_Orderings_Oord__class_Oless__eq(U_398,U_400,c_Groups_Ozero__class_Ozero(U_398))
| ~ c_Orderings_Oord__class_Oless(U_398,U_399,c_Groups_Ozero__class_Ozero(U_398))
| ~ class_Groups_Oordered__comm__monoid__add(U_398) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| ~ 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_134_2,plain,
! [U_404,U_403,U_402,U_401] :
( c_Orderings_Oord__class_Oless(U_401,U_403,c_Groups_Oplus__class_Oplus(U_401,U_402,U_404))
| ~ c_Orderings_Oord__class_Oless(U_401,U_403,U_404)
| ~ c_Orderings_Oord__class_Oless__eq(U_401,c_Groups_Ozero__class_Ozero(U_401),U_402)
| ~ class_Groups_Oordered__comm__monoid__add(U_401) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_401,U_402,U_403,U_404] :
( c_Orderings_Oord__class_Oless(U_401,U_403,c_Groups_Oplus__class_Oplus(U_401,U_402,U_404))
| ~ c_Orderings_Oord__class_Oless(U_401,U_403,U_404)
| ~ c_Orderings_Oord__class_Oless__eq(U_401,c_Groups_Ozero__class_Ozero(U_401),U_402)
| ~ class_Groups_Oordered__comm__monoid__add(U_401) ),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
( c_Orderings_Oord__class_Oless(U_401,U_403,c_Groups_Oplus__class_Oplus(U_401,U_402,U_404))
| ~ c_Orderings_Oord__class_Oless(U_401,U_403,U_404)
| ~ c_Orderings_Oord__class_Oless__eq(U_401,c_Groups_Ozero__class_Ozero(U_401),U_402)
| ~ class_Groups_Oordered__comm__monoid__add(U_401) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| ~ 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_135_2,plain,
! [U_408,U_407,U_406,U_405] :
( c_Orderings_Oord__class_Oless(U_405,U_407,c_Groups_Oplus__class_Oplus(U_405,U_406,U_408))
| ~ c_Orderings_Oord__class_Oless__eq(U_405,U_407,U_408)
| ~ c_Orderings_Oord__class_Oless(U_405,c_Groups_Ozero__class_Ozero(U_405),U_406)
| ~ class_Groups_Oordered__comm__monoid__add(U_405) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_407,U_408,U_406,U_405] :
( c_Orderings_Oord__class_Oless(U_405,U_407,c_Groups_Oplus__class_Oplus(U_405,U_406,U_408))
| ~ c_Orderings_Oord__class_Oless__eq(U_405,U_407,U_408)
| ~ c_Orderings_Oord__class_Oless(U_405,c_Groups_Ozero__class_Ozero(U_405),U_406)
| ~ class_Groups_Oordered__comm__monoid__add(U_405) ),
inference(definitional_conversion,[status(esa)],[f_135_2]) ).
cnf(f_135_4,plain,
( c_Orderings_Oord__class_Oless(U_405,U_407,c_Groups_Oplus__class_Oplus(U_405,U_406,U_408))
| ~ c_Orderings_Oord__class_Oless__eq(U_405,U_407,U_408)
| ~ c_Orderings_Oord__class_Oless(U_405,c_Groups_Ozero__class_Ozero(U_405),U_406)
| ~ class_Groups_Oordered__comm__monoid__add(U_405) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_136_2,plain,
! [U_411,U_410,U_409] :
( c_Orderings_Oord__class_Oless(U_409,c_Groups_Ozero__class_Ozero(U_409),c_Groups_Oplus__class_Oplus(U_409,U_410,U_411))
| ~ c_Orderings_Oord__class_Oless(U_409,c_Groups_Ozero__class_Ozero(U_409),U_411)
| ~ c_Orderings_Oord__class_Oless__eq(U_409,c_Groups_Ozero__class_Ozero(U_409),U_410)
| ~ class_Groups_Oordered__comm__monoid__add(U_409) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_410,U_411,U_409] :
( c_Orderings_Oord__class_Oless(U_409,c_Groups_Ozero__class_Ozero(U_409),c_Groups_Oplus__class_Oplus(U_409,U_410,U_411))
| ~ c_Orderings_Oord__class_Oless(U_409,c_Groups_Ozero__class_Ozero(U_409),U_411)
| ~ c_Orderings_Oord__class_Oless__eq(U_409,c_Groups_Ozero__class_Ozero(U_409),U_410)
| ~ class_Groups_Oordered__comm__monoid__add(U_409) ),
inference(definitional_conversion,[status(esa)],[f_136_2]) ).
cnf(f_136_4,plain,
( c_Orderings_Oord__class_Oless(U_409,c_Groups_Ozero__class_Ozero(U_409),c_Groups_Oplus__class_Oplus(U_409,U_410,U_411))
| ~ c_Orderings_Oord__class_Oless(U_409,c_Groups_Ozero__class_Ozero(U_409),U_411)
| ~ c_Orderings_Oord__class_Oless__eq(U_409,c_Groups_Ozero__class_Ozero(U_409),U_410)
| ~ class_Groups_Oordered__comm__monoid__add(U_409) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_137_2,plain,
! [U_414,U_413,U_412] :
( c_Orderings_Oord__class_Oless(U_412,c_Groups_Ozero__class_Ozero(U_412),c_Groups_Oplus__class_Oplus(U_412,U_413,U_414))
| ~ c_Orderings_Oord__class_Oless__eq(U_412,c_Groups_Ozero__class_Ozero(U_412),U_414)
| ~ c_Orderings_Oord__class_Oless(U_412,c_Groups_Ozero__class_Ozero(U_412),U_413)
| ~ class_Groups_Oordered__comm__monoid__add(U_412) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_413,U_412,U_414] :
( c_Orderings_Oord__class_Oless(U_412,c_Groups_Ozero__class_Ozero(U_412),c_Groups_Oplus__class_Oplus(U_412,U_413,U_414))
| ~ c_Orderings_Oord__class_Oless__eq(U_412,c_Groups_Ozero__class_Ozero(U_412),U_414)
| ~ c_Orderings_Oord__class_Oless(U_412,c_Groups_Ozero__class_Ozero(U_412),U_413)
| ~ class_Groups_Oordered__comm__monoid__add(U_412) ),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
( c_Orderings_Oord__class_Oless(U_412,c_Groups_Ozero__class_Ozero(U_412),c_Groups_Oplus__class_Oplus(U_412,U_413,U_414))
| ~ c_Orderings_Oord__class_Oless__eq(U_412,c_Groups_Ozero__class_Ozero(U_412),U_414)
| ~ c_Orderings_Oord__class_Oless(U_412,c_Groups_Ozero__class_Ozero(U_412),U_413)
| ~ class_Groups_Oordered__comm__monoid__add(U_412) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),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_138_2,plain,
! [U_417,U_416,U_415] :
( c_Orderings_Oord__class_Oless__eq(U_415,c_Groups_Oabs__class_Oabs(U_415,c_Groups_Oplus__class_Oplus(U_415,U_416,U_417)),c_Groups_Oplus__class_Oplus(U_415,c_Groups_Oabs__class_Oabs(U_415,U_416),c_Groups_Oabs__class_Oabs(U_415,U_417)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_415) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_417,U_416,U_415] :
( c_Orderings_Oord__class_Oless__eq(U_415,c_Groups_Oabs__class_Oabs(U_415,c_Groups_Oplus__class_Oplus(U_415,U_416,U_417)),c_Groups_Oplus__class_Oplus(U_415,c_Groups_Oabs__class_Oabs(U_415,U_416),c_Groups_Oabs__class_Oabs(U_415,U_417)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_415) ),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_415,c_Groups_Oabs__class_Oabs(U_415,c_Groups_Oplus__class_Oplus(U_415,U_416,U_417)),c_Groups_Oplus__class_Oplus(U_415,c_Groups_Oabs__class_Oabs(U_415,U_416),c_Groups_Oabs__class_Oabs(U_415,U_417)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_415) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| ~ 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_139_2,plain,
! [U_419,U_418] :
( c_Groups_Oabs__class_Oabs(U_418,U_419) = U_419
| ~ c_Orderings_Oord__class_Oless(U_418,c_Groups_Ozero__class_Ozero(U_418),U_419)
| ~ class_Groups_Oordered__ab__group__add__abs(U_418) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_419,U_418] :
( c_Groups_Oabs__class_Oabs(U_418,U_419) = U_419
| ~ c_Orderings_Oord__class_Oless(U_418,c_Groups_Ozero__class_Ozero(U_418),U_419)
| ~ class_Groups_Oordered__ab__group__add__abs(U_418) ),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
( c_Groups_Oabs__class_Oabs(U_418,U_419) = U_419
| ~ c_Orderings_Oord__class_Oless(U_418,c_Groups_Ozero__class_Ozero(U_418),U_419)
| ~ class_Groups_Oordered__ab__group__add__abs(U_418) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).
fof(f_140_2,plain,
! [U_421,U_420] :
( ( ( c_Orderings_Oord__class_Oless(U_420,c_Groups_Ozero__class_Ozero(U_420),c_Groups_Oabs__class_Oabs(U_420,U_421))
| U_421 = c_Groups_Ozero__class_Ozero(U_420) )
& ( U_421 != c_Groups_Ozero__class_Ozero(U_420)
| ~ c_Orderings_Oord__class_Oless(U_420,c_Groups_Ozero__class_Ozero(U_420),c_Groups_Oabs__class_Oabs(U_420,U_421)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_420) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_420,U_421] :
( c_Orderings_Oord__class_Oless(U_420,c_Groups_Ozero__class_Ozero(U_420),c_Groups_Oabs__class_Oabs(U_420,U_421))
| U_421 = c_Groups_Ozero__class_Ozero(U_420)
| ~ sP43(U_420,U_421) )
& ! [U_420,U_421] :
( U_421 != c_Groups_Ozero__class_Ozero(U_420)
| ~ c_Orderings_Oord__class_Oless(U_420,c_Groups_Ozero__class_Ozero(U_420),c_Groups_Oabs__class_Oabs(U_420,U_421))
| ~ sP43(U_420,U_421) )
& ! [U_420,U_421] :
( sP43(U_420,U_421)
| ~ class_Groups_Oordered__ab__group__add__abs(U_420) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_140_2]) ).
cnf(f_140_4,plain,
( sP43(U_420,U_421)
| ~ class_Groups_Oordered__ab__group__add__abs(U_420) ),
inference(clausify,[status(thm)],[f_140_3]) ).
cnf(f_140_5,plain,
( U_421 != c_Groups_Ozero__class_Ozero(U_420)
| ~ c_Orderings_Oord__class_Oless(U_420,c_Groups_Ozero__class_Ozero(U_420),c_Groups_Oabs__class_Oabs(U_420,U_421))
| ~ sP43(U_420,U_421) ),
inference(clausify,[status(thm)],[f_140_3]) ).
cnf(f_140_6,plain,
( c_Orderings_Oord__class_Oless(U_420,c_Groups_Ozero__class_Ozero(U_420),c_Groups_Oabs__class_Oabs(U_420,U_421))
| U_421 = c_Groups_Ozero__class_Ozero(U_420)
| ~ sP43(U_420,U_421) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
inference(fof_nnf,[status(thm)],[fact_pCons]) ).
fof(f_141_2,plain,
? [U_423] :
( ! [U_422] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_422)),U_423)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_422),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_423) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( ! [U_422] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_422)),sK2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_422),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_423,sK2)],[f_141_2]) ).
fof(f_141_4,plain,
( ! [U_422] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_422)),sK2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_422),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2) ),
inference(definitional_conversion,[status(esa)],[f_141_3]) ).
cnf(f_141_5,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2),
inference(clausify,[status(thm)],[f_141_4]) ).
cnf(f_141_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_422)),sK2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_422),v_r) ),
inference(clausify,[status(thm)],[f_141_4]) ).
fof(f_142_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != V_x_2 ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).
fof(f_142_2,plain,
! [U_425,U_424] :
( ( ( c_Groups_Ozero__class_Ozero(U_424) = U_425
| U_425 != c_Groups_Ozero__class_Ozero(U_424) )
& ( U_425 = c_Groups_Ozero__class_Ozero(U_424)
| c_Groups_Ozero__class_Ozero(U_424) != U_425 ) )
| ~ class_Groups_Ozero(U_424) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_425,U_424] :
( c_Groups_Ozero__class_Ozero(U_424) = U_425
| U_425 != c_Groups_Ozero__class_Ozero(U_424)
| ~ sP44(U_425,U_424) )
& ! [U_425,U_424] :
( U_425 = c_Groups_Ozero__class_Ozero(U_424)
| c_Groups_Ozero__class_Ozero(U_424) != U_425
| ~ sP44(U_425,U_424) )
& ! [U_425,U_424] :
( sP44(U_425,U_424)
| ~ class_Groups_Ozero(U_424) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_142_2]) ).
cnf(f_142_4,plain,
( sP44(U_425,U_424)
| ~ class_Groups_Ozero(U_424) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( U_425 = c_Groups_Ozero__class_Ozero(U_424)
| c_Groups_Ozero__class_Ozero(U_424) != U_425
| ~ sP44(U_425,U_424) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_6,plain,
( c_Groups_Ozero__class_Ozero(U_424) = U_425
| U_425 != c_Groups_Ozero__class_Ozero(U_424)
| ~ sP44(U_425,U_424) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_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_143_2,plain,
! [U_429,U_428,U_427,U_426] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428)),U_429) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_428),U_429))
| ~ class_Groups_Oab__semigroup__mult(U_426) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_427,U_426,U_428,U_429] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428)),U_429) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_428),U_429))
| ~ class_Groups_Oab__semigroup__mult(U_426) ),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428)),U_429) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_428),U_429))
| ~ class_Groups_Oab__semigroup__mult(U_426) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,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_144_2,plain,
! [U_433,U_432,U_431,U_430] :
( c_Groups_Oplus__class_Oplus(U_430,c_Groups_Oplus__class_Oplus(U_430,U_431,U_432),U_433) = c_Groups_Oplus__class_Oplus(U_430,U_431,c_Groups_Oplus__class_Oplus(U_430,U_432,U_433))
| ~ class_Groups_Oab__semigroup__add(U_430) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_431,U_430,U_432,U_433] :
( c_Groups_Oplus__class_Oplus(U_430,c_Groups_Oplus__class_Oplus(U_430,U_431,U_432),U_433) = c_Groups_Oplus__class_Oplus(U_430,U_431,c_Groups_Oplus__class_Oplus(U_430,U_432,U_433))
| ~ class_Groups_Oab__semigroup__add(U_430) ),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
( c_Groups_Oplus__class_Oplus(U_430,c_Groups_Oplus__class_Oplus(U_430,U_431,U_432),U_433) = c_Groups_Oplus__class_Oplus(U_430,U_431,c_Groups_Oplus__class_Oplus(U_430,U_432,U_433))
| ~ class_Groups_Oab__semigroup__add(U_430) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2)
| V_b_2 != V_ca_2 )
& ( V_b_2 = V_ca_2
| c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) != c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_145_2,plain,
! [U_437,U_436,U_435,U_434] :
( ( ( c_Groups_Oplus__class_Oplus(U_434,U_435,U_436) = c_Groups_Oplus__class_Oplus(U_434,U_435,U_437)
| U_436 != U_437 )
& ( U_436 = U_437
| c_Groups_Oplus__class_Oplus(U_434,U_435,U_436) != c_Groups_Oplus__class_Oplus(U_434,U_435,U_437) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_434) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
( ! [U_434,U_436,U_435,U_437] :
( c_Groups_Oplus__class_Oplus(U_434,U_435,U_436) = c_Groups_Oplus__class_Oplus(U_434,U_435,U_437)
| U_436 != U_437
| ~ sP45(U_434,U_436,U_435,U_437) )
& ! [U_434,U_436,U_435,U_437] :
( U_436 = U_437
| c_Groups_Oplus__class_Oplus(U_434,U_435,U_436) != c_Groups_Oplus__class_Oplus(U_434,U_435,U_437)
| ~ sP45(U_434,U_436,U_435,U_437) )
& ! [U_434,U_436,U_435,U_437] :
( sP45(U_434,U_436,U_435,U_437)
| ~ class_Groups_Ocancel__semigroup__add(U_434) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_145_2]) ).
cnf(f_145_4,plain,
( sP45(U_434,U_436,U_435,U_437)
| ~ class_Groups_Ocancel__semigroup__add(U_434) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_5,plain,
( U_436 = U_437
| c_Groups_Oplus__class_Oplus(U_434,U_435,U_436) != c_Groups_Oplus__class_Oplus(U_434,U_435,U_437)
| ~ sP45(U_434,U_436,U_435,U_437) ),
inference(clausify,[status(thm)],[f_145_3]) ).
cnf(f_145_6,plain,
( c_Groups_Oplus__class_Oplus(U_434,U_435,U_436) = c_Groups_Oplus__class_Oplus(U_434,U_435,U_437)
| U_436 != U_437
| ~ sP45(U_434,U_436,U_435,U_437) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [V_ca_2,V_a_2,V_b_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2)
| V_b_2 != V_ca_2 )
& ( V_b_2 = V_ca_2
| c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) != c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_146_2,plain,
! [U_441,U_440,U_439,U_438] :
( ( ( c_Groups_Oplus__class_Oplus(U_438,U_439,U_440) = c_Groups_Oplus__class_Oplus(U_438,U_441,U_440)
| U_439 != U_441 )
& ( U_439 = U_441
| c_Groups_Oplus__class_Oplus(U_438,U_439,U_440) != c_Groups_Oplus__class_Oplus(U_438,U_441,U_440) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_438) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
( ! [U_438,U_439,U_441,U_440] :
( c_Groups_Oplus__class_Oplus(U_438,U_439,U_440) = c_Groups_Oplus__class_Oplus(U_438,U_441,U_440)
| U_439 != U_441
| ~ sP46(U_438,U_439,U_441,U_440) )
& ! [U_438,U_439,U_441,U_440] :
( U_439 = U_441
| c_Groups_Oplus__class_Oplus(U_438,U_439,U_440) != c_Groups_Oplus__class_Oplus(U_438,U_441,U_440)
| ~ sP46(U_438,U_439,U_441,U_440) )
& ! [U_438,U_439,U_441,U_440] :
( sP46(U_438,U_439,U_441,U_440)
| ~ class_Groups_Ocancel__semigroup__add(U_438) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_146_2]) ).
cnf(f_146_4,plain,
( sP46(U_438,U_439,U_441,U_440)
| ~ class_Groups_Ocancel__semigroup__add(U_438) ),
inference(clausify,[status(thm)],[f_146_3]) ).
cnf(f_146_5,plain,
( U_439 = U_441
| c_Groups_Oplus__class_Oplus(U_438,U_439,U_440) != c_Groups_Oplus__class_Oplus(U_438,U_441,U_440)
| ~ sP46(U_438,U_439,U_441,U_440) ),
inference(clausify,[status(thm)],[f_146_3]) ).
cnf(f_146_6,plain,
( c_Groups_Oplus__class_Oplus(U_438,U_439,U_440) = c_Groups_Oplus__class_Oplus(U_438,U_441,U_440)
| U_439 != U_441
| ~ sP46(U_438,U_439,U_441,U_440) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != 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_147_2,plain,
! [U_445,U_444,U_443,U_442] :
( U_444 = U_445
| c_Groups_Oplus__class_Oplus(U_442,U_443,U_444) != c_Groups_Oplus__class_Oplus(U_442,U_443,U_445)
| ~ class_Groups_Ocancel__semigroup__add(U_442) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_445,U_443,U_442,U_444] :
( U_444 = U_445
| c_Groups_Oplus__class_Oplus(U_442,U_443,U_444) != c_Groups_Oplus__class_Oplus(U_442,U_443,U_445)
| ~ class_Groups_Ocancel__semigroup__add(U_442) ),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
( U_444 = U_445
| c_Groups_Oplus__class_Oplus(U_442,U_443,U_444) != c_Groups_Oplus__class_Oplus(U_442,U_443,U_445)
| ~ class_Groups_Ocancel__semigroup__add(U_442) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != 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_148_2,plain,
! [U_449,U_448,U_447,U_446] :
( U_448 = U_449
| c_Groups_Oplus__class_Oplus(U_446,U_447,U_448) != c_Groups_Oplus__class_Oplus(U_446,U_447,U_449)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_446) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_449,U_448,U_447,U_446] :
( U_448 = U_449
| c_Groups_Oplus__class_Oplus(U_446,U_447,U_448) != c_Groups_Oplus__class_Oplus(U_446,U_447,U_449)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_446) ),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
( U_448 = U_449
| c_Groups_Oplus__class_Oplus(U_446,U_447,U_448) != c_Groups_Oplus__class_Oplus(U_446,U_447,U_449)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_446) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
! [V_c,V_a,V_b,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) != 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_149_2,plain,
! [U_453,U_452,U_451,U_450] :
( U_451 = U_453
| c_Groups_Oplus__class_Oplus(U_450,U_451,U_452) != c_Groups_Oplus__class_Oplus(U_450,U_453,U_452)
| ~ class_Groups_Ocancel__semigroup__add(U_450) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_453,U_450,U_451,U_452] :
( U_451 = U_453
| c_Groups_Oplus__class_Oplus(U_450,U_451,U_452) != c_Groups_Oplus__class_Oplus(U_450,U_453,U_452)
| ~ class_Groups_Ocancel__semigroup__add(U_450) ),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
( U_451 = U_453
| c_Groups_Oplus__class_Oplus(U_450,U_451,U_452) != c_Groups_Oplus__class_Oplus(U_450,U_453,U_452)
| ~ class_Groups_Ocancel__semigroup__add(U_450) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Oone__class_Oone(T_a) = V_x_2
| V_x_2 != c_Groups_Oone__class_Oone(T_a) )
& ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
| c_Groups_Oone__class_Oone(T_a) != V_x_2 ) )
| ~ class_Groups_Oone(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).
fof(f_150_2,plain,
! [U_455,U_454] :
( ( ( c_Groups_Oone__class_Oone(U_454) = U_455
| U_455 != c_Groups_Oone__class_Oone(U_454) )
& ( U_455 = c_Groups_Oone__class_Oone(U_454)
| c_Groups_Oone__class_Oone(U_454) != U_455 ) )
| ~ class_Groups_Oone(U_454) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
( ! [U_454,U_455] :
( c_Groups_Oone__class_Oone(U_454) = U_455
| U_455 != c_Groups_Oone__class_Oone(U_454)
| ~ sP47(U_454,U_455) )
& ! [U_454,U_455] :
( U_455 = c_Groups_Oone__class_Oone(U_454)
| c_Groups_Oone__class_Oone(U_454) != U_455
| ~ sP47(U_454,U_455) )
& ! [U_454,U_455] :
( sP47(U_454,U_455)
| ~ class_Groups_Oone(U_454) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_150_2]) ).
cnf(f_150_4,plain,
( sP47(U_454,U_455)
| ~ class_Groups_Oone(U_454) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_5,plain,
( U_455 = c_Groups_Oone__class_Oone(U_454)
| c_Groups_Oone__class_Oone(U_454) != U_455
| ~ sP47(U_454,U_455) ),
inference(clausify,[status(thm)],[f_150_3]) ).
cnf(f_150_6,plain,
( c_Groups_Oone__class_Oone(U_454) = U_455
| U_455 != c_Groups_Oone__class_Oone(U_454)
| ~ sP47(U_454,U_455) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = 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_151_2,plain,
! [U_457,U_456] :
( c_Groups_Oabs__class_Oabs(U_456,c_Groups_Oabs__class_Oabs(U_456,U_457)) = c_Groups_Oabs__class_Oabs(U_456,U_457)
| ~ class_Groups_Oordered__ab__group__add__abs(U_456) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_457,U_456] :
( c_Groups_Oabs__class_Oabs(U_456,c_Groups_Oabs__class_Oabs(U_456,U_457)) = c_Groups_Oabs__class_Oabs(U_456,U_457)
| ~ class_Groups_Oordered__ab__group__add__abs(U_456) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( c_Groups_Oabs__class_Oabs(U_456,c_Groups_Oabs__class_Oabs(U_456,U_457)) = c_Groups_Oabs__class_Oabs(U_456,U_457)
| ~ class_Groups_Oordered__ab__group__add__abs(U_456) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
! [V_a,T_a] :
( 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_152_2,plain,
! [U_459,U_458] :
( c_Groups_Oplus__class_Oplus(U_458,c_Groups_Ozero__class_Ozero(U_458),U_459) = U_459
| ~ class_Groups_Omonoid__add(U_458) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_458,U_459] :
( c_Groups_Oplus__class_Oplus(U_458,c_Groups_Ozero__class_Ozero(U_458),U_459) = U_459
| ~ class_Groups_Omonoid__add(U_458) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( c_Groups_Oplus__class_Oplus(U_458,c_Groups_Ozero__class_Ozero(U_458),U_459) = U_459
| ~ class_Groups_Omonoid__add(U_458) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [V_a,T_a] :
( 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_153_2,plain,
! [U_461,U_460] :
( c_Groups_Oplus__class_Oplus(U_460,c_Groups_Ozero__class_Ozero(U_460),U_461) = U_461
| ~ class_Groups_Ocomm__monoid__add(U_460) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_460,U_461] :
( c_Groups_Oplus__class_Oplus(U_460,c_Groups_Ozero__class_Ozero(U_460),U_461) = U_461
| ~ class_Groups_Ocomm__monoid__add(U_460) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( c_Groups_Oplus__class_Oplus(U_460,c_Groups_Ozero__class_Ozero(U_460),U_461) = U_461
| ~ class_Groups_Ocomm__monoid__add(U_460) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).
fof(f_154_2,plain,
! [U_463,U_462] :
( ( ( c_Groups_Ozero__class_Ozero(U_462) = c_Groups_Oplus__class_Oplus(U_462,U_463,U_463)
| U_463 != c_Groups_Ozero__class_Ozero(U_462) )
& ( U_463 = c_Groups_Ozero__class_Ozero(U_462)
| c_Groups_Ozero__class_Ozero(U_462) != c_Groups_Oplus__class_Oplus(U_462,U_463,U_463) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_462) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
( ! [U_462,U_463] :
( c_Groups_Ozero__class_Ozero(U_462) = c_Groups_Oplus__class_Oplus(U_462,U_463,U_463)
| U_463 != c_Groups_Ozero__class_Ozero(U_462)
| ~ sP48(U_462,U_463) )
& ! [U_462,U_463] :
( U_463 = c_Groups_Ozero__class_Ozero(U_462)
| c_Groups_Ozero__class_Ozero(U_462) != c_Groups_Oplus__class_Oplus(U_462,U_463,U_463)
| ~ sP48(U_462,U_463) )
& ! [U_462,U_463] :
( sP48(U_462,U_463)
| ~ class_Groups_Olinordered__ab__group__add(U_462) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_154_2]) ).
cnf(f_154_4,plain,
( sP48(U_462,U_463)
| ~ class_Groups_Olinordered__ab__group__add(U_462) ),
inference(clausify,[status(thm)],[f_154_3]) ).
cnf(f_154_5,plain,
( U_463 = c_Groups_Ozero__class_Ozero(U_462)
| c_Groups_Ozero__class_Ozero(U_462) != c_Groups_Oplus__class_Oplus(U_462,U_463,U_463)
| ~ sP48(U_462,U_463) ),
inference(clausify,[status(thm)],[f_154_3]) ).
cnf(f_154_6,plain,
( c_Groups_Ozero__class_Ozero(U_462) = c_Groups_Oplus__class_Oplus(U_462,U_463,U_463)
| U_463 != c_Groups_Ozero__class_Ozero(U_462)
| ~ sP48(U_462,U_463) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_1,plain,
! [V_a,T_a] :
( 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_155_2,plain,
! [U_465,U_464] :
( c_Groups_Oplus__class_Oplus(U_464,U_465,c_Groups_Ozero__class_Ozero(U_464)) = U_465
| ~ class_Groups_Omonoid__add(U_464) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_465,U_464] :
( c_Groups_Oplus__class_Oplus(U_464,U_465,c_Groups_Ozero__class_Ozero(U_464)) = U_465
| ~ class_Groups_Omonoid__add(U_464) ),
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
( c_Groups_Oplus__class_Oplus(U_464,U_465,c_Groups_Ozero__class_Ozero(U_464)) = U_465
| ~ class_Groups_Omonoid__add(U_464) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_1,plain,
! [V_a,T_a] :
( 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_156_2,plain,
! [U_467,U_466] :
( c_Groups_Oplus__class_Oplus(U_466,U_467,c_Groups_Ozero__class_Ozero(U_466)) = U_467
| ~ class_Groups_Ocomm__monoid__add(U_466) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_466,U_467] :
( c_Groups_Oplus__class_Oplus(U_466,U_467,c_Groups_Ozero__class_Ozero(U_466)) = U_467
| ~ class_Groups_Ocomm__monoid__add(U_466) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( c_Groups_Oplus__class_Oplus(U_466,U_467,c_Groups_Ozero__class_Ozero(U_466)) = U_467
| ~ class_Groups_Ocomm__monoid__add(U_466) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_157_2,plain,
! [U_471,U_470,U_469,U_468] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_468,c_Groups_Oplus__class_Oplus(U_468,U_469,U_470),c_Groups_Oplus__class_Oplus(U_468,U_471,U_470))
| ~ c_Orderings_Oord__class_Oless__eq(U_468,U_469,U_471) )
& ( c_Orderings_Oord__class_Oless__eq(U_468,U_469,U_471)
| ~ c_Orderings_Oord__class_Oless__eq(U_468,c_Groups_Oplus__class_Oplus(U_468,U_469,U_470),c_Groups_Oplus__class_Oplus(U_468,U_471,U_470)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_468) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_468,U_469,U_470,U_471] :
( c_Orderings_Oord__class_Oless__eq(U_468,c_Groups_Oplus__class_Oplus(U_468,U_469,U_470),c_Groups_Oplus__class_Oplus(U_468,U_471,U_470))
| ~ c_Orderings_Oord__class_Oless__eq(U_468,U_469,U_471)
| ~ sP49(U_468,U_469,U_470,U_471) )
& ! [U_468,U_469,U_470,U_471] :
( c_Orderings_Oord__class_Oless__eq(U_468,U_469,U_471)
| ~ c_Orderings_Oord__class_Oless__eq(U_468,c_Groups_Oplus__class_Oplus(U_468,U_469,U_470),c_Groups_Oplus__class_Oplus(U_468,U_471,U_470))
| ~ sP49(U_468,U_469,U_470,U_471) )
& ! [U_468,U_469,U_470,U_471] :
( sP49(U_468,U_469,U_470,U_471)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_468) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_157_2]) ).
cnf(f_157_4,plain,
( sP49(U_468,U_469,U_470,U_471)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_468) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_468,U_469,U_471)
| ~ c_Orderings_Oord__class_Oless__eq(U_468,c_Groups_Oplus__class_Oplus(U_468,U_469,U_470),c_Groups_Oplus__class_Oplus(U_468,U_471,U_470))
| ~ sP49(U_468,U_469,U_470,U_471) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_468,c_Groups_Oplus__class_Oplus(U_468,U_469,U_470),c_Groups_Oplus__class_Oplus(U_468,U_471,U_470))
| ~ c_Orderings_Oord__class_Oless__eq(U_468,U_469,U_471)
| ~ sP49(U_468,U_469,U_470,U_471) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).
fof(f_158_2,plain,
! [U_475,U_474,U_473,U_472] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_472,c_Groups_Oplus__class_Oplus(U_472,U_473,U_474),c_Groups_Oplus__class_Oplus(U_472,U_473,U_475))
| ~ c_Orderings_Oord__class_Oless__eq(U_472,U_474,U_475) )
& ( c_Orderings_Oord__class_Oless__eq(U_472,U_474,U_475)
| ~ c_Orderings_Oord__class_Oless__eq(U_472,c_Groups_Oplus__class_Oplus(U_472,U_473,U_474),c_Groups_Oplus__class_Oplus(U_472,U_473,U_475)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_472) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
( ! [U_474,U_475,U_472,U_473] :
( c_Orderings_Oord__class_Oless__eq(U_472,c_Groups_Oplus__class_Oplus(U_472,U_473,U_474),c_Groups_Oplus__class_Oplus(U_472,U_473,U_475))
| ~ c_Orderings_Oord__class_Oless__eq(U_472,U_474,U_475)
| ~ sP50(U_474,U_475,U_472,U_473) )
& ! [U_474,U_475,U_472,U_473] :
( c_Orderings_Oord__class_Oless__eq(U_472,U_474,U_475)
| ~ c_Orderings_Oord__class_Oless__eq(U_472,c_Groups_Oplus__class_Oplus(U_472,U_473,U_474),c_Groups_Oplus__class_Oplus(U_472,U_473,U_475))
| ~ sP50(U_474,U_475,U_472,U_473) )
& ! [U_474,U_475,U_472,U_473] :
( sP50(U_474,U_475,U_472,U_473)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_472) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_158_2]) ).
cnf(f_158_4,plain,
( sP50(U_474,U_475,U_472,U_473)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_472) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_472,U_474,U_475)
| ~ c_Orderings_Oord__class_Oless__eq(U_472,c_Groups_Oplus__class_Oplus(U_472,U_473,U_474),c_Groups_Oplus__class_Oplus(U_472,U_473,U_475))
| ~ sP50(U_474,U_475,U_472,U_473) ),
inference(clausify,[status(thm)],[f_158_3]) ).
cnf(f_158_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_472,c_Groups_Oplus__class_Oplus(U_472,U_473,U_474),c_Groups_Oplus__class_Oplus(U_472,U_473,U_475))
| ~ c_Orderings_Oord__class_Oless__eq(U_472,U_474,U_475)
| ~ sP50(U_474,U_475,U_472,U_473) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ 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_159_2,plain,
! [U_479,U_478,U_477,U_476] :
( c_Orderings_Oord__class_Oless__eq(U_476,c_Groups_Oplus__class_Oplus(U_476,U_477,U_479),c_Groups_Oplus__class_Oplus(U_476,U_478,U_479))
| ~ c_Orderings_Oord__class_Oless__eq(U_476,U_477,U_478)
| ~ class_Groups_Oordered__ab__semigroup__add(U_476) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_477,U_476,U_478,U_479] :
( c_Orderings_Oord__class_Oless__eq(U_476,c_Groups_Oplus__class_Oplus(U_476,U_477,U_479),c_Groups_Oplus__class_Oplus(U_476,U_478,U_479))
| ~ c_Orderings_Oord__class_Oless__eq(U_476,U_477,U_478)
| ~ class_Groups_Oordered__ab__semigroup__add(U_476) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_476,c_Groups_Oplus__class_Oplus(U_476,U_477,U_479),c_Groups_Oplus__class_Oplus(U_476,U_478,U_479))
| ~ c_Orderings_Oord__class_Oless__eq(U_476,U_477,U_478)
| ~ class_Groups_Oordered__ab__semigroup__add(U_476) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ 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_160_2,plain,
! [U_483,U_482,U_481,U_480] :
( c_Orderings_Oord__class_Oless__eq(U_480,c_Groups_Oplus__class_Oplus(U_480,U_483,U_481),c_Groups_Oplus__class_Oplus(U_480,U_483,U_482))
| ~ c_Orderings_Oord__class_Oless__eq(U_480,U_481,U_482)
| ~ class_Groups_Oordered__ab__semigroup__add(U_480) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_481,U_482,U_480,U_483] :
( c_Orderings_Oord__class_Oless__eq(U_480,c_Groups_Oplus__class_Oplus(U_480,U_483,U_481),c_Groups_Oplus__class_Oplus(U_480,U_483,U_482))
| ~ c_Orderings_Oord__class_Oless__eq(U_480,U_481,U_482)
| ~ class_Groups_Oordered__ab__semigroup__add(U_480) ),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_480,c_Groups_Oplus__class_Oplus(U_480,U_483,U_481),c_Groups_Oplus__class_Oplus(U_480,U_483,U_482))
| ~ c_Orderings_Oord__class_Oless__eq(U_480,U_481,U_482)
| ~ class_Groups_Oordered__ab__semigroup__add(U_480) ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ 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_161_2,plain,
! [U_488,U_487,U_486,U_485,U_484] :
( c_Orderings_Oord__class_Oless__eq(U_484,c_Groups_Oplus__class_Oplus(U_484,U_485,U_487),c_Groups_Oplus__class_Oplus(U_484,U_486,U_488))
| ~ c_Orderings_Oord__class_Oless__eq(U_484,U_487,U_488)
| ~ c_Orderings_Oord__class_Oless__eq(U_484,U_485,U_486)
| ~ class_Groups_Oordered__ab__semigroup__add(U_484) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_486,U_485,U_484,U_487,U_488] :
( c_Orderings_Oord__class_Oless__eq(U_484,c_Groups_Oplus__class_Oplus(U_484,U_485,U_487),c_Groups_Oplus__class_Oplus(U_484,U_486,U_488))
| ~ c_Orderings_Oord__class_Oless__eq(U_484,U_487,U_488)
| ~ c_Orderings_Oord__class_Oless__eq(U_484,U_485,U_486)
| ~ class_Groups_Oordered__ab__semigroup__add(U_484) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_484,c_Groups_Oplus__class_Oplus(U_484,U_485,U_487),c_Groups_Oplus__class_Oplus(U_484,U_486,U_488))
| ~ c_Orderings_Oord__class_Oless__eq(U_484,U_487,U_488)
| ~ c_Orderings_Oord__class_Oless__eq(U_484,U_485,U_486)
| ~ class_Groups_Oordered__ab__semigroup__add(U_484) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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_162_2,plain,
! [U_492,U_491,U_490,U_489] :
( c_Orderings_Oord__class_Oless__eq(U_489,U_490,U_492)
| ~ c_Orderings_Oord__class_Oless__eq(U_489,c_Groups_Oplus__class_Oplus(U_489,U_490,U_491),c_Groups_Oplus__class_Oplus(U_489,U_492,U_491))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_489) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_489,U_492,U_490,U_491] :
( c_Orderings_Oord__class_Oless__eq(U_489,U_490,U_492)
| ~ c_Orderings_Oord__class_Oless__eq(U_489,c_Groups_Oplus__class_Oplus(U_489,U_490,U_491),c_Groups_Oplus__class_Oplus(U_489,U_492,U_491))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_489) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_489,U_490,U_492)
| ~ c_Orderings_Oord__class_Oless__eq(U_489,c_Groups_Oplus__class_Oplus(U_489,U_490,U_491),c_Groups_Oplus__class_Oplus(U_489,U_492,U_491))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_489) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),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_163_2,plain,
! [U_496,U_495,U_494,U_493] :
( c_Orderings_Oord__class_Oless__eq(U_493,U_495,U_496)
| ~ c_Orderings_Oord__class_Oless__eq(U_493,c_Groups_Oplus__class_Oplus(U_493,U_494,U_495),c_Groups_Oplus__class_Oplus(U_493,U_494,U_496))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_493) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_495,U_493,U_494,U_496] :
( c_Orderings_Oord__class_Oless__eq(U_493,U_495,U_496)
| ~ c_Orderings_Oord__class_Oless__eq(U_493,c_Groups_Oplus__class_Oplus(U_493,U_494,U_495),c_Groups_Oplus__class_Oplus(U_493,U_494,U_496))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_493) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_493,U_495,U_496)
| ~ c_Orderings_Oord__class_Oless__eq(U_493,c_Groups_Oplus__class_Oplus(U_493,U_494,U_495),c_Groups_Oplus__class_Oplus(U_493,U_494,U_496))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_493) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_164_2,plain,
! [U_500,U_499,U_498,U_497] :
( ( ( c_Orderings_Oord__class_Oless(U_497,c_Groups_Oplus__class_Oplus(U_497,U_498,U_499),c_Groups_Oplus__class_Oplus(U_497,U_500,U_499))
| ~ c_Orderings_Oord__class_Oless(U_497,U_498,U_500) )
& ( c_Orderings_Oord__class_Oless(U_497,U_498,U_500)
| ~ c_Orderings_Oord__class_Oless(U_497,c_Groups_Oplus__class_Oplus(U_497,U_498,U_499),c_Groups_Oplus__class_Oplus(U_497,U_500,U_499)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_497) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
( ! [U_499,U_497,U_498,U_500] :
( c_Orderings_Oord__class_Oless(U_497,c_Groups_Oplus__class_Oplus(U_497,U_498,U_499),c_Groups_Oplus__class_Oplus(U_497,U_500,U_499))
| ~ c_Orderings_Oord__class_Oless(U_497,U_498,U_500)
| ~ sP51(U_499,U_497,U_498,U_500) )
& ! [U_499,U_497,U_498,U_500] :
( c_Orderings_Oord__class_Oless(U_497,U_498,U_500)
| ~ c_Orderings_Oord__class_Oless(U_497,c_Groups_Oplus__class_Oplus(U_497,U_498,U_499),c_Groups_Oplus__class_Oplus(U_497,U_500,U_499))
| ~ sP51(U_499,U_497,U_498,U_500) )
& ! [U_499,U_497,U_498,U_500] :
( sP51(U_499,U_497,U_498,U_500)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_497) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_164_2]) ).
cnf(f_164_4,plain,
( sP51(U_499,U_497,U_498,U_500)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_497) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_5,plain,
( c_Orderings_Oord__class_Oless(U_497,U_498,U_500)
| ~ c_Orderings_Oord__class_Oless(U_497,c_Groups_Oplus__class_Oplus(U_497,U_498,U_499),c_Groups_Oplus__class_Oplus(U_497,U_500,U_499))
| ~ sP51(U_499,U_497,U_498,U_500) ),
inference(clausify,[status(thm)],[f_164_3]) ).
cnf(f_164_6,plain,
( c_Orderings_Oord__class_Oless(U_497,c_Groups_Oplus__class_Oplus(U_497,U_498,U_499),c_Groups_Oplus__class_Oplus(U_497,U_500,U_499))
| ~ c_Orderings_Oord__class_Oless(U_497,U_498,U_500)
| ~ sP51(U_499,U_497,U_498,U_500) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).
fof(f_165_2,plain,
! [U_504,U_503,U_502,U_501] :
( ( ( c_Orderings_Oord__class_Oless(U_501,c_Groups_Oplus__class_Oplus(U_501,U_502,U_503),c_Groups_Oplus__class_Oplus(U_501,U_502,U_504))
| ~ c_Orderings_Oord__class_Oless(U_501,U_503,U_504) )
& ( c_Orderings_Oord__class_Oless(U_501,U_503,U_504)
| ~ c_Orderings_Oord__class_Oless(U_501,c_Groups_Oplus__class_Oplus(U_501,U_502,U_503),c_Groups_Oplus__class_Oplus(U_501,U_502,U_504)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_501) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
( ! [U_504,U_503,U_502,U_501] :
( c_Orderings_Oord__class_Oless(U_501,c_Groups_Oplus__class_Oplus(U_501,U_502,U_503),c_Groups_Oplus__class_Oplus(U_501,U_502,U_504))
| ~ c_Orderings_Oord__class_Oless(U_501,U_503,U_504)
| ~ sP52(U_504,U_503,U_502,U_501) )
& ! [U_504,U_503,U_502,U_501] :
( c_Orderings_Oord__class_Oless(U_501,U_503,U_504)
| ~ c_Orderings_Oord__class_Oless(U_501,c_Groups_Oplus__class_Oplus(U_501,U_502,U_503),c_Groups_Oplus__class_Oplus(U_501,U_502,U_504))
| ~ sP52(U_504,U_503,U_502,U_501) )
& ! [U_504,U_503,U_502,U_501] :
( sP52(U_504,U_503,U_502,U_501)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_501) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_165_2]) ).
cnf(f_165_4,plain,
( sP52(U_504,U_503,U_502,U_501)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_501) ),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_5,plain,
( c_Orderings_Oord__class_Oless(U_501,U_503,U_504)
| ~ c_Orderings_Oord__class_Oless(U_501,c_Groups_Oplus__class_Oplus(U_501,U_502,U_503),c_Groups_Oplus__class_Oplus(U_501,U_502,U_504))
| ~ sP52(U_504,U_503,U_502,U_501) ),
inference(clausify,[status(thm)],[f_165_3]) ).
cnf(f_165_6,plain,
( c_Orderings_Oord__class_Oless(U_501,c_Groups_Oplus__class_Oplus(U_501,U_502,U_503),c_Groups_Oplus__class_Oplus(U_501,U_502,U_504))
| ~ c_Orderings_Oord__class_Oless(U_501,U_503,U_504)
| ~ sP52(U_504,U_503,U_502,U_501) ),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ 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_166_2,plain,
! [U_508,U_507,U_506,U_505] :
( c_Orderings_Oord__class_Oless(U_505,c_Groups_Oplus__class_Oplus(U_505,U_506,U_508),c_Groups_Oplus__class_Oplus(U_505,U_507,U_508))
| ~ c_Orderings_Oord__class_Oless(U_505,U_506,U_507)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_505) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_507,U_506,U_505,U_508] :
( c_Orderings_Oord__class_Oless(U_505,c_Groups_Oplus__class_Oplus(U_505,U_506,U_508),c_Groups_Oplus__class_Oplus(U_505,U_507,U_508))
| ~ c_Orderings_Oord__class_Oless(U_505,U_506,U_507)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_505) ),
inference(definitional_conversion,[status(esa)],[f_166_2]) ).
cnf(f_166_4,plain,
( c_Orderings_Oord__class_Oless(U_505,c_Groups_Oplus__class_Oplus(U_505,U_506,U_508),c_Groups_Oplus__class_Oplus(U_505,U_507,U_508))
| ~ c_Orderings_Oord__class_Oless(U_505,U_506,U_507)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_505) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ 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_167_2,plain,
! [U_512,U_511,U_510,U_509] :
( c_Orderings_Oord__class_Oless(U_509,c_Groups_Oplus__class_Oplus(U_509,U_512,U_510),c_Groups_Oplus__class_Oplus(U_509,U_512,U_511))
| ~ c_Orderings_Oord__class_Oless(U_509,U_510,U_511)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_509) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
! [U_511,U_512,U_509,U_510] :
( c_Orderings_Oord__class_Oless(U_509,c_Groups_Oplus__class_Oplus(U_509,U_512,U_510),c_Groups_Oplus__class_Oplus(U_509,U_512,U_511))
| ~ c_Orderings_Oord__class_Oless(U_509,U_510,U_511)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_509) ),
inference(definitional_conversion,[status(esa)],[f_167_2]) ).
cnf(f_167_4,plain,
( c_Orderings_Oord__class_Oless(U_509,c_Groups_Oplus__class_Oplus(U_509,U_512,U_510),c_Groups_Oplus__class_Oplus(U_509,U_512,U_511))
| ~ c_Orderings_Oord__class_Oless(U_509,U_510,U_511)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_509) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ 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_168_2,plain,
! [U_517,U_516,U_515,U_514,U_513] :
( c_Orderings_Oord__class_Oless(U_513,c_Groups_Oplus__class_Oplus(U_513,U_514,U_516),c_Groups_Oplus__class_Oplus(U_513,U_515,U_517))
| ~ c_Orderings_Oord__class_Oless(U_513,U_516,U_517)
| ~ c_Orderings_Oord__class_Oless(U_513,U_514,U_515)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_513) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_514,U_513,U_515,U_516,U_517] :
( c_Orderings_Oord__class_Oless(U_513,c_Groups_Oplus__class_Oplus(U_513,U_514,U_516),c_Groups_Oplus__class_Oplus(U_513,U_515,U_517))
| ~ c_Orderings_Oord__class_Oless(U_513,U_516,U_517)
| ~ c_Orderings_Oord__class_Oless(U_513,U_514,U_515)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_513) ),
inference(definitional_conversion,[status(esa)],[f_168_2]) ).
cnf(f_168_4,plain,
( c_Orderings_Oord__class_Oless(U_513,c_Groups_Oplus__class_Oplus(U_513,U_514,U_516),c_Groups_Oplus__class_Oplus(U_513,U_515,U_517))
| ~ c_Orderings_Oord__class_Oless(U_513,U_516,U_517)
| ~ c_Orderings_Oord__class_Oless(U_513,U_514,U_515)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_513) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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_169_2,plain,
! [U_521,U_520,U_519,U_518] :
( c_Orderings_Oord__class_Oless(U_518,U_519,U_521)
| ~ c_Orderings_Oord__class_Oless(U_518,c_Groups_Oplus__class_Oplus(U_518,U_519,U_520),c_Groups_Oplus__class_Oplus(U_518,U_521,U_520))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_518) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_518,U_519,U_520,U_521] :
( c_Orderings_Oord__class_Oless(U_518,U_519,U_521)
| ~ c_Orderings_Oord__class_Oless(U_518,c_Groups_Oplus__class_Oplus(U_518,U_519,U_520),c_Groups_Oplus__class_Oplus(U_518,U_521,U_520))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_518) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( c_Orderings_Oord__class_Oless(U_518,U_519,U_521)
| ~ c_Orderings_Oord__class_Oless(U_518,c_Groups_Oplus__class_Oplus(U_518,U_519,U_520),c_Groups_Oplus__class_Oplus(U_518,U_521,U_520))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_518) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),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_170_2,plain,
! [U_525,U_524,U_523,U_522] :
( c_Orderings_Oord__class_Oless(U_522,U_524,U_525)
| ~ c_Orderings_Oord__class_Oless(U_522,c_Groups_Oplus__class_Oplus(U_522,U_523,U_524),c_Groups_Oplus__class_Oplus(U_522,U_523,U_525))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_522) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_522,U_524,U_525,U_523] :
( c_Orderings_Oord__class_Oless(U_522,U_524,U_525)
| ~ c_Orderings_Oord__class_Oless(U_522,c_Groups_Oplus__class_Oplus(U_522,U_523,U_524),c_Groups_Oplus__class_Oplus(U_522,U_523,U_525))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_522) ),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
( c_Orderings_Oord__class_Oless(U_522,U_524,U_525)
| ~ c_Orderings_Oord__class_Oless(U_522,c_Groups_Oplus__class_Oplus(U_522,U_523,U_524),c_Groups_Oplus__class_Oplus(U_522,U_523,U_525))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_522) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_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_171_2,plain,
! [U_527,U_526] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),c_Groups_Oone__class_Oone(U_526)),U_527) = U_527
| ~ class_Groups_Omonoid__mult(U_526) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_527,U_526] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),c_Groups_Oone__class_Oone(U_526)),U_527) = U_527
| ~ class_Groups_Omonoid__mult(U_526) ),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),c_Groups_Oone__class_Oone(U_526)),U_527) = U_527
| ~ class_Groups_Omonoid__mult(U_526) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_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_172_2,plain,
! [U_529,U_528] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_528),c_Groups_Oone__class_Oone(U_528)),U_529) = U_529
| ~ class_Groups_Ocomm__monoid__mult(U_528) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_528,U_529] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_528),c_Groups_Oone__class_Oone(U_528)),U_529) = U_529
| ~ class_Groups_Ocomm__monoid__mult(U_528) ),
inference(definitional_conversion,[status(esa)],[f_172_2]) ).
cnf(f_172_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_528),c_Groups_Oone__class_Oone(U_528)),U_529) = U_529
| ~ class_Groups_Ocomm__monoid__mult(U_528) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_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_173_2,plain,
! [U_531,U_530] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_530),U_531),c_Groups_Oone__class_Oone(U_530)) = U_531
| ~ class_Groups_Omonoid__mult(U_530) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_530,U_531] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_530),U_531),c_Groups_Oone__class_Oone(U_530)) = U_531
| ~ class_Groups_Omonoid__mult(U_530) ),
inference(definitional_conversion,[status(esa)],[f_173_2]) ).
cnf(f_173_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_530),U_531),c_Groups_Oone__class_Oone(U_530)) = U_531
| ~ class_Groups_Omonoid__mult(U_530) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_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_174_2,plain,
! [U_533,U_532] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_532),U_533),c_Groups_Oone__class_Oone(U_532)) = U_533
| ~ class_Groups_Ocomm__monoid__mult(U_532) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_532,U_533] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_532),U_533),c_Groups_Oone__class_Oone(U_532)) = U_533
| ~ class_Groups_Ocomm__monoid__mult(U_532) ),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_532),U_533),c_Groups_Oone__class_Oone(U_532)) = U_533
| ~ class_Groups_Ocomm__monoid__mult(U_532) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [T_a] :
( 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_175_2,plain,
! [U_534] :
( c_Groups_Oabs__class_Oabs(U_534,c_Groups_Ozero__class_Ozero(U_534)) = c_Groups_Ozero__class_Ozero(U_534)
| ~ class_Groups_Oordered__ab__group__add__abs(U_534) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_534] :
( c_Groups_Oabs__class_Oabs(U_534,c_Groups_Ozero__class_Ozero(U_534)) = c_Groups_Ozero__class_Ozero(U_534)
| ~ class_Groups_Oordered__ab__group__add__abs(U_534) ),
inference(definitional_conversion,[status(esa)],[f_175_2]) ).
cnf(f_175_4,plain,
( c_Groups_Oabs__class_Oabs(U_534,c_Groups_Ozero__class_Ozero(U_534)) = c_Groups_Ozero__class_Ozero(U_534)
| ~ class_Groups_Oordered__ab__group__add__abs(U_534) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Oabs__class_Oabs(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).
fof(f_176_2,plain,
! [U_536,U_535] :
( ( ( c_Groups_Oabs__class_Oabs(U_535,U_536) = c_Groups_Ozero__class_Ozero(U_535)
| U_536 != c_Groups_Ozero__class_Ozero(U_535) )
& ( U_536 = c_Groups_Ozero__class_Ozero(U_535)
| c_Groups_Oabs__class_Oabs(U_535,U_536) != c_Groups_Ozero__class_Ozero(U_535) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_535) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
( ! [U_535,U_536] :
( c_Groups_Oabs__class_Oabs(U_535,U_536) = c_Groups_Ozero__class_Ozero(U_535)
| U_536 != c_Groups_Ozero__class_Ozero(U_535)
| ~ sP53(U_535,U_536) )
& ! [U_535,U_536] :
( U_536 = c_Groups_Ozero__class_Ozero(U_535)
| c_Groups_Oabs__class_Oabs(U_535,U_536) != c_Groups_Ozero__class_Ozero(U_535)
| ~ sP53(U_535,U_536) )
& ! [U_535,U_536] :
( sP53(U_535,U_536)
| ~ class_Groups_Oordered__ab__group__add__abs(U_535) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_176_2]) ).
cnf(f_176_4,plain,
( sP53(U_535,U_536)
| ~ class_Groups_Oordered__ab__group__add__abs(U_535) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_5,plain,
( U_536 = c_Groups_Ozero__class_Ozero(U_535)
| c_Groups_Oabs__class_Oabs(U_535,U_536) != c_Groups_Ozero__class_Ozero(U_535)
| ~ sP53(U_535,U_536) ),
inference(clausify,[status(thm)],[f_176_3]) ).
cnf(f_176_6,plain,
( c_Groups_Oabs__class_Oabs(U_535,U_536) = c_Groups_Ozero__class_Ozero(U_535)
| U_536 != c_Groups_Ozero__class_Ozero(U_535)
| ~ sP53(U_535,U_536) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,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_177_2,plain,
! [U_538,U_537] :
( c_Orderings_Oord__class_Oless__eq(U_537,U_538,c_Groups_Oabs__class_Oabs(U_537,U_538))
| ~ class_Groups_Oordered__ab__group__add__abs(U_537) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_538,U_537] :
( c_Orderings_Oord__class_Oless__eq(U_537,U_538,c_Groups_Oabs__class_Oabs(U_537,U_538))
| ~ class_Groups_Oordered__ab__group__add__abs(U_537) ),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_537,U_538,c_Groups_Oabs__class_Oabs(U_537,U_538))
| ~ class_Groups_Oordered__ab__group__add__abs(U_537) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,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_178_2,plain,
! [U_541,U_540,U_539] :
( c_Orderings_Oord__class_Oless__eq(U_539,U_540,U_541)
| ~ c_Orderings_Oord__class_Oless__eq(U_539,c_Groups_Oabs__class_Oabs(U_539,U_540),U_541)
| ~ class_Groups_Oordered__ab__group__add__abs(U_539) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_539,U_540,U_541] :
( c_Orderings_Oord__class_Oless__eq(U_539,U_540,U_541)
| ~ c_Orderings_Oord__class_Oless__eq(U_539,c_Groups_Oabs__class_Oabs(U_539,U_540),U_541)
| ~ class_Groups_Oordered__ab__group__add__abs(U_539) ),
inference(definitional_conversion,[status(esa)],[f_178_2]) ).
cnf(f_178_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_539,U_540,U_541)
| ~ c_Orderings_Oord__class_Oless__eq(U_539,c_Groups_Oabs__class_Oabs(U_539,U_540),U_541)
| ~ class_Groups_Oordered__ab__group__add__abs(U_539) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),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_179_2,plain,
! [U_544,U_543,U_542] :
( c_Groups_Oabs__class_Oabs(U_542,c_Groups_Oplus__class_Oplus(U_542,c_Groups_Oabs__class_Oabs(U_542,U_543),c_Groups_Oabs__class_Oabs(U_542,U_544))) = c_Groups_Oplus__class_Oplus(U_542,c_Groups_Oabs__class_Oabs(U_542,U_543),c_Groups_Oabs__class_Oabs(U_542,U_544))
| ~ class_Groups_Oordered__ab__group__add__abs(U_542) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_542,U_543,U_544] :
( c_Groups_Oabs__class_Oabs(U_542,c_Groups_Oplus__class_Oplus(U_542,c_Groups_Oabs__class_Oabs(U_542,U_543),c_Groups_Oabs__class_Oabs(U_542,U_544))) = c_Groups_Oplus__class_Oplus(U_542,c_Groups_Oabs__class_Oabs(U_542,U_543),c_Groups_Oabs__class_Oabs(U_542,U_544))
| ~ class_Groups_Oordered__ab__group__add__abs(U_542) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( c_Groups_Oabs__class_Oabs(U_542,c_Groups_Oplus__class_Oplus(U_542,c_Groups_Oabs__class_Oabs(U_542,U_543),c_Groups_Oabs__class_Oabs(U_542,U_544))) = c_Groups_Oplus__class_Oplus(U_542,c_Groups_Oabs__class_Oabs(U_542,U_543),c_Groups_Oabs__class_Oabs(U_542,U_544))
| ~ class_Groups_Oordered__ab__group__add__abs(U_542) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).
fof(f_180_2,plain,
! [U_546,U_545] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),c_Groups_Oplus__class_Oplus(U_545,U_546,U_546))
| ~ c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),U_546) )
& ( c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),U_546)
| ~ c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),c_Groups_Oplus__class_Oplus(U_545,U_546,U_546)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_545) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( ! [U_546,U_545] :
( c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),c_Groups_Oplus__class_Oplus(U_545,U_546,U_546))
| ~ c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),U_546)
| ~ sP54(U_546,U_545) )
& ! [U_546,U_545] :
( c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),U_546)
| ~ c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),c_Groups_Oplus__class_Oplus(U_545,U_546,U_546))
| ~ sP54(U_546,U_545) )
& ! [U_546,U_545] :
( sP54(U_546,U_545)
| ~ class_Groups_Olinordered__ab__group__add(U_545) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_180_2]) ).
cnf(f_180_4,plain,
( sP54(U_546,U_545)
| ~ class_Groups_Olinordered__ab__group__add(U_545) ),
inference(clausify,[status(thm)],[f_180_3]) ).
cnf(f_180_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),U_546)
| ~ c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),c_Groups_Oplus__class_Oplus(U_545,U_546,U_546))
| ~ sP54(U_546,U_545) ),
inference(clausify,[status(thm)],[f_180_3]) ).
cnf(f_180_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),c_Groups_Oplus__class_Oplus(U_545,U_546,U_546))
| ~ c_Orderings_Oord__class_Oless__eq(U_545,c_Groups_Ozero__class_Ozero(U_545),U_546)
| ~ sP54(U_546,U_545) ),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).
fof(f_181_2,plain,
! [U_548,U_547] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_547,c_Groups_Oplus__class_Oplus(U_547,U_548,U_548),c_Groups_Ozero__class_Ozero(U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_547,U_548,c_Groups_Ozero__class_Ozero(U_547)) )
& ( c_Orderings_Oord__class_Oless__eq(U_547,U_548,c_Groups_Ozero__class_Ozero(U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_547,c_Groups_Oplus__class_Oplus(U_547,U_548,U_548),c_Groups_Ozero__class_Ozero(U_547)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_547) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_548,U_547] :
( c_Orderings_Oord__class_Oless__eq(U_547,c_Groups_Oplus__class_Oplus(U_547,U_548,U_548),c_Groups_Ozero__class_Ozero(U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_547,U_548,c_Groups_Ozero__class_Ozero(U_547))
| ~ sP55(U_548,U_547) )
& ! [U_548,U_547] :
( c_Orderings_Oord__class_Oless__eq(U_547,U_548,c_Groups_Ozero__class_Ozero(U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_547,c_Groups_Oplus__class_Oplus(U_547,U_548,U_548),c_Groups_Ozero__class_Ozero(U_547))
| ~ sP55(U_548,U_547) )
& ! [U_548,U_547] :
( sP55(U_548,U_547)
| ~ class_Groups_Olinordered__ab__group__add(U_547) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_181_2]) ).
cnf(f_181_4,plain,
( sP55(U_548,U_547)
| ~ class_Groups_Olinordered__ab__group__add(U_547) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_547,U_548,c_Groups_Ozero__class_Ozero(U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_547,c_Groups_Oplus__class_Oplus(U_547,U_548,U_548),c_Groups_Ozero__class_Ozero(U_547))
| ~ sP55(U_548,U_547) ),
inference(clausify,[status(thm)],[f_181_3]) ).
cnf(f_181_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_547,c_Groups_Oplus__class_Oplus(U_547,U_548,U_548),c_Groups_Ozero__class_Ozero(U_547))
| ~ c_Orderings_Oord__class_Oless__eq(U_547,U_548,c_Groups_Ozero__class_Ozero(U_547))
| ~ sP55(U_548,U_547) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_182_2,plain,
! [U_551,U_550,U_549] :
( c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),c_Groups_Oplus__class_Oplus(U_549,U_550,U_551))
| ~ c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),U_551)
| ~ c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),U_550)
| ~ class_Groups_Oordered__comm__monoid__add(U_549) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_551,U_550,U_549] :
( c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),c_Groups_Oplus__class_Oplus(U_549,U_550,U_551))
| ~ c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),U_551)
| ~ c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),U_550)
| ~ class_Groups_Oordered__comm__monoid__add(U_549) ),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),c_Groups_Oplus__class_Oplus(U_549,U_550,U_551))
| ~ c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),U_551)
| ~ c_Orderings_Oord__class_Oless__eq(U_549,c_Groups_Ozero__class_Ozero(U_549),U_550)
| ~ class_Groups_Oordered__comm__monoid__add(U_549) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_183_2,plain,
! [U_554,U_553,U_552] :
( ( ( c_Groups_Oplus__class_Oplus(U_552,U_553,U_554) = c_Groups_Ozero__class_Ozero(U_552)
| U_554 != c_Groups_Ozero__class_Ozero(U_552)
| U_553 != c_Groups_Ozero__class_Ozero(U_552) )
& ( ( U_554 = c_Groups_Ozero__class_Ozero(U_552)
& U_553 = c_Groups_Ozero__class_Ozero(U_552) )
| c_Groups_Oplus__class_Oplus(U_552,U_553,U_554) != c_Groups_Ozero__class_Ozero(U_552) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_552,c_Groups_Ozero__class_Ozero(U_552),U_554)
| ~ c_Orderings_Oord__class_Oless__eq(U_552,c_Groups_Ozero__class_Ozero(U_552),U_553)
| ~ class_Groups_Oordered__comm__monoid__add(U_552) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_553,U_552,U_554] :
( U_554 = c_Groups_Ozero__class_Ozero(U_552)
| ~ sP56(U_553,U_552,U_554) )
& ! [U_553,U_552,U_554] :
( U_553 = c_Groups_Ozero__class_Ozero(U_552)
| ~ sP56(U_553,U_552,U_554) )
& ! [U_553,U_552,U_554] :
( c_Groups_Oplus__class_Oplus(U_552,U_553,U_554) = c_Groups_Ozero__class_Ozero(U_552)
| U_554 != c_Groups_Ozero__class_Ozero(U_552)
| U_553 != c_Groups_Ozero__class_Ozero(U_552)
| ~ sP57(U_553,U_552,U_554) )
& ! [U_553,U_552,U_554] :
( sP56(U_553,U_552,U_554)
| c_Groups_Oplus__class_Oplus(U_552,U_553,U_554) != c_Groups_Ozero__class_Ozero(U_552)
| ~ sP57(U_553,U_552,U_554) )
& ! [U_553,U_552,U_554] :
( sP57(U_553,U_552,U_554)
| ~ c_Orderings_Oord__class_Oless__eq(U_552,c_Groups_Ozero__class_Ozero(U_552),U_554)
| ~ c_Orderings_Oord__class_Oless__eq(U_552,c_Groups_Ozero__class_Ozero(U_552),U_553)
| ~ class_Groups_Oordered__comm__monoid__add(U_552) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56,sP57])],[f_183_2]) ).
cnf(f_183_4,plain,
( sP57(U_553,U_552,U_554)
| ~ c_Orderings_Oord__class_Oless__eq(U_552,c_Groups_Ozero__class_Ozero(U_552),U_554)
| ~ c_Orderings_Oord__class_Oless__eq(U_552,c_Groups_Ozero__class_Ozero(U_552),U_553)
| ~ class_Groups_Oordered__comm__monoid__add(U_552) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
( sP56(U_553,U_552,U_554)
| c_Groups_Oplus__class_Oplus(U_552,U_553,U_554) != c_Groups_Ozero__class_Ozero(U_552)
| ~ sP57(U_553,U_552,U_554) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_6,plain,
( c_Groups_Oplus__class_Oplus(U_552,U_553,U_554) = c_Groups_Ozero__class_Ozero(U_552)
| U_554 != c_Groups_Ozero__class_Ozero(U_552)
| U_553 != c_Groups_Ozero__class_Ozero(U_552)
| ~ sP57(U_553,U_552,U_554) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_7,plain,
( U_553 = c_Groups_Ozero__class_Ozero(U_552)
| ~ sP56(U_553,U_552,U_554) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_8,plain,
( U_554 = c_Groups_Ozero__class_Ozero(U_552)
| ~ sP56(U_553,U_552,U_554) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| ~ 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_184_2,plain,
! [U_558,U_557,U_556,U_555] :
( c_Orderings_Oord__class_Oless__eq(U_555,U_557,c_Groups_Oplus__class_Oplus(U_555,U_556,U_558))
| ~ c_Orderings_Oord__class_Oless__eq(U_555,U_557,U_558)
| ~ c_Orderings_Oord__class_Oless__eq(U_555,c_Groups_Ozero__class_Ozero(U_555),U_556)
| ~ class_Groups_Oordered__comm__monoid__add(U_555) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
! [U_556,U_555,U_558,U_557] :
( c_Orderings_Oord__class_Oless__eq(U_555,U_557,c_Groups_Oplus__class_Oplus(U_555,U_556,U_558))
| ~ c_Orderings_Oord__class_Oless__eq(U_555,U_557,U_558)
| ~ c_Orderings_Oord__class_Oless__eq(U_555,c_Groups_Ozero__class_Ozero(U_555),U_556)
| ~ class_Groups_Oordered__comm__monoid__add(U_555) ),
inference(definitional_conversion,[status(esa)],[f_184_2]) ).
cnf(f_184_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_555,U_557,c_Groups_Oplus__class_Oplus(U_555,U_556,U_558))
| ~ c_Orderings_Oord__class_Oless__eq(U_555,U_557,U_558)
| ~ c_Orderings_Oord__class_Oless__eq(U_555,c_Groups_Ozero__class_Ozero(U_555),U_556)
| ~ class_Groups_Oordered__comm__monoid__add(U_555) ),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_1,plain,
! [V_a,V_b,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ 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_185_2,plain,
! [U_562,U_561,U_560,U_559] :
( c_Orderings_Oord__class_Oless__eq(U_559,U_561,c_Groups_Oplus__class_Oplus(U_559,U_562,U_560))
| ~ c_Orderings_Oord__class_Oless__eq(U_559,U_561,U_562)
| ~ c_Orderings_Oord__class_Oless__eq(U_559,c_Groups_Ozero__class_Ozero(U_559),U_560)
| ~ class_Groups_Oordered__comm__monoid__add(U_559) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_562,U_559,U_560,U_561] :
( c_Orderings_Oord__class_Oless__eq(U_559,U_561,c_Groups_Oplus__class_Oplus(U_559,U_562,U_560))
| ~ c_Orderings_Oord__class_Oless__eq(U_559,U_561,U_562)
| ~ c_Orderings_Oord__class_Oless__eq(U_559,c_Groups_Ozero__class_Ozero(U_559),U_560)
| ~ class_Groups_Oordered__comm__monoid__add(U_559) ),
inference(definitional_conversion,[status(esa)],[f_185_2]) ).
cnf(f_185_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_559,U_561,c_Groups_Oplus__class_Oplus(U_559,U_562,U_560))
| ~ c_Orderings_Oord__class_Oless__eq(U_559,U_561,U_562)
| ~ c_Orderings_Oord__class_Oless__eq(U_559,c_Groups_Ozero__class_Ozero(U_559),U_560)
| ~ class_Groups_Oordered__comm__monoid__add(U_559) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_186_2,plain,
! [U_565,U_564,U_563] :
( c_Orderings_Oord__class_Oless__eq(U_563,c_Groups_Oplus__class_Oplus(U_563,U_564,U_565),c_Groups_Ozero__class_Ozero(U_563))
| ~ c_Orderings_Oord__class_Oless__eq(U_563,U_565,c_Groups_Ozero__class_Ozero(U_563))
| ~ c_Orderings_Oord__class_Oless__eq(U_563,U_564,c_Groups_Ozero__class_Ozero(U_563))
| ~ class_Groups_Oordered__comm__monoid__add(U_563) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_563,U_565,U_564] :
( c_Orderings_Oord__class_Oless__eq(U_563,c_Groups_Oplus__class_Oplus(U_563,U_564,U_565),c_Groups_Ozero__class_Ozero(U_563))
| ~ c_Orderings_Oord__class_Oless__eq(U_563,U_565,c_Groups_Ozero__class_Ozero(U_563))
| ~ c_Orderings_Oord__class_Oless__eq(U_563,U_564,c_Groups_Ozero__class_Ozero(U_563))
| ~ class_Groups_Oordered__comm__monoid__add(U_563) ),
inference(definitional_conversion,[status(esa)],[f_186_2]) ).
cnf(f_186_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_563,c_Groups_Oplus__class_Oplus(U_563,U_564,U_565),c_Groups_Ozero__class_Ozero(U_563))
| ~ c_Orderings_Oord__class_Oless__eq(U_563,U_565,c_Groups_Ozero__class_Ozero(U_563))
| ~ c_Orderings_Oord__class_Oless__eq(U_563,U_564,c_Groups_Ozero__class_Ozero(U_563))
| ~ class_Groups_Oordered__comm__monoid__add(U_563) ),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).
fof(f_187_2,plain,
! [U_567,U_566] :
( ( ( c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),c_Groups_Oplus__class_Oplus(U_566,U_567,U_567))
| ~ c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),U_567) )
& ( c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),U_567)
| ~ c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),c_Groups_Oplus__class_Oplus(U_566,U_567,U_567)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_566) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
( ! [U_566,U_567] :
( c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),c_Groups_Oplus__class_Oplus(U_566,U_567,U_567))
| ~ c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),U_567)
| ~ sP58(U_566,U_567) )
& ! [U_566,U_567] :
( c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),U_567)
| ~ c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),c_Groups_Oplus__class_Oplus(U_566,U_567,U_567))
| ~ sP58(U_566,U_567) )
& ! [U_566,U_567] :
( sP58(U_566,U_567)
| ~ class_Groups_Olinordered__ab__group__add(U_566) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_187_2]) ).
cnf(f_187_4,plain,
( sP58(U_566,U_567)
| ~ class_Groups_Olinordered__ab__group__add(U_566) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_5,plain,
( c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),U_567)
| ~ c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),c_Groups_Oplus__class_Oplus(U_566,U_567,U_567))
| ~ sP58(U_566,U_567) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_6,plain,
( c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),c_Groups_Oplus__class_Oplus(U_566,U_567,U_567))
| ~ c_Orderings_Oord__class_Oless(U_566,c_Groups_Ozero__class_Ozero(U_566),U_567)
| ~ sP58(U_566,U_567) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).
fof(f_188_2,plain,
! [U_569,U_568] :
( ( ( c_Orderings_Oord__class_Oless(U_568,c_Groups_Oplus__class_Oplus(U_568,U_569,U_569),c_Groups_Ozero__class_Ozero(U_568))
| ~ c_Orderings_Oord__class_Oless(U_568,U_569,c_Groups_Ozero__class_Ozero(U_568)) )
& ( c_Orderings_Oord__class_Oless(U_568,U_569,c_Groups_Ozero__class_Ozero(U_568))
| ~ c_Orderings_Oord__class_Oless(U_568,c_Groups_Oplus__class_Oplus(U_568,U_569,U_569),c_Groups_Ozero__class_Ozero(U_568)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_568) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
( ! [U_569,U_568] :
( c_Orderings_Oord__class_Oless(U_568,c_Groups_Oplus__class_Oplus(U_568,U_569,U_569),c_Groups_Ozero__class_Ozero(U_568))
| ~ c_Orderings_Oord__class_Oless(U_568,U_569,c_Groups_Ozero__class_Ozero(U_568))
| ~ sP59(U_569,U_568) )
& ! [U_569,U_568] :
( c_Orderings_Oord__class_Oless(U_568,U_569,c_Groups_Ozero__class_Ozero(U_568))
| ~ c_Orderings_Oord__class_Oless(U_568,c_Groups_Oplus__class_Oplus(U_568,U_569,U_569),c_Groups_Ozero__class_Ozero(U_568))
| ~ sP59(U_569,U_568) )
& ! [U_569,U_568] :
( sP59(U_569,U_568)
| ~ class_Groups_Olinordered__ab__group__add(U_568) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_188_2]) ).
cnf(f_188_4,plain,
( sP59(U_569,U_568)
| ~ class_Groups_Olinordered__ab__group__add(U_568) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_5,plain,
( c_Orderings_Oord__class_Oless(U_568,U_569,c_Groups_Ozero__class_Ozero(U_568))
| ~ c_Orderings_Oord__class_Oless(U_568,c_Groups_Oplus__class_Oplus(U_568,U_569,U_569),c_Groups_Ozero__class_Ozero(U_568))
| ~ sP59(U_569,U_568) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_6,plain,
( c_Orderings_Oord__class_Oless(U_568,c_Groups_Oplus__class_Oplus(U_568,U_569,U_569),c_Groups_Ozero__class_Ozero(U_568))
| ~ c_Orderings_Oord__class_Oless(U_568,U_569,c_Groups_Ozero__class_Ozero(U_568))
| ~ sP59(U_569,U_568) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_189_2,plain,
! [U_572,U_571,U_570] :
( c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),c_Groups_Oplus__class_Oplus(U_570,U_571,U_572))
| ~ c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),U_572)
| ~ c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),U_571)
| ~ class_Groups_Oordered__comm__monoid__add(U_570) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_572,U_571,U_570] :
( c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),c_Groups_Oplus__class_Oplus(U_570,U_571,U_572))
| ~ c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),U_572)
| ~ c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),U_571)
| ~ class_Groups_Oordered__comm__monoid__add(U_570) ),
inference(definitional_conversion,[status(esa)],[f_189_2]) ).
cnf(f_189_4,plain,
( c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),c_Groups_Oplus__class_Oplus(U_570,U_571,U_572))
| ~ c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),U_572)
| ~ c_Orderings_Oord__class_Oless(U_570,c_Groups_Ozero__class_Ozero(U_570),U_571)
| ~ class_Groups_Oordered__comm__monoid__add(U_570) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ 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_190_2,plain,
! [U_575,U_574,U_573] :
( c_Orderings_Oord__class_Oless(U_573,c_Groups_Oplus__class_Oplus(U_573,U_574,U_575),c_Groups_Ozero__class_Ozero(U_573))
| ~ c_Orderings_Oord__class_Oless(U_573,U_575,c_Groups_Ozero__class_Ozero(U_573))
| ~ c_Orderings_Oord__class_Oless(U_573,U_574,c_Groups_Ozero__class_Ozero(U_573))
| ~ class_Groups_Oordered__comm__monoid__add(U_573) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_573,U_574,U_575] :
( c_Orderings_Oord__class_Oless(U_573,c_Groups_Oplus__class_Oplus(U_573,U_574,U_575),c_Groups_Ozero__class_Ozero(U_573))
| ~ c_Orderings_Oord__class_Oless(U_573,U_575,c_Groups_Ozero__class_Ozero(U_573))
| ~ c_Orderings_Oord__class_Oless(U_573,U_574,c_Groups_Ozero__class_Ozero(U_573))
| ~ class_Groups_Oordered__comm__monoid__add(U_573) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( c_Orderings_Oord__class_Oless(U_573,c_Groups_Oplus__class_Oplus(U_573,U_574,U_575),c_Groups_Ozero__class_Ozero(U_573))
| ~ c_Orderings_Oord__class_Oless(U_573,U_575,c_Groups_Ozero__class_Ozero(U_573))
| ~ c_Orderings_Oord__class_Oless(U_573,U_574,c_Groups_Ozero__class_Ozero(U_573))
| ~ class_Groups_Oordered__comm__monoid__add(U_573) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ 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_191_2,plain,
! [U_580,U_579,U_578,U_577,U_576] :
( c_Orderings_Oord__class_Oless(U_576,c_Groups_Oplus__class_Oplus(U_576,U_577,U_579),c_Groups_Oplus__class_Oplus(U_576,U_578,U_580))
| ~ c_Orderings_Oord__class_Oless__eq(U_576,U_579,U_580)
| ~ c_Orderings_Oord__class_Oless(U_576,U_577,U_578)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_576) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_576,U_577,U_578,U_579,U_580] :
( c_Orderings_Oord__class_Oless(U_576,c_Groups_Oplus__class_Oplus(U_576,U_577,U_579),c_Groups_Oplus__class_Oplus(U_576,U_578,U_580))
| ~ c_Orderings_Oord__class_Oless__eq(U_576,U_579,U_580)
| ~ c_Orderings_Oord__class_Oless(U_576,U_577,U_578)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_576) ),
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
( c_Orderings_Oord__class_Oless(U_576,c_Groups_Oplus__class_Oplus(U_576,U_577,U_579),c_Groups_Oplus__class_Oplus(U_576,U_578,U_580))
| ~ c_Orderings_Oord__class_Oless__eq(U_576,U_579,U_580)
| ~ c_Orderings_Oord__class_Oless(U_576,U_577,U_578)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_576) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ 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_192_2,plain,
! [U_585,U_584,U_583,U_582,U_581] :
( c_Orderings_Oord__class_Oless(U_581,c_Groups_Oplus__class_Oplus(U_581,U_582,U_584),c_Groups_Oplus__class_Oplus(U_581,U_583,U_585))
| ~ c_Orderings_Oord__class_Oless(U_581,U_584,U_585)
| ~ c_Orderings_Oord__class_Oless__eq(U_581,U_582,U_583)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_581) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
! [U_582,U_581,U_583,U_584,U_585] :
( c_Orderings_Oord__class_Oless(U_581,c_Groups_Oplus__class_Oplus(U_581,U_582,U_584),c_Groups_Oplus__class_Oplus(U_581,U_583,U_585))
| ~ c_Orderings_Oord__class_Oless(U_581,U_584,U_585)
| ~ c_Orderings_Oord__class_Oless__eq(U_581,U_582,U_583)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_581) ),
inference(definitional_conversion,[status(esa)],[f_192_2]) ).
cnf(f_192_4,plain,
( c_Orderings_Oord__class_Oless(U_581,c_Groups_Oplus__class_Oplus(U_581,U_582,U_584),c_Groups_Oplus__class_Oplus(U_581,U_583,U_585))
| ~ c_Orderings_Oord__class_Oless(U_581,U_584,U_585)
| ~ c_Orderings_Oord__class_Oless__eq(U_581,U_582,U_583)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_581) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_193_2,plain,
! [U_587,U_586] :
( c_Orderings_Oord__class_Oless__eq(U_586,c_Groups_Ozero__class_Ozero(U_586),c_Groups_Oabs__class_Oabs(U_586,U_587))
| ~ class_Groups_Oordered__ab__group__add__abs(U_586) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
! [U_586,U_587] :
( c_Orderings_Oord__class_Oless__eq(U_586,c_Groups_Ozero__class_Ozero(U_586),c_Groups_Oabs__class_Oabs(U_586,U_587))
| ~ class_Groups_Oordered__ab__group__add__abs(U_586) ),
inference(definitional_conversion,[status(esa)],[f_193_2]) ).
cnf(f_193_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_586,c_Groups_Ozero__class_Ozero(U_586),c_Groups_Oabs__class_Oabs(U_586,U_587))
| ~ class_Groups_Oordered__ab__group__add__abs(U_586) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).
fof(f_194_2,plain,
! [U_589,U_588] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_588,c_Groups_Oabs__class_Oabs(U_588,U_589),c_Groups_Ozero__class_Ozero(U_588))
| U_589 != c_Groups_Ozero__class_Ozero(U_588) )
& ( U_589 = c_Groups_Ozero__class_Ozero(U_588)
| ~ c_Orderings_Oord__class_Oless__eq(U_588,c_Groups_Oabs__class_Oabs(U_588,U_589),c_Groups_Ozero__class_Ozero(U_588)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_588) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ! [U_588,U_589] :
( c_Orderings_Oord__class_Oless__eq(U_588,c_Groups_Oabs__class_Oabs(U_588,U_589),c_Groups_Ozero__class_Ozero(U_588))
| U_589 != c_Groups_Ozero__class_Ozero(U_588)
| ~ sP60(U_588,U_589) )
& ! [U_588,U_589] :
( U_589 = c_Groups_Ozero__class_Ozero(U_588)
| ~ c_Orderings_Oord__class_Oless__eq(U_588,c_Groups_Oabs__class_Oabs(U_588,U_589),c_Groups_Ozero__class_Ozero(U_588))
| ~ sP60(U_588,U_589) )
& ! [U_588,U_589] :
( sP60(U_588,U_589)
| ~ class_Groups_Oordered__ab__group__add__abs(U_588) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_194_2]) ).
cnf(f_194_4,plain,
( sP60(U_588,U_589)
| ~ class_Groups_Oordered__ab__group__add__abs(U_588) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( U_589 = c_Groups_Ozero__class_Ozero(U_588)
| ~ c_Orderings_Oord__class_Oless__eq(U_588,c_Groups_Oabs__class_Oabs(U_588,U_589),c_Groups_Ozero__class_Ozero(U_588))
| ~ sP60(U_588,U_589) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_588,c_Groups_Oabs__class_Oabs(U_588,U_589),c_Groups_Ozero__class_Ozero(U_588))
| U_589 != c_Groups_Ozero__class_Ozero(U_588)
| ~ sP60(U_588,U_589) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| ~ 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_195_2,plain,
! [U_591,U_590] :
( c_Groups_Oabs__class_Oabs(U_590,U_591) = U_591
| ~ c_Orderings_Oord__class_Oless__eq(U_590,c_Groups_Ozero__class_Ozero(U_590),U_591)
| ~ class_Groups_Oordered__ab__group__add__abs(U_590) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_591,U_590] :
( c_Groups_Oabs__class_Oabs(U_590,U_591) = U_591
| ~ c_Orderings_Oord__class_Oless__eq(U_590,c_Groups_Ozero__class_Ozero(U_590),U_591)
| ~ class_Groups_Oordered__ab__group__add__abs(U_590) ),
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
( c_Groups_Oabs__class_Oabs(U_590,U_591) = U_591
| ~ c_Orderings_Oord__class_Oless__eq(U_590,c_Groups_Ozero__class_Ozero(U_590),U_591)
| ~ class_Groups_Oordered__ab__group__add__abs(U_590) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,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_196_2,plain,
! [U_593,U_592] :
( ~ c_Orderings_Oord__class_Oless(U_592,c_Groups_Oabs__class_Oabs(U_592,U_593),c_Groups_Ozero__class_Ozero(U_592))
| ~ class_Groups_Oordered__ab__group__add__abs(U_592) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
! [U_592,U_593] :
( ~ c_Orderings_Oord__class_Oless(U_592,c_Groups_Oabs__class_Oabs(U_592,U_593),c_Groups_Ozero__class_Ozero(U_592))
| ~ class_Groups_Oordered__ab__group__add__abs(U_592) ),
inference(definitional_conversion,[status(esa)],[f_196_2]) ).
cnf(f_196_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_592,c_Groups_Oabs__class_Oabs(U_592,U_593),c_Groups_Ozero__class_Ozero(U_592))
| ~ class_Groups_Oordered__ab__group__add__abs(U_592) ),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_1,plain,
! [V_m,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_197_2,plain,
! [U_595,U_594] :
( c_Groups_Oplus__class_Oplus(U_594,U_595,U_595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_594),c_Groups_Oplus__class_Oplus(U_594,c_Groups_Oone__class_Oone(U_594),c_Groups_Oone__class_Oone(U_594))),U_595)
| ~ class_Rings_Ocomm__semiring__1(U_594) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_594,U_595] :
( c_Groups_Oplus__class_Oplus(U_594,U_595,U_595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_594),c_Groups_Oplus__class_Oplus(U_594,c_Groups_Oone__class_Oone(U_594),c_Groups_Oone__class_Oone(U_594))),U_595)
| ~ class_Rings_Ocomm__semiring__1(U_594) ),
inference(definitional_conversion,[status(esa)],[f_197_2]) ).
cnf(f_197_4,plain,
( c_Groups_Oplus__class_Oplus(U_594,U_595,U_595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_594),c_Groups_Oplus__class_Oplus(U_594,c_Groups_Oone__class_Oone(U_594),c_Groups_Oone__class_Oone(U_594))),U_595)
| ~ class_Rings_Ocomm__semiring__1(U_594) ),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_1,plain,
! [V_a,V_m,T_a] :
( 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),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_198_2,plain,
! [U_598,U_597,U_596] :
( c_Groups_Oplus__class_Oplus(U_596,U_597,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_598),U_597)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),c_Groups_Oplus__class_Oplus(U_596,U_598,c_Groups_Oone__class_Oone(U_596))),U_597)
| ~ class_Rings_Ocomm__semiring__1(U_596) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_596,U_597,U_598] :
( c_Groups_Oplus__class_Oplus(U_596,U_597,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_598),U_597)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),c_Groups_Oplus__class_Oplus(U_596,U_598,c_Groups_Oone__class_Oone(U_596))),U_597)
| ~ class_Rings_Ocomm__semiring__1(U_596) ),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
( c_Groups_Oplus__class_Oplus(U_596,U_597,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_598),U_597)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),c_Groups_Oplus__class_Oplus(U_596,U_598,c_Groups_Oone__class_Oone(U_596))),U_597)
| ~ class_Rings_Ocomm__semiring__1(U_596) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_1,plain,
! [V_m,V_a,T_a] :
( 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),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_199_2,plain,
! [U_601,U_600,U_599] :
( c_Groups_Oplus__class_Oplus(U_599,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_599),U_600),U_601),U_601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_599),c_Groups_Oplus__class_Oplus(U_599,U_600,c_Groups_Oone__class_Oone(U_599))),U_601)
| ~ class_Rings_Ocomm__semiring__1(U_599) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_599,U_600,U_601] :
( c_Groups_Oplus__class_Oplus(U_599,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_599),U_600),U_601),U_601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_599),c_Groups_Oplus__class_Oplus(U_599,U_600,c_Groups_Oone__class_Oone(U_599))),U_601)
| ~ class_Rings_Ocomm__semiring__1(U_599) ),
inference(definitional_conversion,[status(esa)],[f_199_2]) ).
cnf(f_199_4,plain,
( c_Groups_Oplus__class_Oplus(U_599,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_599),U_600),U_601),U_601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_599),c_Groups_Oplus__class_Oplus(U_599,U_600,c_Groups_Oone__class_Oone(U_599))),U_601)
| ~ class_Rings_Ocomm__semiring__1(U_599) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_1,plain,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != 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_200_2,plain,
! [U_607,U_606,U_605,U_604,U_603,U_602] :
( c_Groups_Oplus__class_Oplus(U_602,U_604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_602),U_603),U_606)) != c_Groups_Oplus__class_Oplus(U_602,U_605,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_602),U_603),U_607))
| U_606 = U_607
| U_604 != U_605
| U_603 = c_Groups_Ozero__class_Ozero(U_602)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_602) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_602,U_603,U_604,U_605,U_606,U_607] :
( c_Groups_Oplus__class_Oplus(U_602,U_604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_602),U_603),U_606)) != c_Groups_Oplus__class_Oplus(U_602,U_605,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_602),U_603),U_607))
| U_606 = U_607
| U_604 != U_605
| U_603 = c_Groups_Ozero__class_Ozero(U_602)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_602) ),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
( c_Groups_Oplus__class_Oplus(U_602,U_604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_602),U_603),U_606)) != c_Groups_Oplus__class_Oplus(U_602,U_605,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_602),U_603),U_607))
| U_606 = U_607
| U_604 != U_605
| U_603 = c_Groups_Ozero__class_Ozero(U_602)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_602) ),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).
fof(f_201_2,plain,
! [U_609,U_608] :
( ( ( c_Orderings_Oord__class_Oless(U_608,c_Groups_Oplus__class_Oplus(U_608,U_609,U_609),c_Groups_Ozero__class_Ozero(U_608))
| ~ c_Orderings_Oord__class_Oless(U_608,U_609,c_Groups_Ozero__class_Ozero(U_608)) )
& ( c_Orderings_Oord__class_Oless(U_608,U_609,c_Groups_Ozero__class_Ozero(U_608))
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Oplus__class_Oplus(U_608,U_609,U_609),c_Groups_Ozero__class_Ozero(U_608)) ) )
| ~ class_Rings_Olinordered__idom(U_608) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
( ! [U_609,U_608] :
( c_Orderings_Oord__class_Oless(U_608,c_Groups_Oplus__class_Oplus(U_608,U_609,U_609),c_Groups_Ozero__class_Ozero(U_608))
| ~ c_Orderings_Oord__class_Oless(U_608,U_609,c_Groups_Ozero__class_Ozero(U_608))
| ~ sP61(U_609,U_608) )
& ! [U_609,U_608] :
( c_Orderings_Oord__class_Oless(U_608,U_609,c_Groups_Ozero__class_Ozero(U_608))
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Oplus__class_Oplus(U_608,U_609,U_609),c_Groups_Ozero__class_Ozero(U_608))
| ~ sP61(U_609,U_608) )
& ! [U_609,U_608] :
( sP61(U_609,U_608)
| ~ class_Rings_Olinordered__idom(U_608) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_201_2]) ).
cnf(f_201_4,plain,
( sP61(U_609,U_608)
| ~ class_Rings_Olinordered__idom(U_608) ),
inference(clausify,[status(thm)],[f_201_3]) ).
cnf(f_201_5,plain,
( c_Orderings_Oord__class_Oless(U_608,U_609,c_Groups_Ozero__class_Ozero(U_608))
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Oplus__class_Oplus(U_608,U_609,U_609),c_Groups_Ozero__class_Ozero(U_608))
| ~ sP61(U_609,U_608) ),
inference(clausify,[status(thm)],[f_201_3]) ).
cnf(f_201_6,plain,
( c_Orderings_Oord__class_Oless(U_608,c_Groups_Oplus__class_Oplus(U_608,U_609,U_609),c_Groups_Ozero__class_Ozero(U_608))
| ~ c_Orderings_Oord__class_Oless(U_608,U_609,c_Groups_Ozero__class_Ozero(U_608))
| ~ sP61(U_609,U_608) ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_1,plain,
? [B_m] :
! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(f_202_2,plain,
? [U_611] :
! [U_610] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_610)),U_611)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_610),v_r) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_610] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_610)),sK3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_610),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_611,sK3)],[f_202_2]) ).
fof(f_202_4,plain,
! [U_610] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_610)),sK3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_610),v_r) ),
inference(definitional_conversion,[status(esa)],[f_202_3]) ).
cnf(f_202_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_610)),sK3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_610),v_r) ),
inference(clausify,[status(thm)],[f_202_4]) ).
fof(f_203_1,plain,
! [V_x,T_a] :
( 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_203_2,plain,
! [U_613,U_612] :
( c_Orderings_Oord__class_Oless__eq(U_612,U_613,U_613)
| ~ class_Orderings_Opreorder(U_612) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_613,U_612] :
( c_Orderings_Oord__class_Oless__eq(U_612,U_613,U_613)
| ~ class_Orderings_Opreorder(U_612) ),
inference(definitional_conversion,[status(esa)],[f_203_2]) ).
cnf(f_203_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_612,U_613,U_613)
| ~ class_Orderings_Opreorder(U_612) ),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__1]) ).
fof(f_204_2,plain,
! [U_615,U_614] :
( hAPP(c_Polynomial_Opoly(U_614,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_614))),U_615) = c_Groups_Oone__class_Oone(U_614)
| ~ class_Rings_Ocomm__semiring__1(U_614) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_614,U_615] :
( hAPP(c_Polynomial_Opoly(U_614,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_614))),U_615) = c_Groups_Oone__class_Oone(U_614)
| ~ class_Rings_Ocomm__semiring__1(U_614) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( hAPP(c_Polynomial_Opoly(U_614,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_614))),U_615) = c_Groups_Oone__class_Oone(U_614)
| ~ class_Rings_Ocomm__semiring__1(U_614) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__add]) ).
fof(f_205_2,plain,
! [U_619,U_618,U_617,U_616] :
( hAPP(c_Polynomial_Opoly(U_616,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_616),U_617,U_618)),U_619) = c_Groups_Oplus__class_Oplus(U_616,hAPP(c_Polynomial_Opoly(U_616,U_617),U_619),hAPP(c_Polynomial_Opoly(U_616,U_618),U_619))
| ~ class_Rings_Ocomm__semiring__0(U_616) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_616,U_617,U_618,U_619] :
( hAPP(c_Polynomial_Opoly(U_616,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_616),U_617,U_618)),U_619) = c_Groups_Oplus__class_Oplus(U_616,hAPP(c_Polynomial_Opoly(U_616,U_617),U_619),hAPP(c_Polynomial_Opoly(U_616,U_618),U_619))
| ~ class_Rings_Ocomm__semiring__0(U_616) ),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
( hAPP(c_Polynomial_Opoly(U_616,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_616),U_617,U_618)),U_619) = c_Groups_Oplus__class_Oplus(U_616,hAPP(c_Polynomial_Opoly(U_616,U_617),U_619),hAPP(c_Polynomial_Opoly(U_616,U_618),U_619))
| ~ class_Rings_Ocomm__semiring__0(U_616) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_1,plain,
! [V_q,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J]) ).
fof(f_206_2,plain,
! [U_621,U_620] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_620),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_620)),U_621) = U_621
| ~ class_Groups_Ocomm__monoid__add(U_620) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_621,U_620] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_620),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_620)),U_621) = U_621
| ~ class_Groups_Ocomm__monoid__add(U_620) ),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_620),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_620)),U_621) = U_621
| ~ class_Groups_Ocomm__monoid__add(U_620) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_1,plain,
! [V_p,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J]) ).
fof(f_207_2,plain,
! [U_623,U_622] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_622),U_623,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_622))) = U_623
| ~ class_Groups_Ocomm__monoid__add(U_622) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_622,U_623] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_622),U_623,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_622))) = U_623
| ~ class_Groups_Ocomm__monoid__add(U_622) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_622),U_623,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_622))) = U_623
| ~ class_Groups_Ocomm__monoid__add(U_622) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_1,plain,
! [V_r,V_q,V_p,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left]) ).
fof(f_208_2,plain,
! [U_627,U_626,U_625,U_624] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_624),U_625,U_626)),U_627) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),U_625),U_627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),U_626),U_627))
| ~ class_Rings_Ocomm__semiring__0(U_624) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
! [U_624,U_625,U_626,U_627] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_624),U_625,U_626)),U_627) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),U_625),U_627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),U_626),U_627))
| ~ class_Rings_Ocomm__semiring__0(U_624) ),
inference(definitional_conversion,[status(esa)],[f_208_2]) ).
cnf(f_208_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_624),U_625,U_626)),U_627) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),U_625),U_627),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_624)),U_626),U_627))
| ~ class_Rings_Ocomm__semiring__0(U_624) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ? [B_x] : ~ c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) )
& ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_209_2,plain,
! [U_633,U_632,U_631,U_630] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633)
| ? [U_629] : ~ c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,U_629),hAPP(U_633,U_629)) )
& ( ! [U_628] : c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,U_628),hAPP(U_633,U_628))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633) ) )
| ~ class_Orderings_Oord(U_630) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
! [U_633,U_632,U_631,U_630] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633)
| ~ c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,sK4(U_633,U_632,U_631,U_630)),hAPP(U_633,sK4(U_633,U_632,U_631,U_630))) )
& ( ! [U_628] : c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,U_628),hAPP(U_633,U_628))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633) ) )
| ~ class_Orderings_Oord(U_630) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_629,sK4(U_633,U_632,U_631,U_630))],[f_209_2]) ).
fof(f_209_4,plain,
( ! [U_628,U_630,U_631,U_632,U_633] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633)
| ~ c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,sK4(U_633,U_632,U_631,U_630)),hAPP(U_633,sK4(U_633,U_632,U_631,U_630)))
| ~ sP62(U_628,U_630,U_631,U_632,U_633) )
& ! [U_628,U_630,U_631,U_632,U_633] :
( c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,U_628),hAPP(U_633,U_628))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633)
| ~ sP62(U_628,U_630,U_631,U_632,U_633) )
& ! [U_628,U_630,U_631,U_632,U_633] :
( sP62(U_628,U_630,U_631,U_632,U_633)
| ~ class_Orderings_Oord(U_630) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_209_3]) ).
cnf(f_209_5,plain,
( sP62(U_628,U_630,U_631,U_632,U_633)
| ~ class_Orderings_Oord(U_630) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,U_628),hAPP(U_633,U_628))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633)
| ~ sP62(U_628,U_630,U_631,U_632,U_633) ),
inference(clausify,[status(thm)],[f_209_4]) ).
cnf(f_209_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_631,U_630),U_632,U_633)
| ~ c_Orderings_Oord__class_Oless__eq(U_630,hAPP(U_632,sK4(U_633,U_632,U_631,U_630)),hAPP(U_633,sK4(U_633,U_632,U_631,U_630)))
| ~ sP62(U_628,U_630,U_631,U_632,U_633) ),
inference(clausify,[status(thm)],[f_209_4]) ).
fof(f_210_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| 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_210_2,plain,
! [U_636,U_635,U_634] :
( c_Orderings_Oord__class_Oless__eq(U_634,U_636,U_635)
| c_Orderings_Oord__class_Oless__eq(U_634,U_635,U_636)
| ~ class_Orderings_Olinorder(U_634) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_635,U_634,U_636] :
( c_Orderings_Oord__class_Oless__eq(U_634,U_636,U_635)
| c_Orderings_Oord__class_Oless__eq(U_634,U_635,U_636)
| ~ class_Orderings_Olinorder(U_634) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,U_636,U_635)
| c_Orderings_Oord__class_Oless__eq(U_634,U_635,U_636)
| ~ class_Orderings_Olinorder(U_634) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_211_2,plain,
! [U_639,U_638,U_637] :
( ( ( U_638 = U_639
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_639,U_638)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_638,U_639) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_637,U_639,U_638)
& c_Orderings_Oord__class_Oless__eq(U_637,U_638,U_639) )
| U_638 != U_639 ) )
| ~ class_Orderings_Oorder(U_637) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
( ! [U_638,U_637,U_639] :
( c_Orderings_Oord__class_Oless__eq(U_637,U_639,U_638)
| ~ sP63(U_638,U_637,U_639) )
& ! [U_638,U_637,U_639] :
( c_Orderings_Oord__class_Oless__eq(U_637,U_638,U_639)
| ~ sP63(U_638,U_637,U_639) )
& ! [U_638,U_637,U_639] :
( U_638 = U_639
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_639,U_638)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_638,U_639)
| ~ sP64(U_638,U_637,U_639) )
& ! [U_638,U_637,U_639] :
( sP63(U_638,U_637,U_639)
| U_638 != U_639
| ~ sP64(U_638,U_637,U_639) )
& ! [U_638,U_637,U_639] :
( sP64(U_638,U_637,U_639)
| ~ class_Orderings_Oorder(U_637) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63,sP64])],[f_211_2]) ).
cnf(f_211_4,plain,
( sP64(U_638,U_637,U_639)
| ~ class_Orderings_Oorder(U_637) ),
inference(clausify,[status(thm)],[f_211_3]) ).
cnf(f_211_5,plain,
( sP63(U_638,U_637,U_639)
| U_638 != U_639
| ~ sP64(U_638,U_637,U_639) ),
inference(clausify,[status(thm)],[f_211_3]) ).
cnf(f_211_6,plain,
( U_638 = U_639
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_639,U_638)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_638,U_639)
| ~ sP64(U_638,U_637,U_639) ),
inference(clausify,[status(thm)],[f_211_3]) ).
cnf(f_211_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_637,U_638,U_639)
| ~ sP63(U_638,U_637,U_639) ),
inference(clausify,[status(thm)],[f_211_3]) ).
cnf(f_211_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_637,U_639,U_638)
| ~ sP63(U_638,U_637,U_639) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_1,plain,
! [V_y,V_x,T_a] :
( 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_212_2,plain,
! [U_642,U_641,U_640] :
( c_Orderings_Oord__class_Oless__eq(U_640,U_641,U_642)
| U_641 != U_642
| ~ class_Orderings_Opreorder(U_640) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_640,U_641,U_642] :
( c_Orderings_Oord__class_Oless__eq(U_640,U_641,U_642)
| U_641 != U_642
| ~ class_Orderings_Opreorder(U_640) ),
inference(definitional_conversion,[status(esa)],[f_212_2]) ).
cnf(f_212_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_640,U_641,U_642)
| U_641 != U_642
| ~ class_Orderings_Opreorder(U_640) ),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_213_2,plain,
! [U_647,U_646,U_645,U_644,U_643] :
( c_Orderings_Oord__class_Oless__eq(U_643,hAPP(U_645,U_647),hAPP(U_646,U_647))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_644,U_643),U_645,U_646)
| ~ class_Orderings_Oord(U_643) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_643,U_645,U_647,U_644,U_646] :
( c_Orderings_Oord__class_Oless__eq(U_643,hAPP(U_645,U_647),hAPP(U_646,U_647))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_644,U_643),U_645,U_646)
| ~ class_Orderings_Oord(U_643) ),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_643,hAPP(U_645,U_647),hAPP(U_646,U_647))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_644,U_643),U_645,U_646)
| ~ class_Orderings_Oord(U_643) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_214_2,plain,
! [U_650,U_649,U_648] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_649)
| U_650 != U_649 )
& ( U_650 = U_649
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_649) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_649,U_650)
| ~ class_Orderings_Oorder(U_648) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
( ! [U_650,U_649,U_648] :
( c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_649)
| U_650 != U_649
| ~ sP65(U_650,U_649,U_648) )
& ! [U_650,U_649,U_648] :
( U_650 = U_649
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_649)
| ~ sP65(U_650,U_649,U_648) )
& ! [U_650,U_649,U_648] :
( sP65(U_650,U_649,U_648)
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_649,U_650)
| ~ class_Orderings_Oorder(U_648) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_214_2]) ).
cnf(f_214_4,plain,
( sP65(U_650,U_649,U_648)
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_649,U_650)
| ~ class_Orderings_Oorder(U_648) ),
inference(clausify,[status(thm)],[f_214_3]) ).
cnf(f_214_5,plain,
( U_650 = U_649
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_649)
| ~ sP65(U_650,U_649,U_648) ),
inference(clausify,[status(thm)],[f_214_3]) ).
cnf(f_214_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_649)
| U_650 != U_649
| ~ sP65(U_650,U_649,U_648) ),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ 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_215_2,plain,
! [U_654,U_653,U_652,U_651] :
( c_Orderings_Oord__class_Oless__eq(U_651,U_652,U_654)
| ~ c_Orderings_Oord__class_Oless__eq(U_651,U_653,U_654)
| U_652 != U_653
| ~ class_Orderings_Oord(U_651) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_654,U_652,U_653,U_651] :
( c_Orderings_Oord__class_Oless__eq(U_651,U_652,U_654)
| ~ c_Orderings_Oord__class_Oless__eq(U_651,U_653,U_654)
| U_652 != U_653
| ~ class_Orderings_Oord(U_651) ),
inference(definitional_conversion,[status(esa)],[f_215_2]) ).
cnf(f_215_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_651,U_652,U_654)
| ~ c_Orderings_Oord__class_Oless__eq(U_651,U_653,U_654)
| U_652 != U_653
| ~ class_Orderings_Oord(U_651) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ 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_216_2,plain,
! [U_658,U_657,U_656,U_655] :
( c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_656)
| ~ c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_657)
| U_656 != U_657
| ~ class_Orderings_Oorder(U_655) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_658,U_657,U_655,U_656] :
( c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_656)
| ~ c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_657)
| U_656 != U_657
| ~ class_Orderings_Oorder(U_655) ),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_656)
| ~ c_Orderings_Oord__class_Oless__eq(U_655,U_658,U_657)
| U_656 != U_657
| ~ class_Orderings_Oorder(U_655) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| V_b != V_c
| ~ 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_217_2,plain,
! [U_662,U_661,U_660,U_659] :
( c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_662)
| U_661 != U_662
| ~ c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_661)
| ~ class_Orderings_Oord(U_659) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_660,U_662,U_659,U_661] :
( c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_662)
| U_661 != U_662
| ~ c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_661)
| ~ class_Orderings_Oord(U_659) ),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_662)
| U_661 != U_662
| ~ c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_661)
| ~ class_Orderings_Oord(U_659) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| V_b != V_c
| ~ 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_218_2,plain,
! [U_666,U_665,U_664,U_663] :
( c_Orderings_Oord__class_Oless__eq(U_663,U_666,U_665)
| U_664 != U_666
| ~ c_Orderings_Oord__class_Oless__eq(U_663,U_664,U_665)
| ~ class_Orderings_Oorder(U_663) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_666,U_665,U_663,U_664] :
( c_Orderings_Oord__class_Oless__eq(U_663,U_666,U_665)
| U_664 != U_666
| ~ c_Orderings_Oord__class_Oless__eq(U_663,U_664,U_665)
| ~ class_Orderings_Oorder(U_663) ),
inference(definitional_conversion,[status(esa)],[f_218_2]) ).
cnf(f_218_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_663,U_666,U_665)
| U_664 != U_666
| ~ c_Orderings_Oord__class_Oless__eq(U_663,U_664,U_665)
| ~ class_Orderings_Oorder(U_663) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ 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_219_2,plain,
! [U_669,U_668,U_667] :
( U_668 = U_669
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_669,U_668)
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_668,U_669)
| ~ class_Orderings_Oorder(U_667) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_669,U_667,U_668] :
( U_668 = U_669
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_669,U_668)
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_668,U_669)
| ~ class_Orderings_Oorder(U_667) ),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
( U_668 = U_669
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_669,U_668)
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_668,U_669)
| ~ class_Orderings_Oorder(U_667) ),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ 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_220_2,plain,
! [U_673,U_672,U_671,U_670] :
( c_Orderings_Oord__class_Oless__eq(U_670,U_671,U_673)
| ~ c_Orderings_Oord__class_Oless__eq(U_670,U_672,U_673)
| ~ c_Orderings_Oord__class_Oless__eq(U_670,U_671,U_672)
| ~ class_Orderings_Opreorder(U_670) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_671,U_673,U_670,U_672] :
( c_Orderings_Oord__class_Oless__eq(U_670,U_671,U_673)
| ~ c_Orderings_Oord__class_Oless__eq(U_670,U_672,U_673)
| ~ c_Orderings_Oord__class_Oless__eq(U_670,U_671,U_672)
| ~ class_Orderings_Opreorder(U_670) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_670,U_671,U_673)
| ~ c_Orderings_Oord__class_Oless__eq(U_670,U_672,U_673)
| ~ c_Orderings_Oord__class_Oless__eq(U_670,U_671,U_672)
| ~ class_Orderings_Opreorder(U_670) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [V_x,V_y,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ 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_221_2,plain,
! [U_676,U_675,U_674] :
( U_676 = U_675
| ~ c_Orderings_Oord__class_Oless__eq(U_674,U_676,U_675)
| ~ c_Orderings_Oord__class_Oless__eq(U_674,U_675,U_676)
| ~ class_Orderings_Oorder(U_674) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_676,U_674,U_675] :
( U_676 = U_675
| ~ c_Orderings_Oord__class_Oless__eq(U_674,U_676,U_675)
| ~ c_Orderings_Oord__class_Oless__eq(U_674,U_675,U_676)
| ~ class_Orderings_Oorder(U_674) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( U_676 = U_675
| ~ c_Orderings_Oord__class_Oless__eq(U_674,U_676,U_675)
| ~ c_Orderings_Oord__class_Oless__eq(U_674,U_675,U_676)
| ~ class_Orderings_Oorder(U_674) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ 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_222_2,plain,
! [U_680,U_679,U_678,U_677] :
( c_Orderings_Oord__class_Oless__eq(U_677,U_680,U_679)
| ~ c_Orderings_Oord__class_Oless__eq(U_677,U_680,U_678)
| ~ c_Orderings_Oord__class_Oless__eq(U_677,U_678,U_679)
| ~ class_Orderings_Oorder(U_677) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_677,U_678,U_680,U_679] :
( c_Orderings_Oord__class_Oless__eq(U_677,U_680,U_679)
| ~ c_Orderings_Oord__class_Oless__eq(U_677,U_680,U_678)
| ~ c_Orderings_Oord__class_Oless__eq(U_677,U_678,U_679)
| ~ class_Orderings_Oorder(U_677) ),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_677,U_680,U_679)
| ~ c_Orderings_Oord__class_Oless__eq(U_677,U_680,U_678)
| ~ c_Orderings_Oord__class_Oless__eq(U_677,U_678,U_679)
| ~ class_Orderings_Oorder(U_677) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_223_2,plain,
! [U_685,U_684,U_683,U_682,U_681] :
( c_Orderings_Oord__class_Oless__eq(U_681,hAPP(U_683,U_685),hAPP(U_684,U_685))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_682,U_681),U_683,U_684)
| ~ class_Orderings_Oord(U_681) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_681,U_682,U_683,U_684,U_685] :
( c_Orderings_Oord__class_Oless__eq(U_681,hAPP(U_683,U_685),hAPP(U_684,U_685))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_682,U_681),U_683,U_684)
| ~ class_Orderings_Oord(U_681) ),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_681,hAPP(U_683,U_685),hAPP(U_684,U_685))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_682,U_681),U_683,U_684)
| ~ class_Orderings_Oord(U_681) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| 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_224_2,plain,
! [U_688,U_687,U_686] :
( c_Orderings_Oord__class_Oless__eq(U_686,U_688,U_687)
| c_Orderings_Oord__class_Oless__eq(U_686,U_687,U_688)
| ~ class_Orderings_Olinorder(U_686) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_687,U_686,U_688] :
( c_Orderings_Oord__class_Oless__eq(U_686,U_688,U_687)
| c_Orderings_Oord__class_Oless__eq(U_686,U_687,U_688)
| ~ class_Orderings_Olinorder(U_686) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_686,U_688,U_687)
| c_Orderings_Oord__class_Oless__eq(U_686,U_687,U_688)
| ~ class_Orderings_Olinorder(U_686) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| 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_225_2,plain,
! [U_691,U_690,U_689] :
( c_Orderings_Oord__class_Oless(U_689,U_691,U_690)
| U_690 = U_691
| c_Orderings_Oord__class_Oless(U_689,U_690,U_691)
| ~ class_Orderings_Olinorder(U_689) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_691,U_690,U_689] :
( c_Orderings_Oord__class_Oless(U_689,U_691,U_690)
| U_690 = U_691
| c_Orderings_Oord__class_Oless(U_689,U_690,U_691)
| ~ class_Orderings_Olinorder(U_689) ),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
( c_Orderings_Oord__class_Oless(U_689,U_691,U_690)
| U_690 = U_691
| c_Orderings_Oord__class_Oless(U_689,U_690,U_691)
| ~ class_Orderings_Olinorder(U_689) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ 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_226_2,plain,
! [U_694,U_693,U_692] :
( ~ c_Orderings_Oord__class_Oless(U_692,U_694,U_693)
| ~ c_Orderings_Oord__class_Oless(U_692,U_693,U_694)
| ~ class_Orderings_Opreorder(U_692) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
! [U_694,U_693,U_692] :
( ~ c_Orderings_Oord__class_Oless(U_692,U_694,U_693)
| ~ c_Orderings_Oord__class_Oless(U_692,U_693,U_694)
| ~ class_Orderings_Opreorder(U_692) ),
inference(definitional_conversion,[status(esa)],[f_226_2]) ).
cnf(f_226_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_692,U_694,U_693)
| ~ c_Orderings_Oord__class_Oless(U_692,U_693,U_694)
| ~ class_Orderings_Opreorder(U_692) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ 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_227_2,plain,
! [U_698,U_697,U_696,U_695] :
( c_Orderings_Oord__class_Oless(U_695,U_698,U_697)
| ~ c_Orderings_Oord__class_Oless(U_695,U_698,U_696)
| ~ c_Orderings_Oord__class_Oless(U_695,U_696,U_697)
| ~ class_Orderings_Oorder(U_695) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
! [U_695,U_696,U_697,U_698] :
( c_Orderings_Oord__class_Oless(U_695,U_698,U_697)
| ~ c_Orderings_Oord__class_Oless(U_695,U_698,U_696)
| ~ c_Orderings_Oord__class_Oless(U_695,U_696,U_697)
| ~ class_Orderings_Oorder(U_695) ),
inference(definitional_conversion,[status(esa)],[f_227_2]) ).
cnf(f_227_4,plain,
( c_Orderings_Oord__class_Oless(U_695,U_698,U_697)
| ~ c_Orderings_Oord__class_Oless(U_695,U_698,U_696)
| ~ c_Orderings_Oord__class_Oless(U_695,U_696,U_697)
| ~ class_Orderings_Oorder(U_695) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ 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_228_2,plain,
! [U_702,U_701,U_700,U_699] :
( c_Orderings_Oord__class_Oless(U_699,U_700,U_702)
| ~ c_Orderings_Oord__class_Oless(U_699,U_701,U_702)
| ~ c_Orderings_Oord__class_Oless(U_699,U_700,U_701)
| ~ class_Orderings_Opreorder(U_699) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_700,U_699,U_701,U_702] :
( c_Orderings_Oord__class_Oless(U_699,U_700,U_702)
| ~ c_Orderings_Oord__class_Oless(U_699,U_701,U_702)
| ~ c_Orderings_Oord__class_Oless(U_699,U_700,U_701)
| ~ class_Orderings_Opreorder(U_699) ),
inference(definitional_conversion,[status(esa)],[f_228_2]) ).
cnf(f_228_4,plain,
( c_Orderings_Oord__class_Oless(U_699,U_700,U_702)
| ~ c_Orderings_Oord__class_Oless(U_699,U_701,U_702)
| ~ c_Orderings_Oord__class_Oless(U_699,U_700,U_701)
| ~ class_Orderings_Opreorder(U_699) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| V_b != V_c
| ~ 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_229_2,plain,
! [U_706,U_705,U_704,U_703] :
( c_Orderings_Oord__class_Oless(U_703,U_706,U_705)
| U_704 != U_706
| ~ c_Orderings_Oord__class_Oless(U_703,U_704,U_705)
| ~ class_Orderings_Oorder(U_703) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_703,U_704,U_705,U_706] :
( c_Orderings_Oord__class_Oless(U_703,U_706,U_705)
| U_704 != U_706
| ~ c_Orderings_Oord__class_Oless(U_703,U_704,U_705)
| ~ class_Orderings_Oorder(U_703) ),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
( c_Orderings_Oord__class_Oless(U_703,U_706,U_705)
| U_704 != U_706
| ~ c_Orderings_Oord__class_Oless(U_703,U_704,U_705)
| ~ class_Orderings_Oorder(U_703) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| V_b != V_c
| ~ 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_230_2,plain,
! [U_710,U_709,U_708,U_707] :
( c_Orderings_Oord__class_Oless(U_707,U_708,U_710)
| U_709 != U_710
| ~ c_Orderings_Oord__class_Oless(U_707,U_708,U_709)
| ~ class_Orderings_Oord(U_707) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_707,U_710,U_709,U_708] :
( c_Orderings_Oord__class_Oless(U_707,U_708,U_710)
| U_709 != U_710
| ~ c_Orderings_Oord__class_Oless(U_707,U_708,U_709)
| ~ class_Orderings_Oord(U_707) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( c_Orderings_Oord__class_Oless(U_707,U_708,U_710)
| U_709 != U_710
| ~ c_Orderings_Oord__class_Oless(U_707,U_708,U_709)
| ~ class_Orderings_Oord(U_707) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ 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_231_2,plain,
! [U_714,U_713,U_712,U_711] :
( c_Orderings_Oord__class_Oless(U_711,U_714,U_712)
| ~ c_Orderings_Oord__class_Oless(U_711,U_714,U_713)
| U_712 != U_713
| ~ class_Orderings_Oorder(U_711) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_712,U_711,U_713,U_714] :
( c_Orderings_Oord__class_Oless(U_711,U_714,U_712)
| ~ c_Orderings_Oord__class_Oless(U_711,U_714,U_713)
| U_712 != U_713
| ~ class_Orderings_Oorder(U_711) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( c_Orderings_Oord__class_Oless(U_711,U_714,U_712)
| ~ c_Orderings_Oord__class_Oless(U_711,U_714,U_713)
| U_712 != U_713
| ~ class_Orderings_Oorder(U_711) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| ~ 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_232_2,plain,
! [U_718,U_717,U_716,U_715] :
( c_Orderings_Oord__class_Oless(U_715,U_716,U_718)
| ~ c_Orderings_Oord__class_Oless(U_715,U_717,U_718)
| U_716 != U_717
| ~ class_Orderings_Oord(U_715) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_717,U_715,U_716,U_718] :
( c_Orderings_Oord__class_Oless(U_715,U_716,U_718)
| ~ c_Orderings_Oord__class_Oless(U_715,U_717,U_718)
| U_716 != U_717
| ~ class_Orderings_Oord(U_715) ),
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
( c_Orderings_Oord__class_Oless(U_715,U_716,U_718)
| ~ c_Orderings_Oord__class_Oless(U_715,U_717,U_718)
| U_716 != U_717
| ~ class_Orderings_Oord(U_715) ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [V_a,V_b,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ 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_233_2,plain,
! [U_721,U_720,U_719] :
( ~ c_Orderings_Oord__class_Oless(U_719,U_721,U_720)
| ~ c_Orderings_Oord__class_Oless(U_719,U_720,U_721)
| ~ class_Orderings_Oorder(U_719) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_720,U_721,U_719] :
( ~ c_Orderings_Oord__class_Oless(U_719,U_721,U_720)
| ~ c_Orderings_Oord__class_Oless(U_719,U_720,U_721)
| ~ class_Orderings_Oorder(U_719) ),
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_719,U_721,U_720)
| ~ c_Orderings_Oord__class_Oless(U_719,U_720,U_721)
| ~ class_Orderings_Oorder(U_719) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_1,plain,
! [V_b,V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ 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_234_2,plain,
! [U_724,U_723,U_722] :
( ~ c_Orderings_Oord__class_Oless(U_722,U_724,U_723)
| ~ c_Orderings_Oord__class_Oless(U_722,U_723,U_724)
| ~ class_Orderings_Opreorder(U_722) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_723,U_722,U_724] :
( ~ c_Orderings_Oord__class_Oless(U_722,U_724,U_723)
| ~ c_Orderings_Oord__class_Oless(U_722,U_723,U_724)
| ~ class_Orderings_Opreorder(U_722) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_722,U_724,U_723)
| ~ c_Orderings_Oord__class_Oless(U_722,U_723,U_724)
| ~ class_Orderings_Opreorder(U_722) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_1,plain,
! [V_y,V_x,T_a] :
( V_y != V_x
| ~ 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_235_2,plain,
! [U_727,U_726,U_725] :
( U_727 != U_726
| ~ c_Orderings_Oord__class_Oless(U_725,U_726,U_727)
| ~ class_Orderings_Oorder(U_725) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_725,U_727,U_726] :
( U_727 != U_726
| ~ c_Orderings_Oord__class_Oless(U_725,U_726,U_727)
| ~ class_Orderings_Oorder(U_725) ),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
( U_727 != U_726
| ~ c_Orderings_Oord__class_Oless(U_725,U_726,U_727)
| ~ class_Orderings_Oorder(U_725) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ 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_236_2,plain,
! [U_730,U_729,U_728] :
( U_729 != U_730
| ~ c_Orderings_Oord__class_Oless(U_728,U_729,U_730)
| ~ class_Orderings_Oorder(U_728) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_729,U_730,U_728] :
( U_729 != U_730
| ~ c_Orderings_Oord__class_Oless(U_728,U_729,U_730)
| ~ class_Orderings_Oorder(U_728) ),
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
( U_729 != U_730
| ~ c_Orderings_Oord__class_Oless(U_728,U_729,U_730)
| ~ class_Orderings_Oorder(U_728) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ 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_237_2,plain,
! [U_733,U_732,U_731] :
( ~ c_Orderings_Oord__class_Oless(U_731,U_733,U_732)
| ~ c_Orderings_Oord__class_Oless(U_731,U_732,U_733)
| ~ class_Orderings_Opreorder(U_731) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_733,U_731,U_732] :
( ~ c_Orderings_Oord__class_Oless(U_731,U_733,U_732)
| ~ c_Orderings_Oord__class_Oless(U_731,U_732,U_733)
| ~ class_Orderings_Opreorder(U_731) ),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_731,U_733,U_732)
| ~ c_Orderings_Oord__class_Oless(U_731,U_732,U_733)
| ~ class_Orderings_Opreorder(U_731) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ 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_238_2,plain,
! [U_736,U_735,U_734] :
( ~ c_Orderings_Oord__class_Oless(U_734,U_736,U_735)
| ~ c_Orderings_Oord__class_Oless(U_734,U_735,U_736)
| ~ class_Orderings_Opreorder(U_734) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_736,U_734,U_735] :
( ~ c_Orderings_Oord__class_Oless(U_734,U_736,U_735)
| ~ c_Orderings_Oord__class_Oless(U_734,U_735,U_736)
| ~ class_Orderings_Opreorder(U_734) ),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_734,U_736,U_735)
| ~ c_Orderings_Oord__class_Oless(U_734,U_735,U_736)
| ~ class_Orderings_Opreorder(U_734) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ 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_239_2,plain,
! [U_739,U_738,U_737] :
( U_738 != U_739
| ~ c_Orderings_Oord__class_Oless(U_737,U_738,U_739)
| ~ class_Orderings_Oorder(U_737) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_737,U_739,U_738] :
( U_738 != U_739
| ~ c_Orderings_Oord__class_Oless(U_737,U_738,U_739)
| ~ class_Orderings_Oorder(U_737) ),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
( U_738 != U_739
| ~ c_Orderings_Oord__class_Oless(U_737,U_738,U_739)
| ~ class_Orderings_Oorder(U_737) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| 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_240_2,plain,
! [U_742,U_741,U_740] :
( c_Orderings_Oord__class_Oless(U_740,U_742,U_741)
| c_Orderings_Oord__class_Oless(U_740,U_741,U_742)
| U_741 = U_742
| ~ class_Orderings_Olinorder(U_740) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_740,U_741,U_742] :
( c_Orderings_Oord__class_Oless(U_740,U_742,U_741)
| c_Orderings_Oord__class_Oless(U_740,U_741,U_742)
| U_741 = U_742
| ~ class_Orderings_Olinorder(U_740) ),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
( c_Orderings_Oord__class_Oless(U_740,U_742,U_741)
| c_Orderings_Oord__class_Oless(U_740,U_741,U_742)
| U_741 = U_742
| ~ class_Orderings_Olinorder(U_740) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_241_2,plain,
! [U_745,U_744,U_743] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_743,U_745,U_744)
| U_745 != U_744 )
& ( U_745 = U_744
| c_Orderings_Oord__class_Oless(U_743,U_745,U_744) ) )
| c_Orderings_Oord__class_Oless(U_743,U_744,U_745)
| ~ class_Orderings_Olinorder(U_743) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
( ! [U_744,U_743,U_745] :
( ~ c_Orderings_Oord__class_Oless(U_743,U_745,U_744)
| U_745 != U_744
| ~ sP66(U_744,U_743,U_745) )
& ! [U_744,U_743,U_745] :
( U_745 = U_744
| c_Orderings_Oord__class_Oless(U_743,U_745,U_744)
| ~ sP66(U_744,U_743,U_745) )
& ! [U_744,U_743,U_745] :
( sP66(U_744,U_743,U_745)
| c_Orderings_Oord__class_Oless(U_743,U_744,U_745)
| ~ class_Orderings_Olinorder(U_743) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_241_2]) ).
cnf(f_241_4,plain,
( sP66(U_744,U_743,U_745)
| c_Orderings_Oord__class_Oless(U_743,U_744,U_745)
| ~ class_Orderings_Olinorder(U_743) ),
inference(clausify,[status(thm)],[f_241_3]) ).
cnf(f_241_5,plain,
( U_745 = U_744
| c_Orderings_Oord__class_Oless(U_743,U_745,U_744)
| ~ sP66(U_744,U_743,U_745) ),
inference(clausify,[status(thm)],[f_241_3]) ).
cnf(f_241_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_743,U_745,U_744)
| U_745 != U_744
| ~ sP66(U_744,U_743,U_745) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| 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_242_2,plain,
! [U_748,U_747,U_746] :
( c_Orderings_Oord__class_Oless(U_746,U_748,U_747)
| U_747 = U_748
| c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Orderings_Olinorder(U_746) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_747,U_748,U_746] :
( c_Orderings_Oord__class_Oless(U_746,U_748,U_747)
| U_747 = U_748
| c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Orderings_Olinorder(U_746) ),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
( c_Orderings_Oord__class_Oless(U_746,U_748,U_747)
| U_747 = U_748
| c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Orderings_Olinorder(U_746) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_243_2,plain,
! [U_751,U_750,U_749] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
| ( U_750 != U_751
& ~ c_Orderings_Oord__class_Oless(U_749,U_751,U_750) ) )
& ( U_750 = U_751
| c_Orderings_Oord__class_Oless(U_749,U_751,U_750)
| c_Orderings_Oord__class_Oless(U_749,U_750,U_751) ) )
| ~ class_Orderings_Olinorder(U_749) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
( ! [U_751,U_749,U_750] :
( U_750 != U_751
| ~ sP67(U_751,U_749,U_750) )
& ! [U_751,U_749,U_750] :
( ~ c_Orderings_Oord__class_Oless(U_749,U_751,U_750)
| ~ sP67(U_751,U_749,U_750) )
& ! [U_751,U_749,U_750] :
( ~ c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
| sP67(U_751,U_749,U_750)
| ~ sP68(U_751,U_749,U_750) )
& ! [U_751,U_749,U_750] :
( U_750 = U_751
| c_Orderings_Oord__class_Oless(U_749,U_751,U_750)
| c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
| ~ sP68(U_751,U_749,U_750) )
& ! [U_751,U_749,U_750] :
( sP68(U_751,U_749,U_750)
| ~ class_Orderings_Olinorder(U_749) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67,sP68])],[f_243_2]) ).
cnf(f_243_4,plain,
( sP68(U_751,U_749,U_750)
| ~ class_Orderings_Olinorder(U_749) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( U_750 = U_751
| c_Orderings_Oord__class_Oless(U_749,U_751,U_750)
| c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
| ~ sP68(U_751,U_749,U_750) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_749,U_750,U_751)
| sP67(U_751,U_749,U_750)
| ~ sP68(U_751,U_749,U_750) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_749,U_751,U_750)
| ~ sP67(U_751,U_749,U_750) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_8,plain,
( U_750 != U_751
| ~ sP67(U_751,U_749,U_750) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 != V_y_2
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_244_2,plain,
! [U_754,U_753,U_752] :
( ( ( U_753 != U_754
| ( ~ c_Orderings_Oord__class_Oless(U_752,U_754,U_753)
& ~ c_Orderings_Oord__class_Oless(U_752,U_753,U_754) ) )
& ( c_Orderings_Oord__class_Oless(U_752,U_754,U_753)
| c_Orderings_Oord__class_Oless(U_752,U_753,U_754)
| U_753 = U_754 ) )
| ~ class_Orderings_Olinorder(U_752) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( ! [U_752,U_753,U_754] :
( ~ c_Orderings_Oord__class_Oless(U_752,U_754,U_753)
| ~ sP69(U_752,U_753,U_754) )
& ! [U_752,U_753,U_754] :
( ~ c_Orderings_Oord__class_Oless(U_752,U_753,U_754)
| ~ sP69(U_752,U_753,U_754) )
& ! [U_752,U_753,U_754] :
( U_753 != U_754
| sP69(U_752,U_753,U_754)
| ~ sP70(U_752,U_753,U_754) )
& ! [U_752,U_753,U_754] :
( c_Orderings_Oord__class_Oless(U_752,U_754,U_753)
| c_Orderings_Oord__class_Oless(U_752,U_753,U_754)
| U_753 = U_754
| ~ sP70(U_752,U_753,U_754) )
& ! [U_752,U_753,U_754] :
( sP70(U_752,U_753,U_754)
| ~ class_Orderings_Olinorder(U_752) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69,sP70])],[f_244_2]) ).
cnf(f_244_4,plain,
( sP70(U_752,U_753,U_754)
| ~ class_Orderings_Olinorder(U_752) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( c_Orderings_Oord__class_Oless(U_752,U_754,U_753)
| c_Orderings_Oord__class_Oless(U_752,U_753,U_754)
| U_753 = U_754
| ~ sP70(U_752,U_753,U_754) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_6,plain,
( U_753 != U_754
| sP69(U_752,U_753,U_754)
| ~ sP70(U_752,U_753,U_754) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_752,U_753,U_754)
| ~ sP69(U_752,U_753,U_754) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_752,U_754,U_753)
| ~ sP69(U_752,U_753,U_754) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [V_x,T_a] :
( ~ 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_245_2,plain,
! [U_756,U_755] :
( ~ c_Orderings_Oord__class_Oless(U_755,U_756,U_756)
| ~ class_Orderings_Opreorder(U_755) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_755,U_756] :
( ~ c_Orderings_Oord__class_Oless(U_755,U_756,U_756)
| ~ class_Orderings_Opreorder(U_755) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_755,U_756,U_756)
| ~ class_Orderings_Opreorder(U_755) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_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_246_2,plain,
! [U_761,U_760,U_759,U_758,U_757] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_760),U_761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_760)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_759),U_761))
| ~ class_Rings_Ocomm__semiring__1(U_757) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_758,U_759,U_757,U_760,U_761] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_760),U_761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_760)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_759),U_761))
| ~ class_Rings_Ocomm__semiring__1(U_757) ),
inference(definitional_conversion,[status(esa)],[f_246_2]) ).
cnf(f_246_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_760),U_761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_760)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_759),U_761))
| ~ class_Rings_Ocomm__semiring__1(U_757) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_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_247_2,plain,
! [U_766,U_765,U_764,U_763,U_762] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_763),U_764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_765),U_766)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_763),U_764)),U_766))
| ~ class_Rings_Ocomm__semiring__1(U_762) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_762,U_763,U_764,U_765,U_766] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_763),U_764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_765),U_766)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_763),U_764)),U_766))
| ~ class_Rings_Ocomm__semiring__1(U_762) ),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_763),U_764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_765),U_766)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_762),U_763),U_764)),U_766))
| ~ class_Rings_Ocomm__semiring__1(U_762) ),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_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_248_2,plain,
! [U_771,U_770,U_769,U_768,U_767] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_768),U_769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_770),U_771)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_770),U_771)))
| ~ class_Rings_Ocomm__semiring__1(U_767) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_767,U_768,U_769,U_770,U_771] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_768),U_769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_770),U_771)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_770),U_771)))
| ~ class_Rings_Ocomm__semiring__1(U_767) ),
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_768),U_769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_770),U_771)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_767),U_770),U_771)))
| ~ class_Rings_Ocomm__semiring__1(U_767) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_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_249_2,plain,
! [U_775,U_774,U_773,U_772] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),U_773),U_774)),U_775) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),U_773),U_775)),U_774)
| ~ class_Rings_Ocomm__semiring__1(U_772) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_772,U_773,U_774,U_775] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),U_773),U_774)),U_775) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),U_773),U_775)),U_774)
| ~ class_Rings_Ocomm__semiring__1(U_772) ),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),U_773),U_774)),U_775) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_772),U_773),U_775)),U_774)
| ~ class_Rings_Ocomm__semiring__1(U_772) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_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_250_2,plain,
! [U_779,U_778,U_777,U_776] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_777),U_778)),U_779) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_778),U_779))
| ~ class_Rings_Ocomm__semiring__1(U_776) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_776,U_777,U_778,U_779] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_777),U_778)),U_779) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_778),U_779))
| ~ class_Rings_Ocomm__semiring__1(U_776) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_777),U_778)),U_779) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_776),U_778),U_779))
| ~ class_Rings_Ocomm__semiring__1(U_776) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_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_251_2,plain,
! [U_783,U_782,U_781,U_780] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_782),U_783)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),U_782)),U_783)
| ~ class_Rings_Ocomm__semiring__1(U_780) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_780,U_781,U_782,U_783] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_782),U_783)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),U_782)),U_783)
| ~ class_Rings_Ocomm__semiring__1(U_780) ),
inference(definitional_conversion,[status(esa)],[f_251_2]) ).
cnf(f_251_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_782),U_783)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),U_782)),U_783)
| ~ class_Rings_Ocomm__semiring__1(U_780) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_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_252_2,plain,
! [U_787,U_786,U_785,U_784] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_786),U_787)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_787))
| ~ class_Rings_Ocomm__semiring__1(U_784) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_784,U_785,U_786,U_787] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_786),U_787)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_787))
| ~ class_Rings_Ocomm__semiring__1(U_784) ),
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_786),U_787)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_787))
| ~ class_Rings_Ocomm__semiring__1(U_784) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_790,U_789,U_788] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_789),U_790) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_790),U_789)
| ~ class_Rings_Ocomm__semiring__1(U_788) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
! [U_788,U_789,U_790] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_789),U_790) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_790),U_789)
| ~ class_Rings_Ocomm__semiring__1(U_788) ),
inference(definitional_conversion,[status(esa)],[f_253_2]) ).
cnf(f_253_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_789),U_790) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_790),U_789)
| ~ class_Rings_Ocomm__semiring__1(U_788) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),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_254_2,plain,
! [U_795,U_794,U_793,U_792,U_791] :
( c_Groups_Oplus__class_Oplus(U_791,c_Groups_Oplus__class_Oplus(U_791,U_792,U_793),c_Groups_Oplus__class_Oplus(U_791,U_794,U_795)) = c_Groups_Oplus__class_Oplus(U_791,c_Groups_Oplus__class_Oplus(U_791,U_792,U_794),c_Groups_Oplus__class_Oplus(U_791,U_793,U_795))
| ~ class_Rings_Ocomm__semiring__1(U_791) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_792,U_791,U_793,U_794,U_795] :
( c_Groups_Oplus__class_Oplus(U_791,c_Groups_Oplus__class_Oplus(U_791,U_792,U_793),c_Groups_Oplus__class_Oplus(U_791,U_794,U_795)) = c_Groups_Oplus__class_Oplus(U_791,c_Groups_Oplus__class_Oplus(U_791,U_792,U_794),c_Groups_Oplus__class_Oplus(U_791,U_793,U_795))
| ~ class_Rings_Ocomm__semiring__1(U_791) ),
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
( c_Groups_Oplus__class_Oplus(U_791,c_Groups_Oplus__class_Oplus(U_791,U_792,U_793),c_Groups_Oplus__class_Oplus(U_791,U_794,U_795)) = c_Groups_Oplus__class_Oplus(U_791,c_Groups_Oplus__class_Oplus(U_791,U_792,U_794),c_Groups_Oplus__class_Oplus(U_791,U_793,U_795))
| ~ class_Rings_Ocomm__semiring__1(U_791) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,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_255_2,plain,
! [U_799,U_798,U_797,U_796] :
( c_Groups_Oplus__class_Oplus(U_796,c_Groups_Oplus__class_Oplus(U_796,U_797,U_798),U_799) = c_Groups_Oplus__class_Oplus(U_796,c_Groups_Oplus__class_Oplus(U_796,U_797,U_799),U_798)
| ~ class_Rings_Ocomm__semiring__1(U_796) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_797,U_798,U_796,U_799] :
( c_Groups_Oplus__class_Oplus(U_796,c_Groups_Oplus__class_Oplus(U_796,U_797,U_798),U_799) = c_Groups_Oplus__class_Oplus(U_796,c_Groups_Oplus__class_Oplus(U_796,U_797,U_799),U_798)
| ~ class_Rings_Ocomm__semiring__1(U_796) ),
inference(definitional_conversion,[status(esa)],[f_255_2]) ).
cnf(f_255_4,plain,
( c_Groups_Oplus__class_Oplus(U_796,c_Groups_Oplus__class_Oplus(U_796,U_797,U_798),U_799) = c_Groups_Oplus__class_Oplus(U_796,c_Groups_Oplus__class_Oplus(U_796,U_797,U_799),U_798)
| ~ class_Rings_Ocomm__semiring__1(U_796) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,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_256_2,plain,
! [U_803,U_802,U_801,U_800] :
( c_Groups_Oplus__class_Oplus(U_800,c_Groups_Oplus__class_Oplus(U_800,U_801,U_802),U_803) = c_Groups_Oplus__class_Oplus(U_800,U_801,c_Groups_Oplus__class_Oplus(U_800,U_802,U_803))
| ~ class_Rings_Ocomm__semiring__1(U_800) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_801,U_800,U_802,U_803] :
( c_Groups_Oplus__class_Oplus(U_800,c_Groups_Oplus__class_Oplus(U_800,U_801,U_802),U_803) = c_Groups_Oplus__class_Oplus(U_800,U_801,c_Groups_Oplus__class_Oplus(U_800,U_802,U_803))
| ~ class_Rings_Ocomm__semiring__1(U_800) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( c_Groups_Oplus__class_Oplus(U_800,c_Groups_Oplus__class_Oplus(U_800,U_801,U_802),U_803) = c_Groups_Oplus__class_Oplus(U_800,U_801,c_Groups_Oplus__class_Oplus(U_800,U_802,U_803))
| ~ class_Rings_Ocomm__semiring__1(U_800) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_1,plain,
! [V_d,V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,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_257_2,plain,
! [U_807,U_806,U_805,U_804] :
( c_Groups_Oplus__class_Oplus(U_804,U_805,c_Groups_Oplus__class_Oplus(U_804,U_806,U_807)) = c_Groups_Oplus__class_Oplus(U_804,c_Groups_Oplus__class_Oplus(U_804,U_805,U_806),U_807)
| ~ class_Rings_Ocomm__semiring__1(U_804) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_805,U_804,U_806,U_807] :
( c_Groups_Oplus__class_Oplus(U_804,U_805,c_Groups_Oplus__class_Oplus(U_804,U_806,U_807)) = c_Groups_Oplus__class_Oplus(U_804,c_Groups_Oplus__class_Oplus(U_804,U_805,U_806),U_807)
| ~ class_Rings_Ocomm__semiring__1(U_804) ),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
( c_Groups_Oplus__class_Oplus(U_804,U_805,c_Groups_Oplus__class_Oplus(U_804,U_806,U_807)) = c_Groups_Oplus__class_Oplus(U_804,c_Groups_Oplus__class_Oplus(U_804,U_805,U_806),U_807)
| ~ class_Rings_Ocomm__semiring__1(U_804) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [V_d,V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,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_258_2,plain,
! [U_811,U_810,U_809,U_808] :
( c_Groups_Oplus__class_Oplus(U_808,U_809,c_Groups_Oplus__class_Oplus(U_808,U_810,U_811)) = c_Groups_Oplus__class_Oplus(U_808,U_810,c_Groups_Oplus__class_Oplus(U_808,U_809,U_811))
| ~ class_Rings_Ocomm__semiring__1(U_808) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_810,U_809,U_808,U_811] :
( c_Groups_Oplus__class_Oplus(U_808,U_809,c_Groups_Oplus__class_Oplus(U_808,U_810,U_811)) = c_Groups_Oplus__class_Oplus(U_808,U_810,c_Groups_Oplus__class_Oplus(U_808,U_809,U_811))
| ~ class_Rings_Ocomm__semiring__1(U_808) ),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
( c_Groups_Oplus__class_Oplus(U_808,U_809,c_Groups_Oplus__class_Oplus(U_808,U_810,U_811)) = c_Groups_Oplus__class_Oplus(U_808,U_810,c_Groups_Oplus__class_Oplus(U_808,U_809,U_811))
| ~ class_Rings_Ocomm__semiring__1(U_808) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = 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_259_2,plain,
! [U_814,U_813,U_812] :
( c_Groups_Oplus__class_Oplus(U_812,U_813,U_814) = c_Groups_Oplus__class_Oplus(U_812,U_814,U_813)
| ~ class_Rings_Ocomm__semiring__1(U_812) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_813,U_814,U_812] :
( c_Groups_Oplus__class_Oplus(U_812,U_813,U_814) = c_Groups_Oplus__class_Oplus(U_812,U_814,U_813)
| ~ class_Rings_Ocomm__semiring__1(U_812) ),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
( c_Groups_Oplus__class_Oplus(U_812,U_813,U_814) = c_Groups_Oplus__class_Oplus(U_812,U_814,U_813)
| ~ class_Rings_Ocomm__semiring__1(U_812) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_q_2,V_pa_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
| V_pa_2 != V_q_2 )
& ( V_pa_2 = V_q_2
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,V_q_2) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__eq__iff]) ).
fof(f_260_2,plain,
! [U_817,U_816,U_815] :
( ( ( c_Polynomial_Opoly(U_815,U_816) = c_Polynomial_Opoly(U_815,U_817)
| U_816 != U_817 )
& ( U_816 = U_817
| c_Polynomial_Opoly(U_815,U_816) != c_Polynomial_Opoly(U_815,U_817) ) )
| ~ class_Rings_Oidom(U_815)
| ~ class_Int_Oring__char__0(U_815) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_816,U_817,U_815] :
( c_Polynomial_Opoly(U_815,U_816) = c_Polynomial_Opoly(U_815,U_817)
| U_816 != U_817
| ~ sP71(U_816,U_817,U_815) )
& ! [U_816,U_817,U_815] :
( U_816 = U_817
| c_Polynomial_Opoly(U_815,U_816) != c_Polynomial_Opoly(U_815,U_817)
| ~ sP71(U_816,U_817,U_815) )
& ! [U_816,U_817,U_815] :
( sP71(U_816,U_817,U_815)
| ~ class_Rings_Oidom(U_815)
| ~ class_Int_Oring__char__0(U_815) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_260_2]) ).
cnf(f_260_4,plain,
( sP71(U_816,U_817,U_815)
| ~ class_Rings_Oidom(U_815)
| ~ class_Int_Oring__char__0(U_815) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_5,plain,
( U_816 = U_817
| c_Polynomial_Opoly(U_815,U_816) != c_Polynomial_Opoly(U_815,U_817)
| ~ sP71(U_816,U_817,U_815) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_6,plain,
( c_Polynomial_Opoly(U_815,U_816) = c_Polynomial_Opoly(U_815,U_817)
| U_816 != U_817
| ~ sP71(U_816,U_817,U_815) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [V_pa_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__zero]) ).
fof(f_261_2,plain,
! [U_819,U_818] :
( ( ( c_Polynomial_Opoly(U_818,U_819) = c_Polynomial_Opoly(U_818,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818)))
| U_819 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818)) )
& ( U_819 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818))
| c_Polynomial_Opoly(U_818,U_819) != c_Polynomial_Opoly(U_818,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818))) ) )
| ~ class_Rings_Oidom(U_818)
| ~ class_Int_Oring__char__0(U_818) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( ! [U_819,U_818] :
( c_Polynomial_Opoly(U_818,U_819) = c_Polynomial_Opoly(U_818,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818)))
| U_819 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818))
| ~ sP72(U_819,U_818) )
& ! [U_819,U_818] :
( U_819 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818))
| c_Polynomial_Opoly(U_818,U_819) != c_Polynomial_Opoly(U_818,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818)))
| ~ sP72(U_819,U_818) )
& ! [U_819,U_818] :
( sP72(U_819,U_818)
| ~ class_Rings_Oidom(U_818)
| ~ class_Int_Oring__char__0(U_818) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_261_2]) ).
cnf(f_261_4,plain,
( sP72(U_819,U_818)
| ~ class_Rings_Oidom(U_818)
| ~ class_Int_Oring__char__0(U_818) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_5,plain,
( U_819 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818))
| c_Polynomial_Opoly(U_818,U_819) != c_Polynomial_Opoly(U_818,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818)))
| ~ sP72(U_819,U_818) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_6,plain,
( c_Polynomial_Opoly(U_818,U_819) = c_Polynomial_Opoly(U_818,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818)))
| U_819 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_818))
| ~ sP72(U_819,U_818) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ 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_262_2,plain,
! [U_823,U_822,U_821,U_820] :
( c_Orderings_Oord__class_Oless(U_820,U_823,U_822)
| ~ c_Orderings_Oord__class_Oless(U_820,U_823,U_821)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_821,U_822)
| ~ class_Orderings_Oorder(U_820) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_821,U_822,U_823,U_820] :
( c_Orderings_Oord__class_Oless(U_820,U_823,U_822)
| ~ c_Orderings_Oord__class_Oless(U_820,U_823,U_821)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_821,U_822)
| ~ class_Orderings_Oorder(U_820) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( c_Orderings_Oord__class_Oless(U_820,U_823,U_822)
| ~ c_Orderings_Oord__class_Oless(U_820,U_823,U_821)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_821,U_822)
| ~ class_Orderings_Oorder(U_820) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ 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_263_2,plain,
! [U_827,U_826,U_825,U_824] :
( c_Orderings_Oord__class_Oless(U_824,U_825,U_827)
| ~ c_Orderings_Oord__class_Oless(U_824,U_826,U_827)
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_825,U_826)
| ~ class_Orderings_Opreorder(U_824) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_824,U_825,U_827,U_826] :
( c_Orderings_Oord__class_Oless(U_824,U_825,U_827)
| ~ c_Orderings_Oord__class_Oless(U_824,U_826,U_827)
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_825,U_826)
| ~ class_Orderings_Opreorder(U_824) ),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
( c_Orderings_Oord__class_Oless(U_824,U_825,U_827)
| ~ c_Orderings_Oord__class_Oless(U_824,U_826,U_827)
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_825,U_826)
| ~ class_Orderings_Opreorder(U_824) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ 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_264_2,plain,
! [U_831,U_830,U_829,U_828] :
( c_Orderings_Oord__class_Oless(U_828,U_831,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_828,U_831,U_829)
| ~ c_Orderings_Oord__class_Oless(U_828,U_829,U_830)
| ~ class_Orderings_Oorder(U_828) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_828,U_829,U_830,U_831] :
( c_Orderings_Oord__class_Oless(U_828,U_831,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_828,U_831,U_829)
| ~ c_Orderings_Oord__class_Oless(U_828,U_829,U_830)
| ~ class_Orderings_Oorder(U_828) ),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
( c_Orderings_Oord__class_Oless(U_828,U_831,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_828,U_831,U_829)
| ~ c_Orderings_Oord__class_Oless(U_828,U_829,U_830)
| ~ class_Orderings_Oorder(U_828) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ 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_265_2,plain,
! [U_835,U_834,U_833,U_832] :
( c_Orderings_Oord__class_Oless(U_832,U_833,U_835)
| ~ c_Orderings_Oord__class_Oless__eq(U_832,U_834,U_835)
| ~ c_Orderings_Oord__class_Oless(U_832,U_833,U_834)
| ~ class_Orderings_Opreorder(U_832) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_832,U_835,U_834,U_833] :
( c_Orderings_Oord__class_Oless(U_832,U_833,U_835)
| ~ c_Orderings_Oord__class_Oless__eq(U_832,U_834,U_835)
| ~ c_Orderings_Oord__class_Oless(U_832,U_833,U_834)
| ~ class_Orderings_Opreorder(U_832) ),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_4,plain,
( c_Orderings_Oord__class_Oless(U_832,U_833,U_835)
| ~ c_Orderings_Oord__class_Oless__eq(U_832,U_834,U_835)
| ~ c_Orderings_Oord__class_Oless(U_832,U_833,U_834)
| ~ class_Orderings_Opreorder(U_832) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_1,plain,
! [V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| V_a = V_b
| ~ 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_266_2,plain,
! [U_838,U_837,U_836] :
( c_Orderings_Oord__class_Oless(U_836,U_837,U_838)
| U_838 = U_837
| ~ c_Orderings_Oord__class_Oless__eq(U_836,U_837,U_838)
| ~ class_Orderings_Oorder(U_836) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_838,U_836,U_837] :
( c_Orderings_Oord__class_Oless(U_836,U_837,U_838)
| U_838 = U_837
| ~ c_Orderings_Oord__class_Oless__eq(U_836,U_837,U_838)
| ~ class_Orderings_Oorder(U_836) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( c_Orderings_Oord__class_Oless(U_836,U_837,U_838)
| U_838 = U_837
| ~ c_Orderings_Oord__class_Oless__eq(U_836,U_837,U_838)
| ~ class_Orderings_Oorder(U_836) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| V_a = V_b
| ~ 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_267_2,plain,
! [U_841,U_840,U_839] :
( c_Orderings_Oord__class_Oless(U_839,U_840,U_841)
| U_840 = U_841
| ~ c_Orderings_Oord__class_Oless__eq(U_839,U_840,U_841)
| ~ class_Orderings_Oorder(U_839) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_839,U_841,U_840] :
( c_Orderings_Oord__class_Oless(U_839,U_840,U_841)
| U_840 = U_841
| ~ c_Orderings_Oord__class_Oless__eq(U_839,U_840,U_841)
| ~ class_Orderings_Oorder(U_839) ),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
( c_Orderings_Oord__class_Oless(U_839,U_840,U_841)
| U_840 = U_841
| ~ c_Orderings_Oord__class_Oless__eq(U_839,U_840,U_841)
| ~ class_Orderings_Oorder(U_839) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ 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_268_2,plain,
! [U_844,U_843,U_842] :
( U_843 = U_844
| c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ c_Orderings_Oord__class_Oless__eq(U_842,U_843,U_844)
| ~ class_Orderings_Oorder(U_842) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_844,U_842,U_843] :
( U_843 = U_844
| c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ c_Orderings_Oord__class_Oless__eq(U_842,U_843,U_844)
| ~ class_Orderings_Oorder(U_842) ),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
( U_843 = U_844
| c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ c_Orderings_Oord__class_Oless__eq(U_842,U_843,U_844)
| ~ class_Orderings_Oorder(U_842) ),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_269_2,plain,
! [U_847,U_846,U_845] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_845,U_846,U_847)
| U_846 != U_847 )
& ( U_846 = U_847
| c_Orderings_Oord__class_Oless(U_845,U_846,U_847) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_845,U_846,U_847)
| ~ class_Orderings_Olinorder(U_845) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_845,U_846,U_847] :
( ~ c_Orderings_Oord__class_Oless(U_845,U_846,U_847)
| U_846 != U_847
| ~ sP73(U_845,U_846,U_847) )
& ! [U_845,U_846,U_847] :
( U_846 = U_847
| c_Orderings_Oord__class_Oless(U_845,U_846,U_847)
| ~ sP73(U_845,U_846,U_847) )
& ! [U_845,U_846,U_847] :
( sP73(U_845,U_846,U_847)
| ~ c_Orderings_Oord__class_Oless__eq(U_845,U_846,U_847)
| ~ class_Orderings_Olinorder(U_845) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_269_2]) ).
cnf(f_269_4,plain,
( sP73(U_845,U_846,U_847)
| ~ c_Orderings_Oord__class_Oless__eq(U_845,U_846,U_847)
| ~ class_Orderings_Olinorder(U_845) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( U_846 = U_847
| c_Orderings_Oord__class_Oless(U_845,U_846,U_847)
| ~ sP73(U_845,U_846,U_847) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_845,U_846,U_847)
| U_846 != U_847
| ~ sP73(U_845,U_846,U_847) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ 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_270_2,plain,
! [U_850,U_849,U_848] :
( c_Orderings_Oord__class_Oless__eq(U_848,U_849,U_850)
| ~ c_Orderings_Oord__class_Oless(U_848,U_849,U_850)
| ~ class_Orderings_Opreorder(U_848) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_850,U_849,U_848] :
( c_Orderings_Oord__class_Oless__eq(U_848,U_849,U_850)
| ~ c_Orderings_Oord__class_Oless(U_848,U_849,U_850)
| ~ class_Orderings_Opreorder(U_848) ),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_848,U_849,U_850)
| ~ c_Orderings_Oord__class_Oless(U_848,U_849,U_850)
| ~ class_Orderings_Opreorder(U_848) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [V_x,V_y,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ 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_271_2,plain,
! [U_853,U_852,U_851] :
( ~ c_Orderings_Oord__class_Oless(U_851,U_853,U_852)
| ~ c_Orderings_Oord__class_Oless__eq(U_851,U_852,U_853)
| ~ class_Orderings_Olinorder(U_851) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_851,U_852,U_853] :
( ~ c_Orderings_Oord__class_Oless(U_851,U_853,U_852)
| ~ c_Orderings_Oord__class_Oless__eq(U_851,U_852,U_853)
| ~ class_Orderings_Olinorder(U_851) ),
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_851,U_853,U_852)
| ~ c_Orderings_Oord__class_Oless__eq(U_851,U_852,U_853)
| ~ class_Orderings_Olinorder(U_851) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ 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_272_2,plain,
! [U_856,U_855,U_854] :
( c_Orderings_Oord__class_Oless(U_854,U_856,U_855)
| ~ c_Orderings_Oord__class_Oless__eq(U_854,U_856,U_855)
| U_855 = U_856
| ~ class_Orderings_Oorder(U_854) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_854,U_855,U_856] :
( c_Orderings_Oord__class_Oless(U_854,U_856,U_855)
| ~ c_Orderings_Oord__class_Oless__eq(U_854,U_856,U_855)
| U_855 = U_856
| ~ class_Orderings_Oorder(U_854) ),
inference(definitional_conversion,[status(esa)],[f_272_2]) ).
cnf(f_272_4,plain,
( c_Orderings_Oord__class_Oless(U_854,U_856,U_855)
| ~ c_Orderings_Oord__class_Oless__eq(U_854,U_856,U_855)
| U_855 = U_856
| ~ class_Orderings_Oorder(U_854) ),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ 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_273_2,plain,
! [U_859,U_858,U_857] :
( c_Orderings_Oord__class_Oless(U_857,U_858,U_859)
| ~ c_Orderings_Oord__class_Oless__eq(U_857,U_858,U_859)
| U_858 = U_859
| ~ class_Orderings_Oorder(U_857) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
! [U_858,U_857,U_859] :
( c_Orderings_Oord__class_Oless(U_857,U_858,U_859)
| ~ c_Orderings_Oord__class_Oless__eq(U_857,U_858,U_859)
| U_858 = U_859
| ~ class_Orderings_Oorder(U_857) ),
inference(definitional_conversion,[status(esa)],[f_273_2]) ).
cnf(f_273_4,plain,
( c_Orderings_Oord__class_Oless(U_857,U_858,U_859)
| ~ c_Orderings_Oord__class_Oless__eq(U_857,U_858,U_859)
| U_858 = U_859
| ~ class_Orderings_Oorder(U_857) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_274_2,plain,
! [U_862,U_861,U_860] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_860,U_861,U_862)
| U_861 != U_862 )
& ( U_861 = U_862
| ~ c_Orderings_Oord__class_Oless__eq(U_860,U_861,U_862) ) )
| c_Orderings_Oord__class_Oless(U_860,U_861,U_862)
| ~ class_Orderings_Olinorder(U_860) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
( ! [U_860,U_861,U_862] :
( c_Orderings_Oord__class_Oless__eq(U_860,U_861,U_862)
| U_861 != U_862
| ~ sP74(U_860,U_861,U_862) )
& ! [U_860,U_861,U_862] :
( U_861 = U_862
| ~ c_Orderings_Oord__class_Oless__eq(U_860,U_861,U_862)
| ~ sP74(U_860,U_861,U_862) )
& ! [U_860,U_861,U_862] :
( sP74(U_860,U_861,U_862)
| c_Orderings_Oord__class_Oless(U_860,U_861,U_862)
| ~ class_Orderings_Olinorder(U_860) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_274_2]) ).
cnf(f_274_4,plain,
( sP74(U_860,U_861,U_862)
| c_Orderings_Oord__class_Oless(U_860,U_861,U_862)
| ~ class_Orderings_Olinorder(U_860) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_5,plain,
( U_861 = U_862
| ~ c_Orderings_Oord__class_Oless__eq(U_860,U_861,U_862)
| ~ sP74(U_860,U_861,U_862) ),
inference(clausify,[status(thm)],[f_274_3]) ).
cnf(f_274_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_860,U_861,U_862)
| U_861 != U_862
| ~ sP74(U_860,U_861,U_862) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| 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_275_2,plain,
! [U_865,U_864,U_863] :
( c_Orderings_Oord__class_Oless(U_863,U_865,U_864)
| c_Orderings_Oord__class_Oless__eq(U_863,U_864,U_865)
| ~ class_Orderings_Olinorder(U_863) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
! [U_864,U_865,U_863] :
( c_Orderings_Oord__class_Oless(U_863,U_865,U_864)
| c_Orderings_Oord__class_Oless__eq(U_863,U_864,U_865)
| ~ class_Orderings_Olinorder(U_863) ),
inference(definitional_conversion,[status(esa)],[f_275_2]) ).
cnf(f_275_4,plain,
( c_Orderings_Oord__class_Oless(U_863,U_865,U_864)
| c_Orderings_Oord__class_Oless__eq(U_863,U_864,U_865)
| ~ class_Orderings_Olinorder(U_863) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| 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_276_2,plain,
! [U_868,U_867,U_866] :
( c_Orderings_Oord__class_Oless__eq(U_866,U_868,U_867)
| c_Orderings_Oord__class_Oless(U_866,U_867,U_868)
| ~ class_Orderings_Olinorder(U_866) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_868,U_866,U_867] :
( c_Orderings_Oord__class_Oless__eq(U_866,U_868,U_867)
| c_Orderings_Oord__class_Oless(U_866,U_867,U_868)
| ~ class_Orderings_Olinorder(U_866) ),
inference(definitional_conversion,[status(esa)],[f_276_2]) ).
cnf(f_276_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_866,U_868,U_867)
| c_Orderings_Oord__class_Oless(U_866,U_867,U_868)
| ~ class_Orderings_Olinorder(U_866) ),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_277_2,plain,
! [U_871,U_870,U_869] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_869,U_870,U_871)
| ( U_870 != U_871
& ~ c_Orderings_Oord__class_Oless(U_869,U_870,U_871) ) )
& ( U_870 = U_871
| c_Orderings_Oord__class_Oless(U_869,U_870,U_871)
| ~ c_Orderings_Oord__class_Oless__eq(U_869,U_870,U_871) ) )
| ~ class_Orderings_Oorder(U_869) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
( ! [U_869,U_870,U_871] :
( U_870 != U_871
| ~ sP75(U_869,U_870,U_871) )
& ! [U_869,U_870,U_871] :
( ~ c_Orderings_Oord__class_Oless(U_869,U_870,U_871)
| ~ sP75(U_869,U_870,U_871) )
& ! [U_869,U_870,U_871] :
( c_Orderings_Oord__class_Oless__eq(U_869,U_870,U_871)
| sP75(U_869,U_870,U_871)
| ~ sP76(U_869,U_870,U_871) )
& ! [U_869,U_870,U_871] :
( U_870 = U_871
| c_Orderings_Oord__class_Oless(U_869,U_870,U_871)
| ~ c_Orderings_Oord__class_Oless__eq(U_869,U_870,U_871)
| ~ sP76(U_869,U_870,U_871) )
& ! [U_869,U_870,U_871] :
( sP76(U_869,U_870,U_871)
| ~ class_Orderings_Oorder(U_869) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75,sP76])],[f_277_2]) ).
cnf(f_277_4,plain,
( sP76(U_869,U_870,U_871)
| ~ class_Orderings_Oorder(U_869) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_5,plain,
( U_870 = U_871
| c_Orderings_Oord__class_Oless(U_869,U_870,U_871)
| ~ c_Orderings_Oord__class_Oless__eq(U_869,U_870,U_871)
| ~ sP76(U_869,U_870,U_871) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_869,U_870,U_871)
| sP75(U_869,U_870,U_871)
| ~ sP76(U_869,U_870,U_871) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_869,U_870,U_871)
| ~ sP75(U_869,U_870,U_871) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_8,plain,
( U_870 != U_871
| ~ sP75(U_869,U_870,U_871) ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_278_2,plain,
! [U_874,U_873,U_872] :
( ( ( c_Orderings_Oord__class_Oless(U_872,U_873,U_874)
| c_Orderings_Oord__class_Oless__eq(U_872,U_874,U_873)
| ~ c_Orderings_Oord__class_Oless__eq(U_872,U_873,U_874) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_872,U_874,U_873)
& c_Orderings_Oord__class_Oless__eq(U_872,U_873,U_874) )
| ~ c_Orderings_Oord__class_Oless(U_872,U_873,U_874) ) )
| ~ class_Orderings_Opreorder(U_872) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
( ! [U_873,U_872,U_874] :
( ~ c_Orderings_Oord__class_Oless__eq(U_872,U_874,U_873)
| ~ sP77(U_873,U_872,U_874) )
& ! [U_873,U_872,U_874] :
( c_Orderings_Oord__class_Oless__eq(U_872,U_873,U_874)
| ~ sP77(U_873,U_872,U_874) )
& ! [U_873,U_872,U_874] :
( c_Orderings_Oord__class_Oless(U_872,U_873,U_874)
| c_Orderings_Oord__class_Oless__eq(U_872,U_874,U_873)
| ~ c_Orderings_Oord__class_Oless__eq(U_872,U_873,U_874)
| ~ sP78(U_873,U_872,U_874) )
& ! [U_873,U_872,U_874] :
( sP77(U_873,U_872,U_874)
| ~ c_Orderings_Oord__class_Oless(U_872,U_873,U_874)
| ~ sP78(U_873,U_872,U_874) )
& ! [U_873,U_872,U_874] :
( sP78(U_873,U_872,U_874)
| ~ class_Orderings_Opreorder(U_872) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77,sP78])],[f_278_2]) ).
cnf(f_278_4,plain,
( sP78(U_873,U_872,U_874)
| ~ class_Orderings_Opreorder(U_872) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_5,plain,
( sP77(U_873,U_872,U_874)
| ~ c_Orderings_Oord__class_Oless(U_872,U_873,U_874)
| ~ sP78(U_873,U_872,U_874) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_6,plain,
( c_Orderings_Oord__class_Oless(U_872,U_873,U_874)
| c_Orderings_Oord__class_Oless__eq(U_872,U_874,U_873)
| ~ c_Orderings_Oord__class_Oless__eq(U_872,U_873,U_874)
| ~ sP78(U_873,U_872,U_874) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_872,U_873,U_874)
| ~ sP77(U_873,U_872,U_874) ),
inference(clausify,[status(thm)],[f_278_3]) ).
cnf(f_278_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_872,U_874,U_873)
| ~ sP77(U_873,U_872,U_874) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_279_2,plain,
! [U_877,U_876,U_875] :
( ( ( c_Orderings_Oord__class_Oless(U_875,U_876,U_877)
| U_876 = U_877
| ~ c_Orderings_Oord__class_Oless__eq(U_875,U_876,U_877) )
& ( ( U_876 != U_877
& c_Orderings_Oord__class_Oless__eq(U_875,U_876,U_877) )
| ~ c_Orderings_Oord__class_Oless(U_875,U_876,U_877) ) )
| ~ class_Orderings_Oorder(U_875) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
( ! [U_877,U_875,U_876] :
( U_876 != U_877
| ~ sP79(U_877,U_875,U_876) )
& ! [U_877,U_875,U_876] :
( c_Orderings_Oord__class_Oless__eq(U_875,U_876,U_877)
| ~ sP79(U_877,U_875,U_876) )
& ! [U_877,U_875,U_876] :
( c_Orderings_Oord__class_Oless(U_875,U_876,U_877)
| U_876 = U_877
| ~ c_Orderings_Oord__class_Oless__eq(U_875,U_876,U_877)
| ~ sP80(U_877,U_875,U_876) )
& ! [U_877,U_875,U_876] :
( sP79(U_877,U_875,U_876)
| ~ c_Orderings_Oord__class_Oless(U_875,U_876,U_877)
| ~ sP80(U_877,U_875,U_876) )
& ! [U_877,U_875,U_876] :
( sP80(U_877,U_875,U_876)
| ~ class_Orderings_Oorder(U_875) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79,sP80])],[f_279_2]) ).
cnf(f_279_4,plain,
( sP80(U_877,U_875,U_876)
| ~ class_Orderings_Oorder(U_875) ),
inference(clausify,[status(thm)],[f_279_3]) ).
cnf(f_279_5,plain,
( sP79(U_877,U_875,U_876)
| ~ c_Orderings_Oord__class_Oless(U_875,U_876,U_877)
| ~ sP80(U_877,U_875,U_876) ),
inference(clausify,[status(thm)],[f_279_3]) ).
cnf(f_279_6,plain,
( c_Orderings_Oord__class_Oless(U_875,U_876,U_877)
| U_876 = U_877
| ~ c_Orderings_Oord__class_Oless__eq(U_875,U_876,U_877)
| ~ sP80(U_877,U_875,U_876) ),
inference(clausify,[status(thm)],[f_279_3]) ).
cnf(f_279_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_875,U_876,U_877)
| ~ sP79(U_877,U_875,U_876) ),
inference(clausify,[status(thm)],[f_279_3]) ).
cnf(f_279_8,plain,
( U_876 != U_877
| ~ sP79(U_877,U_875,U_876) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| 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_280_2,plain,
! [U_880,U_879,U_878] :
( c_Orderings_Oord__class_Oless(U_878,U_880,U_879)
| c_Orderings_Oord__class_Oless__eq(U_878,U_879,U_880)
| ~ class_Orderings_Olinorder(U_878) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_878,U_880,U_879] :
( c_Orderings_Oord__class_Oless(U_878,U_880,U_879)
| c_Orderings_Oord__class_Oless__eq(U_878,U_879,U_880)
| ~ class_Orderings_Olinorder(U_878) ),
inference(definitional_conversion,[status(esa)],[f_280_2]) ).
cnf(f_280_4,plain,
( c_Orderings_Oord__class_Oless(U_878,U_880,U_879)
| c_Orderings_Oord__class_Oless__eq(U_878,U_879,U_880)
| ~ class_Orderings_Olinorder(U_878) ),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_281_2,plain,
! [U_883,U_882,U_881] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_881,U_882,U_883)
| ~ c_Orderings_Oord__class_Oless(U_881,U_883,U_882) )
& ( c_Orderings_Oord__class_Oless(U_881,U_883,U_882)
| c_Orderings_Oord__class_Oless__eq(U_881,U_882,U_883) ) )
| ~ class_Orderings_Olinorder(U_881) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
( ! [U_882,U_883,U_881] :
( ~ c_Orderings_Oord__class_Oless__eq(U_881,U_882,U_883)
| ~ c_Orderings_Oord__class_Oless(U_881,U_883,U_882)
| ~ sP81(U_882,U_883,U_881) )
& ! [U_882,U_883,U_881] :
( c_Orderings_Oord__class_Oless(U_881,U_883,U_882)
| c_Orderings_Oord__class_Oless__eq(U_881,U_882,U_883)
| ~ sP81(U_882,U_883,U_881) )
& ! [U_882,U_883,U_881] :
( sP81(U_882,U_883,U_881)
| ~ class_Orderings_Olinorder(U_881) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_281_2]) ).
cnf(f_281_4,plain,
( sP81(U_882,U_883,U_881)
| ~ class_Orderings_Olinorder(U_881) ),
inference(clausify,[status(thm)],[f_281_3]) ).
cnf(f_281_5,plain,
( c_Orderings_Oord__class_Oless(U_881,U_883,U_882)
| c_Orderings_Oord__class_Oless__eq(U_881,U_882,U_883)
| ~ sP81(U_882,U_883,U_881) ),
inference(clausify,[status(thm)],[f_281_3]) ).
cnf(f_281_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_881,U_882,U_883)
| ~ c_Orderings_Oord__class_Oless(U_881,U_883,U_882)
| ~ sP81(U_882,U_883,U_881) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_282_2,plain,
! [U_886,U_885,U_884] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_884,U_885,U_886)
| ~ c_Orderings_Oord__class_Oless__eq(U_884,U_886,U_885) )
& ( c_Orderings_Oord__class_Oless__eq(U_884,U_886,U_885)
| c_Orderings_Oord__class_Oless(U_884,U_885,U_886) ) )
| ~ class_Orderings_Olinorder(U_884) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
( ! [U_886,U_885,U_884] :
( ~ c_Orderings_Oord__class_Oless(U_884,U_885,U_886)
| ~ c_Orderings_Oord__class_Oless__eq(U_884,U_886,U_885)
| ~ sP82(U_886,U_885,U_884) )
& ! [U_886,U_885,U_884] :
( c_Orderings_Oord__class_Oless__eq(U_884,U_886,U_885)
| c_Orderings_Oord__class_Oless(U_884,U_885,U_886)
| ~ sP82(U_886,U_885,U_884) )
& ! [U_886,U_885,U_884] :
( sP82(U_886,U_885,U_884)
| ~ class_Orderings_Olinorder(U_884) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_282_2]) ).
cnf(f_282_4,plain,
( sP82(U_886,U_885,U_884)
| ~ class_Orderings_Olinorder(U_884) ),
inference(clausify,[status(thm)],[f_282_3]) ).
cnf(f_282_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_884,U_886,U_885)
| c_Orderings_Oord__class_Oless(U_884,U_885,U_886)
| ~ sP82(U_886,U_885,U_884) ),
inference(clausify,[status(thm)],[f_282_3]) ).
cnf(f_282_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_884,U_885,U_886)
| ~ c_Orderings_Oord__class_Oless__eq(U_884,U_886,U_885)
| ~ sP82(U_886,U_885,U_884) ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_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_283_2,plain,
! [U_888,U_887] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_887),U_888),c_Groups_Ozero__class_Ozero(U_887)) = c_Groups_Ozero__class_Ozero(U_887)
| ~ class_Rings_Ocomm__semiring__1(U_887) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_888,U_887] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_887),U_888),c_Groups_Ozero__class_Ozero(U_887)) = c_Groups_Ozero__class_Ozero(U_887)
| ~ class_Rings_Ocomm__semiring__1(U_887) ),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_887),U_888),c_Groups_Ozero__class_Ozero(U_887)) = c_Groups_Ozero__class_Ozero(U_887)
| ~ class_Rings_Ocomm__semiring__1(U_887) ),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_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_284_2,plain,
! [U_890,U_889] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_889),c_Groups_Ozero__class_Ozero(U_889)),U_890) = c_Groups_Ozero__class_Ozero(U_889)
| ~ class_Rings_Ocomm__semiring__1(U_889) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_889,U_890] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_889),c_Groups_Ozero__class_Ozero(U_889)),U_890) = c_Groups_Ozero__class_Ozero(U_889)
| ~ class_Rings_Ocomm__semiring__1(U_889) ),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_889),c_Groups_Ozero__class_Ozero(U_889)),U_890) = c_Groups_Ozero__class_Ozero(U_889)
| ~ class_Rings_Ocomm__semiring__1(U_889) ),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).
fof(f_285_2,plain,
! [U_892,U_891] :
( ( ( c_Groups_Oplus__class_Oplus(U_891,U_892,U_892) = c_Groups_Ozero__class_Ozero(U_891)
| U_892 != c_Groups_Ozero__class_Ozero(U_891) )
& ( U_892 = c_Groups_Ozero__class_Ozero(U_891)
| c_Groups_Oplus__class_Oplus(U_891,U_892,U_892) != c_Groups_Ozero__class_Ozero(U_891) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_891) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
( ! [U_891,U_892] :
( c_Groups_Oplus__class_Oplus(U_891,U_892,U_892) = c_Groups_Ozero__class_Ozero(U_891)
| U_892 != c_Groups_Ozero__class_Ozero(U_891)
| ~ sP83(U_891,U_892) )
& ! [U_891,U_892] :
( U_892 = c_Groups_Ozero__class_Ozero(U_891)
| c_Groups_Oplus__class_Oplus(U_891,U_892,U_892) != c_Groups_Ozero__class_Ozero(U_891)
| ~ sP83(U_891,U_892) )
& ! [U_891,U_892] :
( sP83(U_891,U_892)
| ~ class_Groups_Olinordered__ab__group__add(U_891) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_285_2]) ).
cnf(f_285_4,plain,
( sP83(U_891,U_892)
| ~ class_Groups_Olinordered__ab__group__add(U_891) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_5,plain,
( U_892 = c_Groups_Ozero__class_Ozero(U_891)
| c_Groups_Oplus__class_Oplus(U_891,U_892,U_892) != c_Groups_Ozero__class_Ozero(U_891)
| ~ sP83(U_891,U_892) ),
inference(clausify,[status(thm)],[f_285_3]) ).
cnf(f_285_6,plain,
( c_Groups_Oplus__class_Oplus(U_891,U_892,U_892) = c_Groups_Ozero__class_Ozero(U_891)
| U_892 != c_Groups_Ozero__class_Ozero(U_891)
| ~ sP83(U_891,U_892) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_b_2 != c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).
fof(f_286_2,plain,
! [U_895,U_894,U_893] :
( ( ( U_894 = c_Groups_Oplus__class_Oplus(U_893,U_894,U_895)
| U_895 != c_Groups_Ozero__class_Ozero(U_893) )
& ( U_895 = c_Groups_Ozero__class_Ozero(U_893)
| U_894 != c_Groups_Oplus__class_Oplus(U_893,U_894,U_895) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_893) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
( ! [U_895,U_894,U_893] :
( U_894 = c_Groups_Oplus__class_Oplus(U_893,U_894,U_895)
| U_895 != c_Groups_Ozero__class_Ozero(U_893)
| ~ sP84(U_895,U_894,U_893) )
& ! [U_895,U_894,U_893] :
( U_895 = c_Groups_Ozero__class_Ozero(U_893)
| U_894 != c_Groups_Oplus__class_Oplus(U_893,U_894,U_895)
| ~ sP84(U_895,U_894,U_893) )
& ! [U_895,U_894,U_893] :
( sP84(U_895,U_894,U_893)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_893) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_286_2]) ).
cnf(f_286_4,plain,
( sP84(U_895,U_894,U_893)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_893) ),
inference(clausify,[status(thm)],[f_286_3]) ).
cnf(f_286_5,plain,
( U_895 = c_Groups_Ozero__class_Ozero(U_893)
| U_894 != c_Groups_Oplus__class_Oplus(U_893,U_894,U_895)
| ~ sP84(U_895,U_894,U_893) ),
inference(clausify,[status(thm)],[f_286_3]) ).
cnf(f_286_6,plain,
( U_894 = c_Groups_Oplus__class_Oplus(U_893,U_894,U_895)
| U_895 != c_Groups_Ozero__class_Ozero(U_893)
| ~ sP84(U_895,U_894,U_893) ),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_1,plain,
! [V_a,T_a] :
( 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_287_2,plain,
! [U_897,U_896] :
( c_Groups_Oplus__class_Oplus(U_896,U_897,c_Groups_Ozero__class_Ozero(U_896)) = U_897
| ~ class_Rings_Ocomm__semiring__1(U_896) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_897,U_896] :
( c_Groups_Oplus__class_Oplus(U_896,U_897,c_Groups_Ozero__class_Ozero(U_896)) = U_897
| ~ class_Rings_Ocomm__semiring__1(U_896) ),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
( c_Groups_Oplus__class_Oplus(U_896,U_897,c_Groups_Ozero__class_Ozero(U_896)) = U_897
| ~ class_Rings_Ocomm__semiring__1(U_896) ),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_1,plain,
! [V_a,T_a] :
( 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_288_2,plain,
! [U_899,U_898] :
( c_Groups_Oplus__class_Oplus(U_898,c_Groups_Ozero__class_Ozero(U_898),U_899) = U_899
| ~ class_Rings_Ocomm__semiring__1(U_898) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_898,U_899] :
( c_Groups_Oplus__class_Oplus(U_898,c_Groups_Ozero__class_Ozero(U_898),U_899) = U_899
| ~ class_Rings_Ocomm__semiring__1(U_898) ),
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
( c_Groups_Oplus__class_Oplus(U_898,c_Groups_Ozero__class_Ozero(U_898),U_899) = U_899
| ~ class_Rings_Ocomm__semiring__1(U_898) ),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_1,plain,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).
fof(f_289_2,plain,
! [U_904,U_903,U_902,U_901,U_900] :
( ( ( c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_904)) = c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_902))
| ( U_902 != U_904
& U_901 != U_903 ) )
& ( U_902 = U_904
| U_901 = U_903
| c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_904)) != c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_902)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_900) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
( ! [U_901,U_902,U_903,U_904] :
( U_902 != U_904
| ~ sP85(U_901,U_902,U_903,U_904) )
& ! [U_901,U_902,U_903,U_904] :
( U_901 != U_903
| ~ sP85(U_901,U_902,U_903,U_904) )
& ! [U_901,U_900,U_902,U_903,U_904] :
( c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_904)) = c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_902))
| sP85(U_901,U_902,U_903,U_904)
| ~ sP86(U_901,U_900,U_902,U_903,U_904) )
& ! [U_901,U_900,U_902,U_903,U_904] :
( U_902 = U_904
| U_901 = U_903
| c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_904)) != c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_902))
| ~ sP86(U_901,U_900,U_902,U_903,U_904) )
& ! [U_901,U_900,U_902,U_903,U_904] :
( sP86(U_901,U_900,U_902,U_903,U_904)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_900) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85,sP86])],[f_289_2]) ).
cnf(f_289_4,plain,
( sP86(U_901,U_900,U_902,U_903,U_904)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_900) ),
inference(clausify,[status(thm)],[f_289_3]) ).
cnf(f_289_5,plain,
( U_902 = U_904
| U_901 = U_903
| c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_904)) != c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_902))
| ~ sP86(U_901,U_900,U_902,U_903,U_904) ),
inference(clausify,[status(thm)],[f_289_3]) ).
cnf(f_289_6,plain,
( c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_904)) = c_Groups_Oplus__class_Oplus(U_900,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_901),U_904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_900),U_903),U_902))
| sP85(U_901,U_902,U_903,U_904)
| ~ sP86(U_901,U_900,U_902,U_903,U_904) ),
inference(clausify,[status(thm)],[f_289_3]) ).
cnf(f_289_7,plain,
( U_901 != U_903
| ~ sP85(U_901,U_902,U_903,U_904) ),
inference(clausify,[status(thm)],[f_289_3]) ).
cnf(f_289_8,plain,
( U_902 != U_904
| ~ sP85(U_901,U_902,U_903,U_904) ),
inference(clausify,[status(thm)],[f_289_3]) ).
fof(f_290_1,plain,
! [V_b,V_m,V_a,T_a] :
( 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),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_290_2,plain,
! [U_908,U_907,U_906,U_905] :
( c_Groups_Oplus__class_Oplus(U_905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_908),U_907)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),c_Groups_Oplus__class_Oplus(U_905,U_906,U_908)),U_907)
| ~ class_Rings_Ocomm__semiring__1(U_905) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_905,U_908,U_907,U_906] :
( c_Groups_Oplus__class_Oplus(U_905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_908),U_907)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),c_Groups_Oplus__class_Oplus(U_905,U_906,U_908)),U_907)
| ~ class_Rings_Ocomm__semiring__1(U_905) ),
inference(definitional_conversion,[status(esa)],[f_290_2]) ).
cnf(f_290_4,plain,
( c_Groups_Oplus__class_Oplus(U_905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_908),U_907)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),c_Groups_Oplus__class_Oplus(U_905,U_906,U_908)),U_907)
| ~ class_Rings_Ocomm__semiring__1(U_905) ),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = 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_291_2,plain,
! [U_912,U_911,U_910,U_909] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),c_Groups_Oplus__class_Oplus(U_909,U_910,U_911)),U_912) = c_Groups_Oplus__class_Oplus(U_909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_911),U_912))
| ~ class_Rings_Ocomm__semiring__1(U_909) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_911,U_909,U_910,U_912] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),c_Groups_Oplus__class_Oplus(U_909,U_910,U_911)),U_912) = c_Groups_Oplus__class_Oplus(U_909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_911),U_912))
| ~ class_Rings_Ocomm__semiring__1(U_909) ),
inference(definitional_conversion,[status(esa)],[f_291_2]) ).
cnf(f_291_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),c_Groups_Oplus__class_Oplus(U_909,U_910,U_911)),U_912) = c_Groups_Oplus__class_Oplus(U_909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_911),U_912))
| ~ class_Rings_Ocomm__semiring__1(U_909) ),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( ( V_ca_2 != V_d_2
& V_a_2 != V_b_2 )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) )
& ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
| V_ca_2 = V_d_2
| V_a_2 = V_b_2 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).
fof(f_292_2,plain,
! [U_917,U_916,U_915,U_914,U_913] :
( ( ( ( U_916 != U_917
& U_914 != U_915 )
| c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917)) = c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_916)) )
& ( c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917)) != c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_916))
| U_916 = U_917
| U_914 = U_915 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_913) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
( ! [U_914,U_915,U_916,U_917] :
( U_916 != U_917
| ~ sP87(U_914,U_915,U_916,U_917) )
& ! [U_914,U_915,U_916,U_917] :
( U_914 != U_915
| ~ sP87(U_914,U_915,U_916,U_917) )
& ! [U_913,U_914,U_915,U_916,U_917] :
( sP87(U_914,U_915,U_916,U_917)
| c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917)) = c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_916))
| ~ sP88(U_913,U_914,U_915,U_916,U_917) )
& ! [U_913,U_914,U_915,U_916,U_917] :
( c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917)) != c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_916))
| U_916 = U_917
| U_914 = U_915
| ~ sP88(U_913,U_914,U_915,U_916,U_917) )
& ! [U_913,U_914,U_915,U_916,U_917] :
( sP88(U_913,U_914,U_915,U_916,U_917)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_913) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87,sP88])],[f_292_2]) ).
cnf(f_292_4,plain,
( sP88(U_913,U_914,U_915,U_916,U_917)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_913) ),
inference(clausify,[status(thm)],[f_292_3]) ).
cnf(f_292_5,plain,
( c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917)) != c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_916))
| U_916 = U_917
| U_914 = U_915
| ~ sP88(U_913,U_914,U_915,U_916,U_917) ),
inference(clausify,[status(thm)],[f_292_3]) ).
cnf(f_292_6,plain,
( sP87(U_914,U_915,U_916,U_917)
| c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917)) = c_Groups_Oplus__class_Oplus(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_917),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_916))
| ~ sP88(U_913,U_914,U_915,U_916,U_917) ),
inference(clausify,[status(thm)],[f_292_3]) ).
cnf(f_292_7,plain,
( U_914 != U_915
| ~ sP87(U_914,U_915,U_916,U_917) ),
inference(clausify,[status(thm)],[f_292_3]) ).
cnf(f_292_8,plain,
( U_916 != U_917
| ~ sP87(U_914,U_915,U_916,U_917) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [V_z,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = 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_293_2,plain,
! [U_921,U_920,U_919,U_918] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),c_Groups_Oplus__class_Oplus(U_918,U_920,U_921)) = c_Groups_Oplus__class_Oplus(U_918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_921))
| ~ class_Rings_Ocomm__semiring__1(U_918) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_920,U_919,U_921,U_918] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),c_Groups_Oplus__class_Oplus(U_918,U_920,U_921)) = c_Groups_Oplus__class_Oplus(U_918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_921))
| ~ class_Rings_Ocomm__semiring__1(U_918) ),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),c_Groups_Oplus__class_Oplus(U_918,U_920,U_921)) = c_Groups_Oplus__class_Oplus(U_918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_921))
| ~ class_Rings_Ocomm__semiring__1(U_918) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_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_294_2,plain,
! [U_923,U_922] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_922),U_923),c_Groups_Oone__class_Oone(U_922)) = U_923
| ~ class_Rings_Ocomm__semiring__1(U_922) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_923,U_922] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_922),U_923),c_Groups_Oone__class_Oone(U_922)) = U_923
| ~ class_Rings_Ocomm__semiring__1(U_922) ),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_922),U_923),c_Groups_Oone__class_Oone(U_922)) = U_923
| ~ class_Rings_Ocomm__semiring__1(U_922) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_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_295_2,plain,
! [U_925,U_924] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_924),c_Groups_Oone__class_Oone(U_924)),U_925) = U_925
| ~ class_Rings_Ocomm__semiring__1(U_924) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_924,U_925] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_924),c_Groups_Oone__class_Oone(U_924)),U_925) = U_925
| ~ class_Rings_Ocomm__semiring__1(U_924) ),
inference(definitional_conversion,[status(esa)],[f_295_2]) ).
cnf(f_295_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_924),c_Groups_Oone__class_Oone(U_924)),U_925) = U_925
| ~ class_Rings_Ocomm__semiring__1(U_924) ),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__0]) ).
fof(f_296_2,plain,
! [U_927,U_926] :
( hAPP(c_Polynomial_Opoly(U_926,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_926))),U_927) = c_Groups_Ozero__class_Ozero(U_926)
| ~ class_Rings_Ocomm__semiring__0(U_926) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_926,U_927] :
( hAPP(c_Polynomial_Opoly(U_926,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_926))),U_927) = c_Groups_Ozero__class_Ozero(U_926)
| ~ class_Rings_Ocomm__semiring__0(U_926) ),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
( hAPP(c_Polynomial_Opoly(U_926,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_926))),U_927) = c_Groups_Ozero__class_Ozero(U_926)
| ~ class_Rings_Ocomm__semiring__0(U_926) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__mult]) ).
fof(f_297_2,plain,
! [U_931,U_930,U_929,U_928] :
( hAPP(c_Polynomial_Opoly(U_928,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_928)),U_929),U_930)),U_931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_928),hAPP(c_Polynomial_Opoly(U_928,U_929),U_931)),hAPP(c_Polynomial_Opoly(U_928,U_930),U_931))
| ~ class_Rings_Ocomm__semiring__0(U_928) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_931,U_930,U_928,U_929] :
( hAPP(c_Polynomial_Opoly(U_928,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_928)),U_929),U_930)),U_931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_928),hAPP(c_Polynomial_Opoly(U_928,U_929),U_931)),hAPP(c_Polynomial_Opoly(U_928,U_930),U_931))
| ~ class_Rings_Ocomm__semiring__0(U_928) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( hAPP(c_Polynomial_Opoly(U_928,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_928)),U_929),U_930)),U_931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_928),hAPP(c_Polynomial_Opoly(U_928,U_929),U_931)),hAPP(c_Polynomial_Opoly(U_928,U_930),U_931))
| ~ class_Rings_Ocomm__semiring__0(U_928) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [V_y,T_a] :
( ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Opos__bounded]) ).
fof(f_298_2,plain,
! [U_935,U_934] :
( ? [U_933] :
( ! [U_932] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_934,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_932),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_934,U_932)),U_933))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_933) )
| ~ class_RealVector_Oreal__normed__algebra(U_934) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_935,U_934] :
( ( ! [U_932] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_934,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_932),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_934,U_932)),sK5(U_935,U_934)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK5(U_935,U_934)) )
| ~ class_RealVector_Oreal__normed__algebra(U_934) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_933,sK5(U_935,U_934))],[f_298_2]) ).
fof(f_298_4,plain,
( ! [U_932,U_934,U_935] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_934,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_932),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_934,U_932)),sK5(U_935,U_934)))
| ~ sP89(U_932,U_934,U_935) )
& ! [U_932,U_934,U_935] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK5(U_935,U_934))
| ~ sP89(U_932,U_934,U_935) )
& ! [U_932,U_934,U_935] :
( sP89(U_932,U_934,U_935)
| ~ class_RealVector_Oreal__normed__algebra(U_934) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_298_3]) ).
cnf(f_298_5,plain,
( sP89(U_932,U_934,U_935)
| ~ class_RealVector_Oreal__normed__algebra(U_934) ),
inference(clausify,[status(thm)],[f_298_4]) ).
cnf(f_298_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK5(U_935,U_934))
| ~ sP89(U_932,U_934,U_935) ),
inference(clausify,[status(thm)],[f_298_4]) ).
cnf(f_298_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_934,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_932),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_934,U_932)),sK5(U_935,U_934)))
| ~ sP89(U_932,U_934,U_935) ),
inference(clausify,[status(thm)],[f_298_4]) ).
fof(f_299_1,plain,
! [V_x,T_a] :
( ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Opos__bounded]) ).
fof(f_299_2,plain,
! [U_939,U_938] :
( ? [U_937] :
( ! [U_936] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_939),U_936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_938,U_936)),U_937))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_937) )
| ~ class_RealVector_Oreal__normed__algebra(U_938) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_939,U_938] :
( ( ! [U_936] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_939),U_936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_938,U_936)),sK6(U_939,U_938)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK6(U_939,U_938)) )
| ~ class_RealVector_Oreal__normed__algebra(U_938) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_937,sK6(U_939,U_938))],[f_299_2]) ).
fof(f_299_4,plain,
( ! [U_938,U_936,U_939] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_939),U_936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_938,U_936)),sK6(U_939,U_938)))
| ~ sP90(U_938,U_936,U_939) )
& ! [U_938,U_936,U_939] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK6(U_939,U_938))
| ~ sP90(U_938,U_936,U_939) )
& ! [U_938,U_936,U_939] :
( sP90(U_938,U_936,U_939)
| ~ class_RealVector_Oreal__normed__algebra(U_938) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_299_3]) ).
cnf(f_299_5,plain,
( sP90(U_938,U_936,U_939)
| ~ class_RealVector_Oreal__normed__algebra(U_938) ),
inference(clausify,[status(thm)],[f_299_4]) ).
cnf(f_299_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK6(U_939,U_938))
| ~ sP90(U_938,U_936,U_939) ),
inference(clausify,[status(thm)],[f_299_4]) ).
cnf(f_299_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_939),U_936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_938,U_936)),sK6(U_939,U_938)))
| ~ sP90(U_938,U_936,U_939) ),
inference(clausify,[status(thm)],[f_299_4]) ).
fof(f_300_1,plain,
! [T_a] :
( ? [B_K] :
( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Opos__bounded]) ).
fof(f_300_2,plain,
! [U_943] :
( ? [U_942] :
( ! [U_941,U_940] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_941),U_940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_943,U_941)),c_RealVector_Onorm__class_Onorm(U_943,U_940))),U_942))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_942) )
| ~ class_RealVector_Oreal__normed__algebra(U_943) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_943] :
( ( ! [U_941,U_940] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_941),U_940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_943,U_941)),c_RealVector_Onorm__class_Onorm(U_943,U_940))),sK7(U_943)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_943)) )
| ~ class_RealVector_Oreal__normed__algebra(U_943) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_942,sK7(U_943))],[f_300_2]) ).
fof(f_300_4,plain,
( ! [U_941,U_940,U_943] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_941),U_940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_943,U_941)),c_RealVector_Onorm__class_Onorm(U_943,U_940))),sK7(U_943)))
| ~ sP91(U_941,U_940,U_943) )
& ! [U_941,U_940,U_943] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_943))
| ~ sP91(U_941,U_940,U_943) )
& ! [U_941,U_940,U_943] :
( sP91(U_941,U_940,U_943)
| ~ class_RealVector_Oreal__normed__algebra(U_943) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_300_3]) ).
cnf(f_300_5,plain,
( sP91(U_941,U_940,U_943)
| ~ class_RealVector_Oreal__normed__algebra(U_943) ),
inference(clausify,[status(thm)],[f_300_4]) ).
cnf(f_300_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_943))
| ~ sP91(U_941,U_940,U_943) ),
inference(clausify,[status(thm)],[f_300_4]) ).
cnf(f_300_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_941),U_940)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_943,U_941)),c_RealVector_Onorm__class_Onorm(U_943,U_940))),sK7(U_943)))
| ~ sP91(U_941,U_940,U_943) ),
inference(clausify,[status(thm)],[f_300_4]) ).
fof(f_301_1,plain,
! [V_y,T_a] :
( ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ononneg__bounded]) ).
fof(f_301_2,plain,
! [U_947,U_946] :
( ? [U_945] :
( ! [U_944] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_944),U_947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_946,U_944)),U_945))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_945) )
| ~ class_RealVector_Oreal__normed__algebra(U_946) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_947,U_946] :
( ( ! [U_944] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_944),U_947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_946,U_944)),sK8(U_947,U_946)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_947,U_946)) )
| ~ class_RealVector_Oreal__normed__algebra(U_946) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_945,sK8(U_947,U_946))],[f_301_2]) ).
fof(f_301_4,plain,
( ! [U_944,U_946,U_947] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_944),U_947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_946,U_944)),sK8(U_947,U_946)))
| ~ sP92(U_944,U_946,U_947) )
& ! [U_944,U_946,U_947] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_947,U_946))
| ~ sP92(U_944,U_946,U_947) )
& ! [U_944,U_946,U_947] :
( sP92(U_944,U_946,U_947)
| ~ class_RealVector_Oreal__normed__algebra(U_946) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_301_3]) ).
cnf(f_301_5,plain,
( sP92(U_944,U_946,U_947)
| ~ class_RealVector_Oreal__normed__algebra(U_946) ),
inference(clausify,[status(thm)],[f_301_4]) ).
cnf(f_301_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_947,U_946))
| ~ sP92(U_944,U_946,U_947) ),
inference(clausify,[status(thm)],[f_301_4]) ).
cnf(f_301_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_944),U_947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_946,U_944)),sK8(U_947,U_946)))
| ~ sP92(U_944,U_946,U_947) ),
inference(clausify,[status(thm)],[f_301_4]) ).
fof(f_302_1,plain,
! [V_x,T_a] :
( ? [B_K] :
( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ononneg__bounded]) ).
fof(f_302_2,plain,
! [U_951,U_950] :
( ? [U_949] :
( ! [U_948] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_951),U_948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_950,U_948)),U_949))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_949) )
| ~ class_RealVector_Oreal__normed__algebra(U_950) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_951,U_950] :
( ( ! [U_948] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_951),U_948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_950,U_948)),sK9(U_951,U_950)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK9(U_951,U_950)) )
| ~ class_RealVector_Oreal__normed__algebra(U_950) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_949,sK9(U_951,U_950))],[f_302_2]) ).
fof(f_302_4,plain,
( ! [U_948,U_950,U_951] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_951),U_948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_950,U_948)),sK9(U_951,U_950)))
| ~ sP93(U_948,U_950,U_951) )
& ! [U_948,U_950,U_951] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK9(U_951,U_950))
| ~ sP93(U_948,U_950,U_951) )
& ! [U_948,U_950,U_951] :
( sP93(U_948,U_950,U_951)
| ~ class_RealVector_Oreal__normed__algebra(U_950) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_302_3]) ).
cnf(f_302_5,plain,
( sP93(U_948,U_950,U_951)
| ~ class_RealVector_Oreal__normed__algebra(U_950) ),
inference(clausify,[status(thm)],[f_302_4]) ).
cnf(f_302_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK9(U_951,U_950))
| ~ sP93(U_948,U_950,U_951) ),
inference(clausify,[status(thm)],[f_302_4]) ).
cnf(f_302_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_951),U_948)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_950,U_948)),sK9(U_951,U_950)))
| ~ sP93(U_948,U_950,U_951) ),
inference(clausify,[status(thm)],[f_302_4]) ).
fof(f_303_1,plain,
! [T_a] :
( ? [B_K] :
( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ononneg__bounded]) ).
fof(f_303_2,plain,
! [U_955] :
( ? [U_954] :
( ! [U_953,U_952] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_955,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_955),U_953),U_952)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_955,U_953)),c_RealVector_Onorm__class_Onorm(U_955,U_952))),U_954))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_954) )
| ~ class_RealVector_Oreal__normed__algebra(U_955) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_955] :
( ( ! [U_953,U_952] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_955,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_955),U_953),U_952)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_955,U_953)),c_RealVector_Onorm__class_Onorm(U_955,U_952))),sK10(U_955)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_955)) )
| ~ class_RealVector_Oreal__normed__algebra(U_955) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_954,sK10(U_955))],[f_303_2]) ).
fof(f_303_4,plain,
( ! [U_952,U_953,U_955] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_955,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_955),U_953),U_952)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_955,U_953)),c_RealVector_Onorm__class_Onorm(U_955,U_952))),sK10(U_955)))
| ~ sP94(U_952,U_953,U_955) )
& ! [U_952,U_953,U_955] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_955))
| ~ sP94(U_952,U_953,U_955) )
& ! [U_952,U_953,U_955] :
( sP94(U_952,U_953,U_955)
| ~ class_RealVector_Oreal__normed__algebra(U_955) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_303_3]) ).
cnf(f_303_5,plain,
( sP94(U_952,U_953,U_955)
| ~ class_RealVector_Oreal__normed__algebra(U_955) ),
inference(clausify,[status(thm)],[f_303_4]) ).
cnf(f_303_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_955))
| ~ sP94(U_952,U_953,U_955) ),
inference(clausify,[status(thm)],[f_303_4]) ).
cnf(f_303_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_955,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_955),U_953),U_952)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_955,U_953)),c_RealVector_Onorm__class_Onorm(U_955,U_952))),sK10(U_955)))
| ~ sP94(U_952,U_953,U_955) ),
inference(clausify,[status(thm)],[f_303_4]) ).
fof(f_304_1,plain,
! [V_y,T_a] :
( ? [B_K] :
! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Obounded]) ).
fof(f_304_2,plain,
! [U_959,U_958] :
( ? [U_957] :
! [U_956] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_958),U_956),U_959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_958,U_956)),U_957))
| ~ class_RealVector_Oreal__normed__algebra(U_958) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_959,U_958] :
( ! [U_956] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_958),U_956),U_959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_958,U_956)),sK11(U_959,U_958)))
| ~ class_RealVector_Oreal__normed__algebra(U_958) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_957,sK11(U_959,U_958))],[f_304_2]) ).
fof(f_304_4,plain,
! [U_956,U_958,U_959] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_958),U_956),U_959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_958,U_956)),sK11(U_959,U_958)))
| ~ class_RealVector_Oreal__normed__algebra(U_958) ),
inference(definitional_conversion,[status(esa)],[f_304_3]) ).
cnf(f_304_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_958),U_956),U_959)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_958,U_956)),sK11(U_959,U_958)))
| ~ class_RealVector_Oreal__normed__algebra(U_958) ),
inference(clausify,[status(thm)],[f_304_4]) ).
fof(f_305_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
| c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_305_2,plain,
! [U_963,U_962,U_961,U_960] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_961,U_960),U_962,U_963)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_963,U_962)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_962,U_963) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_963,U_962)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_962,U_963) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_961,U_960),U_962,U_963) ) )
| ~ class_Orderings_Oord(U_960) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
( ! [U_961,U_960,U_962,U_963] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_963,U_962)
| ~ sP95(U_961,U_960,U_962,U_963) )
& ! [U_961,U_960,U_962,U_963] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_962,U_963)
| ~ sP95(U_961,U_960,U_962,U_963) )
& ! [U_961,U_960,U_962,U_963] :
( c_Orderings_Oord__class_Oless(tc_fun(U_961,U_960),U_962,U_963)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_963,U_962)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_962,U_963)
| ~ sP96(U_961,U_960,U_962,U_963) )
& ! [U_961,U_960,U_962,U_963] :
( sP95(U_961,U_960,U_962,U_963)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_961,U_960),U_962,U_963)
| ~ sP96(U_961,U_960,U_962,U_963) )
& ! [U_961,U_960,U_962,U_963] :
( sP96(U_961,U_960,U_962,U_963)
| ~ class_Orderings_Oord(U_960) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95,sP96])],[f_305_2]) ).
cnf(f_305_4,plain,
( sP96(U_961,U_960,U_962,U_963)
| ~ class_Orderings_Oord(U_960) ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_5,plain,
( sP95(U_961,U_960,U_962,U_963)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_961,U_960),U_962,U_963)
| ~ sP96(U_961,U_960,U_962,U_963) ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_6,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_961,U_960),U_962,U_963)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_963,U_962)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_962,U_963)
| ~ sP96(U_961,U_960,U_962,U_963) ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_962,U_963)
| ~ sP95(U_961,U_960,U_962,U_963) ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_961,U_960),U_963,U_962)
| ~ sP95(U_961,U_960,U_962,U_963) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_1,plain,
! [V_p,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right]) ).
fof(f_306_2,plain,
! [U_965,U_964] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_964)),U_965),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_964))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_964))
| ~ class_Rings_Ocomm__semiring__0(U_964) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_965,U_964] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_964)),U_965),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_964))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_964))
| ~ class_Rings_Ocomm__semiring__0(U_964) ),
inference(definitional_conversion,[status(esa)],[f_306_2]) ).
cnf(f_306_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_964)),U_965),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_964))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_964))
| ~ class_Rings_Ocomm__semiring__0(U_964) ),
inference(clausify,[status(thm)],[f_306_3]) ).
fof(f_307_1,plain,
! [V_q,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left]) ).
fof(f_307_2,plain,
! [U_967,U_966] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_966)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_966))),U_967) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_966))
| ~ class_Rings_Ocomm__semiring__0(U_966) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_966,U_967] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_966)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_966))),U_967) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_966))
| ~ class_Rings_Ocomm__semiring__0(U_966) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_966)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_966))),U_967) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_966))
| ~ class_Rings_Ocomm__semiring__0(U_966) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_1,plain,
! [V_a_2,V_pa_2,T_a] :
( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
& ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__root]) ).
fof(f_308_2,plain,
! [U_970,U_969,U_968] :
( ( ( hAPP(c_Polynomial_Opoly(U_968,U_969),U_970) = c_Groups_Ozero__class_Ozero(U_968)
| ( c_Polynomial_Oorder(U_968,U_970,U_969) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_969 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_968)) ) )
& ( c_Polynomial_Oorder(U_968,U_970,U_969) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_969 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_968))
| hAPP(c_Polynomial_Opoly(U_968,U_969),U_970) != c_Groups_Ozero__class_Ozero(U_968) ) )
| ~ class_Rings_Oidom(U_968) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
( ! [U_968,U_969,U_970] :
( c_Polynomial_Oorder(U_968,U_970,U_969) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP97(U_968,U_969,U_970) )
& ! [U_968,U_969,U_970] :
( U_969 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_968))
| ~ sP97(U_968,U_969,U_970) )
& ! [U_968,U_969,U_970] :
( hAPP(c_Polynomial_Opoly(U_968,U_969),U_970) = c_Groups_Ozero__class_Ozero(U_968)
| sP97(U_968,U_969,U_970)
| ~ sP98(U_968,U_969,U_970) )
& ! [U_968,U_969,U_970] :
( c_Polynomial_Oorder(U_968,U_970,U_969) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_969 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_968))
| hAPP(c_Polynomial_Opoly(U_968,U_969),U_970) != c_Groups_Ozero__class_Ozero(U_968)
| ~ sP98(U_968,U_969,U_970) )
& ! [U_968,U_969,U_970] :
( sP98(U_968,U_969,U_970)
| ~ class_Rings_Oidom(U_968) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97,sP98])],[f_308_2]) ).
cnf(f_308_4,plain,
( sP98(U_968,U_969,U_970)
| ~ class_Rings_Oidom(U_968) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_5,plain,
( c_Polynomial_Oorder(U_968,U_970,U_969) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_969 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_968))
| hAPP(c_Polynomial_Opoly(U_968,U_969),U_970) != c_Groups_Ozero__class_Ozero(U_968)
| ~ sP98(U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_6,plain,
( hAPP(c_Polynomial_Opoly(U_968,U_969),U_970) = c_Groups_Ozero__class_Ozero(U_968)
| sP97(U_968,U_969,U_970)
| ~ sP98(U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_7,plain,
( U_969 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_968))
| ~ sP97(U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_8,plain,
( c_Polynomial_Oorder(U_968,U_970,U_969) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP97(U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_1,plain,
! [T_a] :
( ? [B_K] :
! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Obounded]) ).
fof(f_309_2,plain,
! [U_974] :
( ? [U_973] :
! [U_972,U_971] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_974),U_972),U_971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_974,U_972)),c_RealVector_Onorm__class_Onorm(U_974,U_971))),U_973))
| ~ class_RealVector_Oreal__normed__algebra(U_974) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_974] :
( ! [U_972,U_971] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_974),U_972),U_971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_974,U_972)),c_RealVector_Onorm__class_Onorm(U_974,U_971))),sK12(U_974)))
| ~ class_RealVector_Oreal__normed__algebra(U_974) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_973,sK12(U_974))],[f_309_2]) ).
fof(f_309_4,plain,
! [U_974,U_972,U_971] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_974),U_972),U_971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_974,U_972)),c_RealVector_Onorm__class_Onorm(U_974,U_971))),sK12(U_974)))
| ~ class_RealVector_Oreal__normed__algebra(U_974) ),
inference(definitional_conversion,[status(esa)],[f_309_3]) ).
cnf(f_309_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_974),U_972),U_971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_974,U_972)),c_RealVector_Onorm__class_Onorm(U_974,U_971))),sK12(U_974)))
| ~ class_RealVector_Oreal__normed__algebra(U_974) ),
inference(clausify,[status(thm)],[f_309_4]) ).
fof(f_310_1,plain,
! [V_x,T_a] :
( ? [B_K] :
! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Obounded]) ).
fof(f_310_2,plain,
! [U_978,U_977] :
( ? [U_976] :
! [U_975] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_977,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_977),U_978),U_975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_977,U_975)),U_976))
| ~ class_RealVector_Oreal__normed__algebra(U_977) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_978,U_977] :
( ! [U_975] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_977,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_977),U_978),U_975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_977,U_975)),sK13(U_978,U_977)))
| ~ class_RealVector_Oreal__normed__algebra(U_977) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_976,sK13(U_978,U_977))],[f_310_2]) ).
fof(f_310_4,plain,
! [U_975,U_977,U_978] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_977,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_977),U_978),U_975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_977,U_975)),sK13(U_978,U_977)))
| ~ class_RealVector_Oreal__normed__algebra(U_977) ),
inference(definitional_conversion,[status(esa)],[f_310_3]) ).
cnf(f_310_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_977,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_977),U_978),U_975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_977,U_975)),sK13(U_978,U_977)))
| ~ class_RealVector_Oreal__normed__algebra(U_977) ),
inference(clausify,[status(thm)],[f_310_4]) ).
fof(f_311_1,plain,
! [V_x,T_a] :
( ( ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_x = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__sgn]) ).
fof(f_311_2,plain,
! [U_980,U_979] :
( ( ( c_RealVector_Onorm__class_Onorm(U_979,c_Groups_Osgn__class_Osgn(U_979,U_980)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_980 = c_Groups_Ozero__class_Ozero(U_979) )
& ( c_RealVector_Onorm__class_Onorm(U_979,c_Groups_Osgn__class_Osgn(U_979,U_980)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_980 != c_Groups_Ozero__class_Ozero(U_979) ) )
| ~ class_RealVector_Oreal__normed__vector(U_979) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
( ! [U_979,U_980] :
( c_RealVector_Onorm__class_Onorm(U_979,c_Groups_Osgn__class_Osgn(U_979,U_980)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_980 = c_Groups_Ozero__class_Ozero(U_979)
| ~ sP99(U_979,U_980) )
& ! [U_979,U_980] :
( c_RealVector_Onorm__class_Onorm(U_979,c_Groups_Osgn__class_Osgn(U_979,U_980)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_980 != c_Groups_Ozero__class_Ozero(U_979)
| ~ sP99(U_979,U_980) )
& ! [U_979,U_980] :
( sP99(U_979,U_980)
| ~ class_RealVector_Oreal__normed__vector(U_979) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_311_2]) ).
cnf(f_311_4,plain,
( sP99(U_979,U_980)
| ~ class_RealVector_Oreal__normed__vector(U_979) ),
inference(clausify,[status(thm)],[f_311_3]) ).
cnf(f_311_5,plain,
( c_RealVector_Onorm__class_Onorm(U_979,c_Groups_Osgn__class_Osgn(U_979,U_980)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_980 != c_Groups_Ozero__class_Ozero(U_979)
| ~ sP99(U_979,U_980) ),
inference(clausify,[status(thm)],[f_311_3]) ).
cnf(f_311_6,plain,
( c_RealVector_Onorm__class_Onorm(U_979,c_Groups_Osgn__class_Osgn(U_979,U_980)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_980 = c_Groups_Ozero__class_Ozero(U_979)
| ~ sP99(U_979,U_980) ),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_1,plain,
! [T_a,V_z_2,V_f_2,T_b] :
( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2
| hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) != V_z_2
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_poly__rec__0]) ).
fof(f_312_2,plain,
! [U_984,U_983,U_982,U_981] :
( c_Polynomial_Opoly__rec(U_984,U_981,U_983,U_982,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_981))) = U_983
| hAPP(hAPP(hAPP(U_982,c_Groups_Ozero__class_Ozero(U_981)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_981))),U_983) != U_983
| ~ class_Groups_Ozero(U_981) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_984,U_983,U_981,U_982] :
( c_Polynomial_Opoly__rec(U_984,U_981,U_983,U_982,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_981))) = U_983
| hAPP(hAPP(hAPP(U_982,c_Groups_Ozero__class_Ozero(U_981)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_981))),U_983) != U_983
| ~ class_Groups_Ozero(U_981) ),
inference(definitional_conversion,[status(esa)],[f_312_2]) ).
cnf(f_312_4,plain,
( c_Polynomial_Opoly__rec(U_984,U_981,U_983,U_982,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_981))) = U_983
| hAPP(hAPP(hAPP(U_982,c_Groups_Ozero__class_Ozero(U_981)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_981))),U_983) != U_983
| ~ class_Groups_Ozero(U_981) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ? [B_z] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x),V_y)
& c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))
& 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_313_2,plain,
! [U_988,U_987,U_986] :
( c_Orderings_Oord__class_Oless__eq(U_986,U_987,U_988)
| ? [U_985] :
( ~ c_Orderings_Oord__class_Oless__eq(U_986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_986),U_985),U_987),U_988)
& c_Orderings_Oord__class_Oless(U_986,U_985,c_Groups_Oone__class_Oone(U_986))
& c_Orderings_Oord__class_Oless(U_986,c_Groups_Ozero__class_Ozero(U_986),U_985) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_986) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_988,U_987,U_986] :
( c_Orderings_Oord__class_Oless__eq(U_986,U_987,U_988)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_986),sK14(U_988,U_987,U_986)),U_987),U_988)
& c_Orderings_Oord__class_Oless(U_986,sK14(U_988,U_987,U_986),c_Groups_Oone__class_Oone(U_986))
& c_Orderings_Oord__class_Oless(U_986,c_Groups_Ozero__class_Ozero(U_986),sK14(U_988,U_987,U_986)) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_986) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_985,sK14(U_988,U_987,U_986))],[f_313_2]) ).
fof(f_313_4,plain,
( ! [U_986,U_987,U_988] :
( ~ c_Orderings_Oord__class_Oless__eq(U_986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_986),sK14(U_988,U_987,U_986)),U_987),U_988)
| ~ sP100(U_986,U_987,U_988) )
& ! [U_986,U_987,U_988] :
( c_Orderings_Oord__class_Oless(U_986,sK14(U_988,U_987,U_986),c_Groups_Oone__class_Oone(U_986))
| ~ sP100(U_986,U_987,U_988) )
& ! [U_986,U_987,U_988] :
( c_Orderings_Oord__class_Oless(U_986,c_Groups_Ozero__class_Ozero(U_986),sK14(U_988,U_987,U_986))
| ~ sP100(U_986,U_987,U_988) )
& ! [U_986,U_987,U_988] :
( c_Orderings_Oord__class_Oless__eq(U_986,U_987,U_988)
| sP100(U_986,U_987,U_988)
| ~ class_Fields_Olinordered__field__inverse__zero(U_986) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_313_3]) ).
cnf(f_313_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_986,U_987,U_988)
| sP100(U_986,U_987,U_988)
| ~ class_Fields_Olinordered__field__inverse__zero(U_986) ),
inference(clausify,[status(thm)],[f_313_4]) ).
cnf(f_313_6,plain,
( c_Orderings_Oord__class_Oless(U_986,c_Groups_Ozero__class_Ozero(U_986),sK14(U_988,U_987,U_986))
| ~ sP100(U_986,U_987,U_988) ),
inference(clausify,[status(thm)],[f_313_4]) ).
cnf(f_313_7,plain,
( c_Orderings_Oord__class_Oless(U_986,sK14(U_988,U_987,U_986),c_Groups_Oone__class_Oone(U_986))
| ~ sP100(U_986,U_987,U_988) ),
inference(clausify,[status(thm)],[f_313_4]) ).
cnf(f_313_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_986,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_986),sK14(U_988,U_987,U_986)),U_987),U_988)
| ~ sP100(U_986,U_987,U_988) ),
inference(clausify,[status(thm)],[f_313_4]) ).
fof(f_314_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_314_2,plain,
! [U_990,U_989] :
( c_Groups_Osgn__class_Osgn(U_989,c_Groups_Osgn__class_Osgn(U_989,U_990)) = c_Groups_Osgn__class_Osgn(U_989,U_990)
| ~ class_Rings_Olinordered__idom(U_989) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
! [U_990,U_989] :
( c_Groups_Osgn__class_Osgn(U_989,c_Groups_Osgn__class_Osgn(U_989,U_990)) = c_Groups_Osgn__class_Osgn(U_989,U_990)
| ~ class_Rings_Olinordered__idom(U_989) ),
inference(definitional_conversion,[status(esa)],[f_314_2]) ).
cnf(f_314_4,plain,
( c_Groups_Osgn__class_Osgn(U_989,c_Groups_Osgn__class_Osgn(U_989,U_990)) = c_Groups_Osgn__class_Osgn(U_989,U_990)
| ~ class_Rings_Olinordered__idom(U_989) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Osgn__class_Osgn(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__zero__iff]) ).
fof(f_315_2,plain,
! [U_992,U_991] :
( ( ( c_Groups_Osgn__class_Osgn(U_991,U_992) = c_Groups_Ozero__class_Ozero(U_991)
| U_992 != c_Groups_Ozero__class_Ozero(U_991) )
& ( U_992 = c_Groups_Ozero__class_Ozero(U_991)
| c_Groups_Osgn__class_Osgn(U_991,U_992) != c_Groups_Ozero__class_Ozero(U_991) ) )
| ~ class_RealVector_Oreal__normed__vector(U_991) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
( ! [U_991,U_992] :
( c_Groups_Osgn__class_Osgn(U_991,U_992) = c_Groups_Ozero__class_Ozero(U_991)
| U_992 != c_Groups_Ozero__class_Ozero(U_991)
| ~ sP101(U_991,U_992) )
& ! [U_991,U_992] :
( U_992 = c_Groups_Ozero__class_Ozero(U_991)
| c_Groups_Osgn__class_Osgn(U_991,U_992) != c_Groups_Ozero__class_Ozero(U_991)
| ~ sP101(U_991,U_992) )
& ! [U_991,U_992] :
( sP101(U_991,U_992)
| ~ class_RealVector_Oreal__normed__vector(U_991) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_315_2]) ).
cnf(f_315_4,plain,
( sP101(U_991,U_992)
| ~ class_RealVector_Oreal__normed__vector(U_991) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_5,plain,
( U_992 = c_Groups_Ozero__class_Ozero(U_991)
| c_Groups_Osgn__class_Osgn(U_991,U_992) != c_Groups_Ozero__class_Ozero(U_991)
| ~ sP101(U_991,U_992) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_6,plain,
( c_Groups_Osgn__class_Osgn(U_991,U_992) = c_Groups_Ozero__class_Ozero(U_991)
| U_992 != c_Groups_Ozero__class_Ozero(U_991)
| ~ sP101(U_991,U_992) ),
inference(clausify,[status(thm)],[f_315_3]) ).
fof(f_316_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).
fof(f_316_2,plain,
! [U_994,U_993] :
( ( ( c_Groups_Osgn__class_Osgn(U_993,U_994) = c_Groups_Ozero__class_Ozero(U_993)
| U_994 != c_Groups_Ozero__class_Ozero(U_993) )
& ( U_994 = c_Groups_Ozero__class_Ozero(U_993)
| c_Groups_Osgn__class_Osgn(U_993,U_994) != c_Groups_Ozero__class_Ozero(U_993) ) )
| ~ class_Rings_Olinordered__idom(U_993) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
( ! [U_994,U_993] :
( c_Groups_Osgn__class_Osgn(U_993,U_994) = c_Groups_Ozero__class_Ozero(U_993)
| U_994 != c_Groups_Ozero__class_Ozero(U_993)
| ~ sP102(U_994,U_993) )
& ! [U_994,U_993] :
( U_994 = c_Groups_Ozero__class_Ozero(U_993)
| c_Groups_Osgn__class_Osgn(U_993,U_994) != c_Groups_Ozero__class_Ozero(U_993)
| ~ sP102(U_994,U_993) )
& ! [U_994,U_993] :
( sP102(U_994,U_993)
| ~ class_Rings_Olinordered__idom(U_993) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_316_2]) ).
cnf(f_316_4,plain,
( sP102(U_994,U_993)
| ~ class_Rings_Olinordered__idom(U_993) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_5,plain,
( U_994 = c_Groups_Ozero__class_Ozero(U_993)
| c_Groups_Osgn__class_Osgn(U_993,U_994) != c_Groups_Ozero__class_Ozero(U_993)
| ~ sP102(U_994,U_993) ),
inference(clausify,[status(thm)],[f_316_3]) ).
cnf(f_316_6,plain,
( c_Groups_Osgn__class_Osgn(U_993,U_994) = c_Groups_Ozero__class_Ozero(U_993)
| U_994 != c_Groups_Ozero__class_Ozero(U_993)
| ~ sP102(U_994,U_993) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_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_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__zero]) ).
fof(f_317_2,plain,
! [U_995] :
( c_Groups_Osgn__class_Osgn(U_995,c_Groups_Ozero__class_Ozero(U_995)) = c_Groups_Ozero__class_Ozero(U_995)
| ~ class_RealVector_Oreal__normed__vector(U_995) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_995] :
( c_Groups_Osgn__class_Osgn(U_995,c_Groups_Ozero__class_Ozero(U_995)) = c_Groups_Ozero__class_Ozero(U_995)
| ~ class_RealVector_Oreal__normed__vector(U_995) ),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_4,plain,
( c_Groups_Osgn__class_Osgn(U_995,c_Groups_Ozero__class_Ozero(U_995)) = c_Groups_Ozero__class_Ozero(U_995)
| ~ class_RealVector_Oreal__normed__vector(U_995) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_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_318_2,plain,
! [U_996] :
( c_Groups_Osgn__class_Osgn(U_996,c_Groups_Ozero__class_Ozero(U_996)) = c_Groups_Ozero__class_Ozero(U_996)
| ~ class_Groups_Osgn__if(U_996) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_996] :
( c_Groups_Osgn__class_Osgn(U_996,c_Groups_Ozero__class_Ozero(U_996)) = c_Groups_Ozero__class_Ozero(U_996)
| ~ class_Groups_Osgn__if(U_996) ),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_4,plain,
( c_Groups_Osgn__class_Osgn(U_996,c_Groups_Ozero__class_Ozero(U_996)) = c_Groups_Ozero__class_Ozero(U_996)
| ~ class_Groups_Osgn__if(U_996) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y))
| ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__mult]) ).
fof(f_319_2,plain,
! [U_999,U_998,U_997] :
( c_Groups_Osgn__class_Osgn(U_997,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_997),U_998),U_999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_997),c_Groups_Osgn__class_Osgn(U_997,U_998)),c_Groups_Osgn__class_Osgn(U_997,U_999))
| ~ class_RealVector_Oreal__normed__div__algebra(U_997) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_997,U_998,U_999] :
( c_Groups_Osgn__class_Osgn(U_997,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_997),U_998),U_999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_997),c_Groups_Osgn__class_Osgn(U_997,U_998)),c_Groups_Osgn__class_Osgn(U_997,U_999))
| ~ class_RealVector_Oreal__normed__div__algebra(U_997) ),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
( c_Groups_Osgn__class_Osgn(U_997,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_997),U_998),U_999)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_997),c_Groups_Osgn__class_Osgn(U_997,U_998)),c_Groups_Osgn__class_Osgn(U_997,U_999))
| ~ class_RealVector_Oreal__normed__div__algebra(U_997) ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_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_320_2,plain,
! [U_1002,U_1001,U_1000] :
( c_Groups_Osgn__class_Osgn(U_1000,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1000),U_1001),U_1002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1000),c_Groups_Osgn__class_Osgn(U_1000,U_1001)),c_Groups_Osgn__class_Osgn(U_1000,U_1002))
| ~ class_Rings_Olinordered__idom(U_1000) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1000,U_1001,U_1002] :
( c_Groups_Osgn__class_Osgn(U_1000,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1000),U_1001),U_1002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1000),c_Groups_Osgn__class_Osgn(U_1000,U_1001)),c_Groups_Osgn__class_Osgn(U_1000,U_1002))
| ~ class_Rings_Olinordered__idom(U_1000) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( c_Groups_Osgn__class_Osgn(U_1000,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1000),U_1001),U_1002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1000),c_Groups_Osgn__class_Osgn(U_1000,U_1001)),c_Groups_Osgn__class_Osgn(U_1000,U_1002))
| ~ class_Rings_Olinordered__idom(U_1000) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__one]) ).
fof(f_321_2,plain,
! [U_1003] :
( c_Groups_Osgn__class_Osgn(U_1003,c_Groups_Oone__class_Oone(U_1003)) = c_Groups_Oone__class_Oone(U_1003)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1003) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1003] :
( c_Groups_Osgn__class_Osgn(U_1003,c_Groups_Oone__class_Oone(U_1003)) = c_Groups_Oone__class_Oone(U_1003)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1003) ),
inference(definitional_conversion,[status(esa)],[f_321_2]) ).
cnf(f_321_4,plain,
( c_Groups_Osgn__class_Osgn(U_1003,c_Groups_Oone__class_Oone(U_1003)) = c_Groups_Oone__class_Oone(U_1003)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1003) ),
inference(clausify,[status(thm)],[f_321_3]) ).
fof(f_322_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).
fof(f_322_2,plain,
! [U_1005,U_1004] :
( ( ( c_Orderings_Oord__class_Oless(U_1004,c_Groups_Osgn__class_Osgn(U_1004,U_1005),c_Groups_Ozero__class_Ozero(U_1004))
| ~ c_Orderings_Oord__class_Oless(U_1004,U_1005,c_Groups_Ozero__class_Ozero(U_1004)) )
& ( c_Orderings_Oord__class_Oless(U_1004,U_1005,c_Groups_Ozero__class_Ozero(U_1004))
| ~ c_Orderings_Oord__class_Oless(U_1004,c_Groups_Osgn__class_Osgn(U_1004,U_1005),c_Groups_Ozero__class_Ozero(U_1004)) ) )
| ~ class_Rings_Olinordered__idom(U_1004) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
( ! [U_1004,U_1005] :
( c_Orderings_Oord__class_Oless(U_1004,c_Groups_Osgn__class_Osgn(U_1004,U_1005),c_Groups_Ozero__class_Ozero(U_1004))
| ~ c_Orderings_Oord__class_Oless(U_1004,U_1005,c_Groups_Ozero__class_Ozero(U_1004))
| ~ sP103(U_1004,U_1005) )
& ! [U_1004,U_1005] :
( c_Orderings_Oord__class_Oless(U_1004,U_1005,c_Groups_Ozero__class_Ozero(U_1004))
| ~ c_Orderings_Oord__class_Oless(U_1004,c_Groups_Osgn__class_Osgn(U_1004,U_1005),c_Groups_Ozero__class_Ozero(U_1004))
| ~ sP103(U_1004,U_1005) )
& ! [U_1004,U_1005] :
( sP103(U_1004,U_1005)
| ~ class_Rings_Olinordered__idom(U_1004) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_322_2]) ).
cnf(f_322_4,plain,
( sP103(U_1004,U_1005)
| ~ class_Rings_Olinordered__idom(U_1004) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_5,plain,
( c_Orderings_Oord__class_Oless(U_1004,U_1005,c_Groups_Ozero__class_Ozero(U_1004))
| ~ c_Orderings_Oord__class_Oless(U_1004,c_Groups_Osgn__class_Osgn(U_1004,U_1005),c_Groups_Ozero__class_Ozero(U_1004))
| ~ sP103(U_1004,U_1005) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_6,plain,
( c_Orderings_Oord__class_Oless(U_1004,c_Groups_Osgn__class_Osgn(U_1004,U_1005),c_Groups_Ozero__class_Ozero(U_1004))
| ~ c_Orderings_Oord__class_Oless(U_1004,U_1005,c_Groups_Ozero__class_Ozero(U_1004))
| ~ sP103(U_1004,U_1005) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).
fof(f_323_2,plain,
! [U_1007,U_1006] :
( ( ( c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),c_Groups_Osgn__class_Osgn(U_1006,U_1007))
| ~ c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),U_1007) )
& ( c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),U_1007)
| ~ c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),c_Groups_Osgn__class_Osgn(U_1006,U_1007)) ) )
| ~ class_Rings_Olinordered__idom(U_1006) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
( ! [U_1007,U_1006] :
( c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),c_Groups_Osgn__class_Osgn(U_1006,U_1007))
| ~ c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),U_1007)
| ~ sP104(U_1007,U_1006) )
& ! [U_1007,U_1006] :
( c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),U_1007)
| ~ c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),c_Groups_Osgn__class_Osgn(U_1006,U_1007))
| ~ sP104(U_1007,U_1006) )
& ! [U_1007,U_1006] :
( sP104(U_1007,U_1006)
| ~ class_Rings_Olinordered__idom(U_1006) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_323_2]) ).
cnf(f_323_4,plain,
( sP104(U_1007,U_1006)
| ~ class_Rings_Olinordered__idom(U_1006) ),
inference(clausify,[status(thm)],[f_323_3]) ).
cnf(f_323_5,plain,
( c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),U_1007)
| ~ c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),c_Groups_Osgn__class_Osgn(U_1006,U_1007))
| ~ sP104(U_1007,U_1006) ),
inference(clausify,[status(thm)],[f_323_3]) ).
cnf(f_323_6,plain,
( c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),c_Groups_Osgn__class_Osgn(U_1006,U_1007))
| ~ c_Orderings_Oord__class_Oless(U_1006,c_Groups_Ozero__class_Ozero(U_1006),U_1007)
| ~ sP104(U_1007,U_1006) ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),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_324_2,plain,
! [U_1009,U_1008] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1008),c_Groups_Osgn__class_Osgn(U_1008,U_1009)),c_Groups_Oabs__class_Oabs(U_1008,U_1009)) = U_1009
| ~ class_Rings_Olinordered__idom(U_1008) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
! [U_1009,U_1008] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1008),c_Groups_Osgn__class_Osgn(U_1008,U_1009)),c_Groups_Oabs__class_Oabs(U_1008,U_1009)) = U_1009
| ~ class_Rings_Olinordered__idom(U_1008) ),
inference(definitional_conversion,[status(esa)],[f_324_2]) ).
cnf(f_324_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1008),c_Groups_Osgn__class_Osgn(U_1008,U_1009)),c_Groups_Oabs__class_Oabs(U_1008,U_1009)) = U_1009
| ~ class_Rings_Olinordered__idom(U_1008) ),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_1,plain,
! [V_k,T_a] :
( 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_325_2,plain,
! [U_1011,U_1010] :
( c_Groups_Oabs__class_Oabs(U_1010,U_1011) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1010),U_1011),c_Groups_Osgn__class_Osgn(U_1010,U_1011))
| ~ class_Rings_Olinordered__idom(U_1010) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1010,U_1011] :
( c_Groups_Oabs__class_Oabs(U_1010,U_1011) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1010),U_1011),c_Groups_Osgn__class_Osgn(U_1010,U_1011))
| ~ class_Rings_Olinordered__idom(U_1010) ),
inference(definitional_conversion,[status(esa)],[f_325_2]) ).
cnf(f_325_4,plain,
( c_Groups_Oabs__class_Oabs(U_1010,U_1011) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1010),U_1011),c_Groups_Osgn__class_Osgn(U_1010,U_1011))
| ~ class_Rings_Olinordered__idom(U_1010) ),
inference(clausify,[status(thm)],[f_325_3]) ).
fof(f_326_1,plain,
! [V_x] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sgn__pos]) ).
fof(f_326_2,plain,
! [U_1012] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1012) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1012) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1012] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1012) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1012) ),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1012) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1012) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| ~ 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_327_2,plain,
! [U_1014,U_1013] :
( c_Groups_Osgn__class_Osgn(U_1013,U_1014) = c_Groups_Oone__class_Oone(U_1013)
| ~ c_Orderings_Oord__class_Oless(U_1013,c_Groups_Ozero__class_Ozero(U_1013),U_1014)
| ~ class_Rings_Olinordered__idom(U_1013) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_1013,U_1014] :
( c_Groups_Osgn__class_Osgn(U_1013,U_1014) = c_Groups_Oone__class_Oone(U_1013)
| ~ c_Orderings_Oord__class_Oless(U_1013,c_Groups_Ozero__class_Ozero(U_1013),U_1014)
| ~ class_Rings_Olinordered__idom(U_1013) ),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
( c_Groups_Osgn__class_Osgn(U_1013,U_1014) = c_Groups_Oone__class_Oone(U_1013)
| ~ c_Orderings_Oord__class_Oless(U_1013,c_Groups_Ozero__class_Ozero(U_1013),U_1014)
| ~ class_Rings_Olinordered__idom(U_1013) ),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| c_Groups_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).
fof(f_328_2,plain,
! [U_1016,U_1015] :
( ( ( c_Groups_Osgn__class_Osgn(U_1015,U_1016) = c_Groups_Oone__class_Oone(U_1015)
| ~ c_Orderings_Oord__class_Oless(U_1015,c_Groups_Ozero__class_Ozero(U_1015),U_1016) )
& ( c_Orderings_Oord__class_Oless(U_1015,c_Groups_Ozero__class_Ozero(U_1015),U_1016)
| c_Groups_Osgn__class_Osgn(U_1015,U_1016) != c_Groups_Oone__class_Oone(U_1015) ) )
| ~ class_Rings_Olinordered__idom(U_1015) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
( ! [U_1016,U_1015] :
( c_Groups_Osgn__class_Osgn(U_1015,U_1016) = c_Groups_Oone__class_Oone(U_1015)
| ~ c_Orderings_Oord__class_Oless(U_1015,c_Groups_Ozero__class_Ozero(U_1015),U_1016)
| ~ sP105(U_1016,U_1015) )
& ! [U_1016,U_1015] :
( c_Orderings_Oord__class_Oless(U_1015,c_Groups_Ozero__class_Ozero(U_1015),U_1016)
| c_Groups_Osgn__class_Osgn(U_1015,U_1016) != c_Groups_Oone__class_Oone(U_1015)
| ~ sP105(U_1016,U_1015) )
& ! [U_1016,U_1015] :
( sP105(U_1016,U_1015)
| ~ class_Rings_Olinordered__idom(U_1015) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_328_2]) ).
cnf(f_328_4,plain,
( sP105(U_1016,U_1015)
| ~ class_Rings_Olinordered__idom(U_1015) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_5,plain,
( c_Orderings_Oord__class_Oless(U_1015,c_Groups_Ozero__class_Ozero(U_1015),U_1016)
| c_Groups_Osgn__class_Osgn(U_1015,U_1016) != c_Groups_Oone__class_Oone(U_1015)
| ~ sP105(U_1016,U_1015) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_6,plain,
( c_Groups_Osgn__class_Osgn(U_1015,U_1016) = c_Groups_Oone__class_Oone(U_1015)
| ~ c_Orderings_Oord__class_Oless(U_1015,c_Groups_Ozero__class_Ozero(U_1015),U_1016)
| ~ sP105(U_1016,U_1015) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_1,plain,
! [V_n] : ~ 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_329_2,plain,
! [U_1017] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1017,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
! [U_1017] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1017,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_329_2]) ).
cnf(f_329_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1017,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_1,plain,
! [V_n] : 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_330_2,plain,
! [U_1018] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1018),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_1018] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1018),
inference(definitional_conversion,[status(esa)],[f_330_2]) ).
cnf(f_330_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1018),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ? [B_e] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e))
& 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_331_2,plain,
! [U_1022,U_1021,U_1020] :
( c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,U_1022)
| ? [U_1019] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,c_Groups_Oplus__class_Oplus(U_1020,U_1022,U_1019))
& c_Orderings_Oord__class_Oless(U_1020,c_Groups_Ozero__class_Ozero(U_1020),U_1019) )
| ~ class_Fields_Olinordered__field(U_1020) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1022,U_1021,U_1020] :
( c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,U_1022)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,c_Groups_Oplus__class_Oplus(U_1020,U_1022,sK15(U_1022,U_1021,U_1020)))
& c_Orderings_Oord__class_Oless(U_1020,c_Groups_Ozero__class_Ozero(U_1020),sK15(U_1022,U_1021,U_1020)) )
| ~ class_Fields_Olinordered__field(U_1020) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1019,sK15(U_1022,U_1021,U_1020))],[f_331_2]) ).
fof(f_331_4,plain,
( ! [U_1020,U_1021,U_1022] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,c_Groups_Oplus__class_Oplus(U_1020,U_1022,sK15(U_1022,U_1021,U_1020)))
| ~ sP106(U_1020,U_1021,U_1022) )
& ! [U_1020,U_1021,U_1022] :
( c_Orderings_Oord__class_Oless(U_1020,c_Groups_Ozero__class_Ozero(U_1020),sK15(U_1022,U_1021,U_1020))
| ~ sP106(U_1020,U_1021,U_1022) )
& ! [U_1020,U_1021,U_1022] :
( c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,U_1022)
| sP106(U_1020,U_1021,U_1022)
| ~ class_Fields_Olinordered__field(U_1020) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_331_3]) ).
cnf(f_331_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,U_1022)
| sP106(U_1020,U_1021,U_1022)
| ~ class_Fields_Olinordered__field(U_1020) ),
inference(clausify,[status(thm)],[f_331_4]) ).
cnf(f_331_6,plain,
( c_Orderings_Oord__class_Oless(U_1020,c_Groups_Ozero__class_Ozero(U_1020),sK15(U_1022,U_1021,U_1020))
| ~ sP106(U_1020,U_1021,U_1022) ),
inference(clausify,[status(thm)],[f_331_4]) ).
cnf(f_331_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,c_Groups_Oplus__class_Oplus(U_1020,U_1022,sK15(U_1022,U_1021,U_1020)))
| ~ sP106(U_1020,U_1021,U_1022) ),
inference(clausify,[status(thm)],[f_331_4]) ).
fof(f_332_1,plain,
! [V_n,T_a] :
( ( ( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Oone__class_Oone(T_a)
| V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__1]) ).
fof(f_332_2,plain,
! [U_1024,U_1023] :
( ( ( hAPP(c_Polynomial_Ocoeff(U_1023,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1023))),U_1024) = c_Groups_Ozero__class_Ozero(U_1023)
| U_1024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Polynomial_Ocoeff(U_1023,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1023))),U_1024) = c_Groups_Oone__class_Oone(U_1023)
| U_1024 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Ocomm__semiring__1(U_1023) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
( ! [U_1023,U_1024] :
( hAPP(c_Polynomial_Ocoeff(U_1023,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1023))),U_1024) = c_Groups_Ozero__class_Ozero(U_1023)
| U_1024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP107(U_1023,U_1024) )
& ! [U_1023,U_1024] :
( hAPP(c_Polynomial_Ocoeff(U_1023,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1023))),U_1024) = c_Groups_Oone__class_Oone(U_1023)
| U_1024 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP107(U_1023,U_1024) )
& ! [U_1023,U_1024] :
( sP107(U_1023,U_1024)
| ~ class_Rings_Ocomm__semiring__1(U_1023) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_332_2]) ).
cnf(f_332_4,plain,
( sP107(U_1023,U_1024)
| ~ class_Rings_Ocomm__semiring__1(U_1023) ),
inference(clausify,[status(thm)],[f_332_3]) ).
cnf(f_332_5,plain,
( hAPP(c_Polynomial_Ocoeff(U_1023,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1023))),U_1024) = c_Groups_Oone__class_Oone(U_1023)
| U_1024 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP107(U_1023,U_1024) ),
inference(clausify,[status(thm)],[f_332_3]) ).
cnf(f_332_6,plain,
( hAPP(c_Polynomial_Ocoeff(U_1023,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1023))),U_1024) = c_Groups_Ozero__class_Ozero(U_1023)
| U_1024 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP107(U_1023,U_1024) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq]) ).
fof(f_333_2,plain,
! [U_1029,U_1028,U_1027,U_1026,U_1025] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,c_Groups_Oplus__class_Oplus(U_1025,U_1026,U_1027),c_Groups_Oplus__class_Oplus(U_1025,U_1028,U_1029))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,U_1026,U_1028)),c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,U_1027,U_1029))))
| ~ class_RealVector_Oreal__normed__vector(U_1025) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_1026,U_1025,U_1027,U_1028,U_1029] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,c_Groups_Oplus__class_Oplus(U_1025,U_1026,U_1027),c_Groups_Oplus__class_Oplus(U_1025,U_1028,U_1029))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,U_1026,U_1028)),c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,U_1027,U_1029))))
| ~ class_RealVector_Oreal__normed__vector(U_1025) ),
inference(definitional_conversion,[status(esa)],[f_333_2]) ).
cnf(f_333_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,c_Groups_Oplus__class_Oplus(U_1025,U_1026,U_1027),c_Groups_Oplus__class_Oplus(U_1025,U_1028,U_1029))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,U_1026,U_1028)),c_RealVector_Onorm__class_Onorm(U_1025,c_Groups_Ominus__class_Ominus(U_1025,U_1027,U_1029))))
| ~ class_RealVector_Oreal__normed__vector(U_1025) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| ~ 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_334_2,plain,
! [U_1031,U_1030] :
( c_Groups_Osgn__class_Osgn(U_1030,U_1031) = c_Groups_Ouminus__class_Ouminus(U_1030,c_Groups_Oone__class_Oone(U_1030))
| ~ c_Orderings_Oord__class_Oless(U_1030,U_1031,c_Groups_Ozero__class_Ozero(U_1030))
| ~ class_Rings_Olinordered__idom(U_1030) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1030,U_1031] :
( c_Groups_Osgn__class_Osgn(U_1030,U_1031) = c_Groups_Ouminus__class_Ouminus(U_1030,c_Groups_Oone__class_Oone(U_1030))
| ~ c_Orderings_Oord__class_Oless(U_1030,U_1031,c_Groups_Ozero__class_Ozero(U_1030))
| ~ class_Rings_Olinordered__idom(U_1030) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( c_Groups_Osgn__class_Osgn(U_1030,U_1031) = c_Groups_Ouminus__class_Ouminus(U_1030,c_Groups_Oone__class_Oone(U_1030))
| ~ c_Orderings_Oord__class_Oless(U_1030,U_1031,c_Groups_Ozero__class_Ozero(U_1030))
| ~ class_Rings_Olinordered__idom(U_1030) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,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 = 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)))
& 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 != 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)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,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_335_2,plain,
! [U_1036,U_1035,U_1034] :
( ( hBOOL(hAPP(U_1034,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1035,U_1036)))
| ? [U_1033] :
( ~ hBOOL(hAPP(U_1034,U_1033))
& U_1035 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1036,U_1033) )
| ( ~ hBOOL(hAPP(U_1034,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1035,U_1036) ) )
& ( ( ! [U_1032] :
( hBOOL(hAPP(U_1034,U_1032))
| U_1035 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1036,U_1032) )
& ( hBOOL(hAPP(U_1034,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1035,U_1036) ) )
| ~ hBOOL(hAPP(U_1034,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1035,U_1036))) ) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
( ! [U_1042,U_1040,U_1038] :
( hBOOL(hAPP(U_1038,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1040,U_1042)))
| ? [U_1033] :
( ~ hBOOL(hAPP(U_1038,U_1033))
& U_1040 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1042,U_1033) )
| ( ~ hBOOL(hAPP(U_1038,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1040,U_1042) ) )
& ! [U_1041,U_1039,U_1037] :
( ( ! [U_1032] :
( hBOOL(hAPP(U_1037,U_1032))
| U_1039 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1041,U_1032) )
& ( hBOOL(hAPP(U_1037,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1039,U_1041) ) )
| ~ hBOOL(hAPP(U_1037,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1039,U_1041))) ) ),
inference(miniscope,[status(thm)],[f_335_2]) ).
fof(f_335_4,plain,
( ! [U_1042,U_1040,U_1038] :
( hBOOL(hAPP(U_1038,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1040,U_1042)))
| ( ~ hBOOL(hAPP(U_1038,sK16(U_1042,U_1040,U_1038)))
& U_1040 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1042,sK16(U_1042,U_1040,U_1038)) )
| ( ~ hBOOL(hAPP(U_1038,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1040,U_1042) ) )
& ! [U_1041,U_1039,U_1037] :
( ( ! [U_1032] :
( hBOOL(hAPP(U_1037,U_1032))
| U_1039 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1041,U_1032) )
& ( hBOOL(hAPP(U_1037,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1039,U_1041) ) )
| ~ hBOOL(hAPP(U_1037,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1039,U_1041))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_1033,sK16(U_1042,U_1040,U_1038))],[f_335_3]) ).
fof(f_335_5,plain,
( ! [U_1038,U_1040,U_1042] :
( ~ hBOOL(hAPP(U_1038,sK16(U_1042,U_1040,U_1038)))
| ~ sP110(U_1038,U_1040,U_1042) )
& ! [U_1038,U_1040,U_1042] :
( U_1040 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1042,sK16(U_1042,U_1040,U_1038))
| ~ sP110(U_1038,U_1040,U_1042) )
& ! [U_1038,U_1040,U_1042] :
( ~ hBOOL(hAPP(U_1038,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP109(U_1038,U_1040,U_1042) )
& ! [U_1038,U_1040,U_1042] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1040,U_1042)
| ~ sP109(U_1038,U_1040,U_1042) )
& ! [U_1039,U_1041,U_1032,U_1037] :
( hBOOL(hAPP(U_1037,U_1032))
| U_1039 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1041,U_1032)
| ~ sP108(U_1039,U_1041,U_1032,U_1037) )
& ! [U_1039,U_1041,U_1032,U_1037] :
( hBOOL(hAPP(U_1037,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1039,U_1041)
| ~ sP108(U_1039,U_1041,U_1032,U_1037) )
& ! [U_1038,U_1040,U_1042] :
( hBOOL(hAPP(U_1038,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1040,U_1042)))
| sP110(U_1038,U_1040,U_1042)
| sP109(U_1038,U_1040,U_1042) )
& ! [U_1039,U_1041,U_1032,U_1037] :
( sP108(U_1039,U_1041,U_1032,U_1037)
| ~ hBOOL(hAPP(U_1037,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1039,U_1041))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108,sP109,sP110])],[f_335_4]) ).
cnf(f_335_6,plain,
( sP108(U_1039,U_1041,U_1032,U_1037)
| ~ hBOOL(hAPP(U_1037,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1039,U_1041))) ),
inference(clausify,[status(thm)],[f_335_5]) ).
cnf(f_335_7,plain,
( hBOOL(hAPP(U_1038,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1040,U_1042)))
| sP110(U_1038,U_1040,U_1042)
| sP109(U_1038,U_1040,U_1042) ),
inference(clausify,[status(thm)],[f_335_5]) ).
cnf(f_335_8,plain,
( hBOOL(hAPP(U_1037,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1039,U_1041)
| ~ sP108(U_1039,U_1041,U_1032,U_1037) ),
inference(clausify,[status(thm)],[f_335_5]) ).
cnf(f_335_9,plain,
( hBOOL(hAPP(U_1037,U_1032))
| U_1039 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1041,U_1032)
| ~ sP108(U_1039,U_1041,U_1032,U_1037) ),
inference(clausify,[status(thm)],[f_335_5]) ).
cnf(f_335_10,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1040,U_1042)
| ~ sP109(U_1038,U_1040,U_1042) ),
inference(clausify,[status(thm)],[f_335_5]) ).
cnf(f_335_11,plain,
( ~ hBOOL(hAPP(U_1038,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP109(U_1038,U_1040,U_1042) ),
inference(clausify,[status(thm)],[f_335_5]) ).
cnf(f_335_12,plain,
( U_1040 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1042,sK16(U_1042,U_1040,U_1038))
| ~ sP110(U_1038,U_1040,U_1042) ),
inference(clausify,[status(thm)],[f_335_5]) ).
cnf(f_335_13,plain,
( ~ hBOOL(hAPP(U_1038,sK16(U_1042,U_1040,U_1038)))
| ~ sP110(U_1038,U_1040,U_1042) ),
inference(clausify,[status(thm)],[f_335_5]) ).
fof(f_336_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,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 = 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)))
& 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 != 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)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,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_336_2,plain,
! [U_1047,U_1046,U_1045] :
( ( hBOOL(hAPP(U_1045,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1046,U_1047)))
| ? [U_1044] :
( ~ hBOOL(hAPP(U_1045,U_1044))
& U_1046 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1047,U_1044) )
| ( ~ hBOOL(hAPP(U_1045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1046,U_1047) ) )
& ( ( ! [U_1043] :
( hBOOL(hAPP(U_1045,U_1043))
| U_1046 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1047,U_1043) )
& ( hBOOL(hAPP(U_1045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1046,U_1047) ) )
| ~ hBOOL(hAPP(U_1045,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1046,U_1047))) ) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
( ! [U_1053,U_1051,U_1049] :
( hBOOL(hAPP(U_1049,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1051,U_1053)))
| ? [U_1044] :
( ~ hBOOL(hAPP(U_1049,U_1044))
& U_1051 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1053,U_1044) )
| ( ~ hBOOL(hAPP(U_1049,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1051,U_1053) ) )
& ! [U_1052,U_1050,U_1048] :
( ( ! [U_1043] :
( hBOOL(hAPP(U_1048,U_1043))
| U_1050 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1052,U_1043) )
& ( hBOOL(hAPP(U_1048,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1050,U_1052) ) )
| ~ hBOOL(hAPP(U_1048,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1050,U_1052))) ) ),
inference(miniscope,[status(thm)],[f_336_2]) ).
fof(f_336_4,plain,
( ! [U_1053,U_1051,U_1049] :
( hBOOL(hAPP(U_1049,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1051,U_1053)))
| ( ~ hBOOL(hAPP(U_1049,sK17(U_1053,U_1051,U_1049)))
& U_1051 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1053,sK17(U_1053,U_1051,U_1049)) )
| ( ~ hBOOL(hAPP(U_1049,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1051,U_1053) ) )
& ! [U_1052,U_1050,U_1048] :
( ( ! [U_1043] :
( hBOOL(hAPP(U_1048,U_1043))
| U_1050 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1052,U_1043) )
& ( hBOOL(hAPP(U_1048,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1050,U_1052) ) )
| ~ hBOOL(hAPP(U_1048,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1050,U_1052))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_1044,sK17(U_1053,U_1051,U_1049))],[f_336_3]) ).
fof(f_336_5,plain,
( ! [U_1053,U_1049,U_1051] :
( ~ hBOOL(hAPP(U_1049,sK17(U_1053,U_1051,U_1049)))
| ~ sP113(U_1053,U_1049,U_1051) )
& ! [U_1053,U_1049,U_1051] :
( U_1051 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1053,sK17(U_1053,U_1051,U_1049))
| ~ sP113(U_1053,U_1049,U_1051) )
& ! [U_1053,U_1049,U_1051] :
( ~ hBOOL(hAPP(U_1049,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP112(U_1053,U_1049,U_1051) )
& ! [U_1053,U_1049,U_1051] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1051,U_1053)
| ~ sP112(U_1053,U_1049,U_1051) )
& ! [U_1043,U_1052,U_1048,U_1050] :
( hBOOL(hAPP(U_1048,U_1043))
| U_1050 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1052,U_1043)
| ~ sP111(U_1043,U_1052,U_1048,U_1050) )
& ! [U_1043,U_1052,U_1048,U_1050] :
( hBOOL(hAPP(U_1048,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1050,U_1052)
| ~ sP111(U_1043,U_1052,U_1048,U_1050) )
& ! [U_1053,U_1049,U_1051] :
( hBOOL(hAPP(U_1049,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1051,U_1053)))
| sP113(U_1053,U_1049,U_1051)
| sP112(U_1053,U_1049,U_1051) )
& ! [U_1043,U_1052,U_1048,U_1050] :
( sP111(U_1043,U_1052,U_1048,U_1050)
| ~ hBOOL(hAPP(U_1048,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1050,U_1052))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111,sP112,sP113])],[f_336_4]) ).
cnf(f_336_6,plain,
( sP111(U_1043,U_1052,U_1048,U_1050)
| ~ hBOOL(hAPP(U_1048,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1050,U_1052))) ),
inference(clausify,[status(thm)],[f_336_5]) ).
cnf(f_336_7,plain,
( hBOOL(hAPP(U_1049,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1051,U_1053)))
| sP113(U_1053,U_1049,U_1051)
| sP112(U_1053,U_1049,U_1051) ),
inference(clausify,[status(thm)],[f_336_5]) ).
cnf(f_336_8,plain,
( hBOOL(hAPP(U_1048,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1050,U_1052)
| ~ sP111(U_1043,U_1052,U_1048,U_1050) ),
inference(clausify,[status(thm)],[f_336_5]) ).
cnf(f_336_9,plain,
( hBOOL(hAPP(U_1048,U_1043))
| U_1050 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1052,U_1043)
| ~ sP111(U_1043,U_1052,U_1048,U_1050) ),
inference(clausify,[status(thm)],[f_336_5]) ).
cnf(f_336_10,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1051,U_1053)
| ~ sP112(U_1053,U_1049,U_1051) ),
inference(clausify,[status(thm)],[f_336_5]) ).
cnf(f_336_11,plain,
( ~ hBOOL(hAPP(U_1049,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP112(U_1053,U_1049,U_1051) ),
inference(clausify,[status(thm)],[f_336_5]) ).
cnf(f_336_12,plain,
( U_1051 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1053,sK17(U_1053,U_1051,U_1049))
| ~ sP113(U_1053,U_1049,U_1051) ),
inference(clausify,[status(thm)],[f_336_5]) ).
cnf(f_336_13,plain,
( ~ hBOOL(hAPP(U_1049,sK17(U_1053,U_1051,U_1049)))
| ~ sP113(U_1053,U_1049,U_1051) ),
inference(clausify,[status(thm)],[f_336_5]) ).
fof(f_337_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,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_337_2,plain,
! [U_1055,U_1054] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1054,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1054,U_1055)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_1054,U_1055] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1054,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1054,U_1055)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_337_2]) ).
cnf(f_337_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1054,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1054,U_1055)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_1,plain,
! [V_q,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J]) ).
fof(f_338_2,plain,
! [U_1057,U_1056] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1056),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1056)),U_1057) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1056),U_1057)
| ~ class_Groups_Oab__group__add(U_1056) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1057,U_1056] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1056),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1056)),U_1057) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1056),U_1057)
| ~ class_Groups_Oab__group__add(U_1056) ),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1056),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1056)),U_1057) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1056),U_1057)
| ~ class_Groups_Oab__group__add(U_1056) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_1,plain,
! [V_n] : 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_339_2,plain,
! [U_1058] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1058) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_1058] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1058) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_339_2]) ).
cnf(f_339_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1058) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).
fof(f_340_2,plain,
! [U_1060,U_1059] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1059,U_1060))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1060,U_1059) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1060,U_1059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1059,U_1060)) ) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
( ! [U_1064,U_1062] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1062,U_1064))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1064,U_1062) )
& ! [U_1063,U_1061] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1063,U_1061)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1061,U_1063)) ) ),
inference(miniscope,[status(thm)],[f_340_2]) ).
fof(f_340_4,plain,
( ! [U_1064,U_1062] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1062,U_1064))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1064,U_1062) )
& ! [U_1061,U_1063] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1063,U_1061)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1061,U_1063)) ) ),
inference(definitional_conversion,[status(esa)],[f_340_3]) ).
cnf(f_340_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1063,U_1061)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1061,U_1063)) ),
inference(clausify,[status(thm)],[f_340_4]) ).
cnf(f_340_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1062,U_1064))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1064,U_1062) ),
inference(clausify,[status(thm)],[f_340_4]) ).
fof(f_341_1,plain,
! [V_m] : 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_341_2,plain,
! [U_1065] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1065,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1065,
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1065] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1065,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1065,
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1065,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1065,
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_1,plain,
! [V_m] : 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_342_2,plain,
! [U_1066] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1066,U_1066) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_1066] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1066,U_1066) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1066,U_1066) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ 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_343_2,plain,
! [U_1068,U_1067] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1068,U_1067),U_1068)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1068)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1067) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
! [U_1068,U_1067] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1068,U_1067),U_1068)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1068)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1067) ),
inference(definitional_conversion,[status(esa)],[f_343_2]) ).
cnf(f_343_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1068,U_1067),U_1068)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1068)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1067) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_1,plain,
! [V_n,V_m] :
( V_m = V_n
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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_344_2,plain,
! [U_1070,U_1069] :
( U_1069 = U_1070
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1070,U_1069) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1069,U_1070) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_1070,U_1069] :
( U_1069 = U_1070
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1070,U_1069) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1069,U_1070) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_344_2]) ).
cnf(f_344_4,plain,
( U_1069 = U_1070
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1070,U_1069) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1069,U_1070) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ( V_m != V_n
& ~ 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_345_2,plain,
! [U_1072,U_1071] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1071,U_1072)
| ( U_1071 != U_1072
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1071,U_1072) ) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
( ! [U_1071,U_1072] :
( U_1071 != U_1072
| ~ sP114(U_1071,U_1072) )
& ! [U_1071,U_1072] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1071,U_1072)
| ~ sP114(U_1071,U_1072) )
& ! [U_1071,U_1072] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1071,U_1072)
| sP114(U_1071,U_1072) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_345_2]) ).
cnf(f_345_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1071,U_1072)
| sP114(U_1071,U_1072) ),
inference(clausify,[status(thm)],[f_345_3]) ).
cnf(f_345_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1071,U_1072)
| ~ sP114(U_1071,U_1072) ),
inference(clausify,[status(thm)],[f_345_3]) ).
cnf(f_345_6,plain,
( U_1071 != U_1072
| ~ sP114(U_1071,U_1072) ),
inference(clausify,[status(thm)],[f_345_3]) ).
fof(f_346_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).
fof(f_346_2,plain,
! [U_1075,U_1074,U_1073] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1074,U_1073),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1075,U_1073))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,U_1075) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,U_1075)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1074,U_1073),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1075,U_1073)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1073,U_1075)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1073,U_1074) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
( ! [U_1075,U_1073,U_1074] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1074,U_1073),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1075,U_1073))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,U_1075)
| ~ sP115(U_1075,U_1073,U_1074) )
& ! [U_1075,U_1073,U_1074] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,U_1075)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1074,U_1073),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1075,U_1073))
| ~ sP115(U_1075,U_1073,U_1074) )
& ! [U_1075,U_1073,U_1074] :
( sP115(U_1075,U_1073,U_1074)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1073,U_1075)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1073,U_1074) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_346_2]) ).
cnf(f_346_4,plain,
( sP115(U_1075,U_1073,U_1074)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1073,U_1075)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1073,U_1074) ),
inference(clausify,[status(thm)],[f_346_3]) ).
cnf(f_346_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,U_1075)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1074,U_1073),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1075,U_1073))
| ~ sP115(U_1075,U_1073,U_1074) ),
inference(clausify,[status(thm)],[f_346_3]) ).
cnf(f_346_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1074,U_1073),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1075,U_1073))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,U_1075)
| ~ sP115(U_1075,U_1073,U_1074) ),
inference(clausify,[status(thm)],[f_346_3]) ).
fof(f_347_1,plain,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).
fof(f_347_2,plain,
! [U_1078,U_1077,U_1076] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1076,U_1078),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1077,U_1078))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1078,U_1076)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1076,U_1077) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_1077,U_1078,U_1076] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1076,U_1078),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1077,U_1078))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1078,U_1076)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1076,U_1077) ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1076,U_1078),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1077,U_1078))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1078,U_1076)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1076,U_1077) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| V_m = V_n
| ~ 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_348_2,plain,
! [U_1080,U_1079] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1079,U_1080)
| U_1079 = U_1080
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1079,U_1080) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
! [U_1080,U_1079] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1079,U_1080)
| U_1079 = U_1080
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1079,U_1080) ),
inference(definitional_conversion,[status(esa)],[f_348_2]) ).
cnf(f_348_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1079,U_1080)
| U_1079 = U_1080
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1079,U_1080) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_1,plain,
! [V_n,V_m] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_349_2,plain,
! [U_1082,U_1081] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1081,U_1082) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1081,U_1082) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_1082,U_1081] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1081,U_1082) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1081,U_1082) ),
inference(definitional_conversion,[status(esa)],[f_349_2]) ).
cnf(f_349_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1081,U_1082) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1081,U_1082) ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).
fof(f_350_2,plain,
! [U_1084,U_1083] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1083,U_1084)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1083,U_1084) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1084,U_1083] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1083,U_1084)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1083,U_1084) ),
inference(definitional_conversion,[status(esa)],[f_350_2]) ).
cnf(f_350_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1083,U_1084)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1083,U_1084) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).
fof(f_351_2,plain,
! [U_1086,U_1085] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1085,U_1086) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1085,U_1086) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1085,U_1086)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1085,U_1086) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
( ! [U_1090,U_1088] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1088,U_1090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1088,U_1090) )
& ! [U_1089,U_1087] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1087,U_1089)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1087,U_1089) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_351_2]) ).
fof(f_351_4,plain,
( ! [U_1090,U_1088] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1088,U_1090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1088,U_1090) )
& ! [U_1087,U_1089] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1087,U_1089)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1087,U_1089) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_351_3]) ).
cnf(f_351_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1087,U_1089)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1087,U_1089) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_351_4]) ).
cnf(f_351_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1088,U_1090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1088,U_1090) ),
inference(clausify,[status(thm)],[f_351_4]) ).
fof(f_352_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ( V_ma_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).
fof(f_352_2,plain,
! [U_1092,U_1091] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1091,U_1092)
| ( U_1091 != U_1092
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1091,U_1092) ) )
& ( U_1091 = U_1092
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1091,U_1092)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1091,U_1092) ) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
( ! [U_1096,U_1094] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1094,U_1096)
| ( U_1094 != U_1096
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1094,U_1096) ) )
& ! [U_1095,U_1093] :
( U_1093 = U_1095
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1093,U_1095)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1093,U_1095) ) ),
inference(miniscope,[status(thm)],[f_352_2]) ).
fof(f_352_4,plain,
( ! [U_1096,U_1094] :
( U_1094 != U_1096
| ~ sP116(U_1096,U_1094) )
& ! [U_1096,U_1094] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1094,U_1096)
| ~ sP116(U_1096,U_1094) )
& ! [U_1096,U_1094] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1094,U_1096)
| sP116(U_1096,U_1094) )
& ! [U_1093,U_1095] :
( U_1093 = U_1095
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1093,U_1095)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1093,U_1095) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_352_3]) ).
cnf(f_352_5,plain,
( U_1093 = U_1095
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1093,U_1095)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_352_4]) ).
cnf(f_352_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1094,U_1096)
| sP116(U_1096,U_1094) ),
inference(clausify,[status(thm)],[f_352_4]) ).
cnf(f_352_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1094,U_1096)
| ~ sP116(U_1096,U_1094) ),
inference(clausify,[status(thm)],[f_352_4]) ).
cnf(f_352_8,plain,
( U_1094 != U_1096
| ~ sP116(U_1096,U_1094) ),
inference(clausify,[status(thm)],[f_352_4]) ).
fof(f_353_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| V_ma_2 = V_n_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( ( V_ma_2 != V_n_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).
fof(f_353_2,plain,
! [U_1098,U_1097] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1097,U_1098)
| U_1097 = U_1098
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1097,U_1098) )
& ( ( U_1097 != U_1098
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1097,U_1098) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1097,U_1098) ) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
( ! [U_1102,U_1100] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1100,U_1102)
| U_1100 = U_1102
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1100,U_1102) )
& ! [U_1101,U_1099] :
( ( U_1099 != U_1101
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1099,U_1101) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1099,U_1101) ) ),
inference(miniscope,[status(thm)],[f_353_2]) ).
fof(f_353_4,plain,
( ! [U_1101,U_1099] :
( U_1099 != U_1101
| ~ sP117(U_1101,U_1099) )
& ! [U_1101,U_1099] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1099,U_1101)
| ~ sP117(U_1101,U_1099) )
& ! [U_1100,U_1102] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1100,U_1102)
| U_1100 = U_1102
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1100,U_1102) )
& ! [U_1101,U_1099] :
( sP117(U_1101,U_1099)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1099,U_1101) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_353_3]) ).
cnf(f_353_5,plain,
( sP117(U_1101,U_1099)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1099,U_1101) ),
inference(clausify,[status(thm)],[f_353_4]) ).
cnf(f_353_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1100,U_1102)
| U_1100 = U_1102
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1100,U_1102) ),
inference(clausify,[status(thm)],[f_353_4]) ).
cnf(f_353_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1099,U_1101)
| ~ sP117(U_1101,U_1099) ),
inference(clausify,[status(thm)],[f_353_4]) ).
cnf(f_353_8,plain,
( U_1099 != U_1101
| ~ sP117(U_1101,U_1099) ),
inference(clausify,[status(thm)],[f_353_4]) ).
fof(f_354_1,plain,
! [V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = 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_354_2,plain,
! [U_1104,U_1103] :
( c_Groups_Ominus__class_Ominus(U_1103,c_Groups_Ozero__class_Ozero(U_1103),U_1104) = c_Groups_Ouminus__class_Ouminus(U_1103,U_1104)
| ~ class_Groups_Ogroup__add(U_1103) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_1103,U_1104] :
( c_Groups_Ominus__class_Ominus(U_1103,c_Groups_Ozero__class_Ozero(U_1103),U_1104) = c_Groups_Ouminus__class_Ouminus(U_1103,U_1104)
| ~ class_Groups_Ogroup__add(U_1103) ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( c_Groups_Ominus__class_Ominus(U_1103,c_Groups_Ozero__class_Ozero(U_1103),U_1104) = c_Groups_Ouminus__class_Ouminus(U_1103,U_1104)
| ~ class_Groups_Ogroup__add(U_1103) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [V_P_2,V_n_2,V_ma_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
& V_ma_2 = V_n_2 )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_355_2,plain,
! [U_1107,U_1106,U_1105] :
( hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| ( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1106,U_1105) )
| ( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
& U_1105 = U_1106 )
| ( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1105,U_1106) ) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
( ! [U_1105,U_1106,U_1107] :
( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| ~ sP120(U_1105,U_1106,U_1107) )
& ! [U_1105,U_1106,U_1107] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1106,U_1105)
| ~ sP120(U_1105,U_1106,U_1107) )
& ! [U_1105,U_1106,U_1107] :
( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| ~ sP119(U_1105,U_1106,U_1107) )
& ! [U_1105,U_1106,U_1107] :
( U_1105 = U_1106
| ~ sP119(U_1105,U_1106,U_1107) )
& ! [U_1105,U_1106,U_1107] :
( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| ~ sP118(U_1105,U_1106,U_1107) )
& ! [U_1105,U_1106,U_1107] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1105,U_1106)
| ~ sP118(U_1105,U_1106,U_1107) )
& ! [U_1105,U_1106,U_1107] :
( hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| sP120(U_1105,U_1106,U_1107)
| sP119(U_1105,U_1106,U_1107)
| sP118(U_1105,U_1106,U_1107) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118,sP119,sP120])],[f_355_2]) ).
cnf(f_355_4,plain,
( hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| sP120(U_1105,U_1106,U_1107)
| sP119(U_1105,U_1106,U_1107)
| sP118(U_1105,U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1105,U_1106)
| ~ sP118(U_1105,U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_6,plain,
( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| ~ sP118(U_1105,U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_7,plain,
( U_1105 = U_1106
| ~ sP119(U_1105,U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_8,plain,
( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| ~ sP119(U_1105,U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1106,U_1105)
| ~ sP120(U_1105,U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_10,plain,
( ~ hBOOL(hAPP(hAPP(U_1107,U_1106),U_1105))
| ~ sP120(U_1105,U_1106,U_1107) ),
inference(clausify,[status(thm)],[f_355_3]) ).
fof(f_356_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).
fof(f_356_2,plain,
! [U_1110,U_1109,U_1108] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1110,U_1109),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1110,U_1108))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1108,U_1110)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1108,U_1109) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
! [U_1110,U_1108,U_1109] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1110,U_1109),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1110,U_1108))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1108,U_1110)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1108,U_1109) ),
inference(definitional_conversion,[status(esa)],[f_356_2]) ).
cnf(f_356_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1110,U_1109),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1110,U_1108))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1108,U_1110)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1108,U_1109) ),
inference(clausify,[status(thm)],[f_356_3]) ).
fof(f_357_1,plain,
! [V_n,V_k,V_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).
fof(f_357_2,plain,
! [U_1113,U_1112,U_1111] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1111,U_1113),U_1112)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1111,U_1112) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
! [U_1112,U_1113,U_1111] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1111,U_1113),U_1112)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1111,U_1112) ),
inference(definitional_conversion,[status(esa)],[f_357_2]) ).
cnf(f_357_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1111,U_1113),U_1112)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1111,U_1112) ),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_1,plain,
! [V_t,V_s] :
( V_s != V_t
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).
fof(f_358_2,plain,
! [U_1115,U_1114] :
( U_1114 != U_1115
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1114,U_1115) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_1115,U_1114] :
( U_1114 != U_1115
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1114,U_1115) ),
inference(definitional_conversion,[status(esa)],[f_358_2]) ).
cnf(f_358_4,plain,
( U_1114 != U_1115
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1114,U_1115) ),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_1,plain,
! [V_m,V_n] :
( V_m != V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).
fof(f_359_2,plain,
! [U_1117,U_1116] :
( U_1117 != U_1116
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116,U_1117) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_1117,U_1116] :
( U_1117 != U_1116
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116,U_1117) ),
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
( U_1117 != U_1116
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116,U_1117) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).
fof(f_360_2,plain,
! [U_1118] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1118,U_1118),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_1118] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1118,U_1118),
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1118,U_1118),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)
| 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_361_2,plain,
! [U_1120,U_1119] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1120,U_1119)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1119,U_1120)
| U_1119 = U_1120 ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_1119,U_1120] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1120,U_1119)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1119,U_1120)
| U_1119 = U_1120 ),
inference(definitional_conversion,[status(esa)],[f_361_2]) ).
cnf(f_361_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1120,U_1119)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1119,U_1120)
| U_1119 = U_1120 ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_n_2,V_ma_2] :
( ( V_ma_2 != V_n_2
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| V_ma_2 = V_n_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).
fof(f_362_2,plain,
! [U_1122,U_1121] :
( ( U_1121 != U_1122
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1122,U_1121)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1121,U_1122) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1122,U_1121)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1121,U_1122)
| U_1121 = U_1122 ) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
( ! [U_1126,U_1124] :
( U_1124 != U_1126
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1126,U_1124)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1124,U_1126) ) )
& ! [U_1125,U_1123] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1125,U_1123)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1123,U_1125)
| U_1123 = U_1125 ) ),
inference(miniscope,[status(thm)],[f_362_2]) ).
fof(f_362_4,plain,
( ! [U_1126,U_1124] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1126,U_1124)
| ~ sP121(U_1126,U_1124) )
& ! [U_1126,U_1124] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1124,U_1126)
| ~ sP121(U_1126,U_1124) )
& ! [U_1126,U_1124] :
( U_1124 != U_1126
| sP121(U_1126,U_1124) )
& ! [U_1123,U_1125] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1125,U_1123)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1123,U_1125)
| U_1123 = U_1125 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_362_3]) ).
cnf(f_362_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1125,U_1123)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1123,U_1125)
| U_1123 = U_1125 ),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_6,plain,
( U_1124 != U_1126
| sP121(U_1126,U_1124) ),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1124,U_1126)
| ~ sP121(U_1126,U_1124) ),
inference(clausify,[status(thm)],[f_362_4]) ).
cnf(f_362_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1126,U_1124)
| ~ sP121(U_1126,U_1124) ),
inference(clausify,[status(thm)],[f_362_4]) ).
fof(f_363_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).
fof(f_363_2,plain,
! [U_1127] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1127,U_1127),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
! [U_1127] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1127,U_1127),
inference(definitional_conversion,[status(esa)],[f_363_2]) ).
cnf(f_363_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1127,U_1127),
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).
fof(f_364_2,plain,
! [U_1130,U_1129,U_1128] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128,U_1130)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1128,U_1129),U_1130) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
! [U_1130,U_1129,U_1128] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128,U_1130)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1128,U_1129),U_1130) ),
inference(definitional_conversion,[status(esa)],[f_364_2]) ).
cnf(f_364_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128,U_1130)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1128,U_1129),U_1130) ),
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [V_n,V_m,V_l,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) ),
inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).
fof(f_365_2,plain,
! [U_1134,U_1133,U_1132,U_1131] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1133,U_1134)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1133,U_1132) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1131,U_1134)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1131,U_1132) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
! [U_1134,U_1133,U_1131,U_1132] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1133,U_1134)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1133,U_1132) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1131,U_1134)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1131,U_1132) ),
inference(definitional_conversion,[status(esa)],[f_365_2]) ).
cnf(f_365_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1133,U_1134)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1133,U_1132) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1131,U_1134)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1131,U_1132) ),
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).
fof(f_366_2,plain,
! [U_1138,U_1137,U_1136,U_1135] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1135,U_1137),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1136,U_1138))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1137,U_1138)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1135,U_1136) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
! [U_1135,U_1137,U_1138,U_1136] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1135,U_1137),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1136,U_1138))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1137,U_1138)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1135,U_1136) ),
inference(definitional_conversion,[status(esa)],[f_366_2]) ).
cnf(f_366_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1135,U_1137),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1136,U_1138))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1137,U_1138)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1135,U_1136) ),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).
fof(f_367_2,plain,
! [U_1141,U_1140,U_1139] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1139,U_1141),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1140,U_1141))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1139,U_1140) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_1140,U_1139,U_1141] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1139,U_1141),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1140,U_1141))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1139,U_1140) ),
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1139,U_1141),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1140,U_1141))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1139,U_1140) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).
fof(f_368_2,plain,
! [U_1144,U_1143,U_1142] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1144,U_1143))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,U_1143) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_1143,U_1142,U_1144] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1144,U_1143))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,U_1143) ),
inference(definitional_conversion,[status(esa)],[f_368_2]) ).
cnf(f_368_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1144,U_1143))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,U_1143) ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).
fof(f_369_2,plain,
! [U_1147,U_1146,U_1145] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1145,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1146,U_1147))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1145,U_1146) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
! [U_1146,U_1145,U_1147] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1145,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1146,U_1147))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1145,U_1146) ),
inference(definitional_conversion,[status(esa)],[f_369_2]) ).
cnf(f_369_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1145,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1146,U_1147))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1145,U_1146) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_1,plain,
! [V_n,V_m] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).
fof(f_370_2,plain,
! [U_1149,U_1148] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1149,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1148,U_1149)) = U_1148
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1148,U_1149) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
! [U_1149,U_1148] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1149,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1148,U_1149)) = U_1148
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1148,U_1149) ),
inference(definitional_conversion,[status(esa)],[f_370_2]) ).
cnf(f_370_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1149,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1148,U_1149)) = U_1148
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1148,U_1149) ),
inference(clausify,[status(thm)],[f_370_3]) ).
fof(f_371_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).
fof(f_371_2,plain,
! [U_1152,U_1151,U_1150] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1150,U_1151),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1150,U_1152))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1151,U_1152) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1151,U_1152)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1150,U_1151),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1150,U_1152)) ) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
( ! [U_1158,U_1156] :
( ! [U_1154] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1154,U_1156),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1154,U_1158))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1156,U_1158) )
& ! [U_1157,U_1155] :
( ! [U_1153] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1153,U_1155),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1153,U_1157))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1155,U_1157) ) ),
inference(miniscope,[status(thm)],[f_371_2]) ).
fof(f_371_4,plain,
( ! [U_1154,U_1158,U_1156] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1154,U_1156),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1154,U_1158))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1156,U_1158) )
& ! [U_1153,U_1155,U_1157] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1153,U_1155),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1153,U_1157))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1155,U_1157) ) ),
inference(definitional_conversion,[status(esa)],[f_371_3]) ).
cnf(f_371_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1153,U_1155),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1153,U_1157))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1155,U_1157) ),
inference(clausify,[status(thm)],[f_371_4]) ).
cnf(f_371_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1154,U_1156),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1154,U_1158))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1156,U_1158) ),
inference(clausify,[status(thm)],[f_371_4]) ).
fof(f_372_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,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_372_2,plain,
! [U_1161,U_1160,U_1159] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1159,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1160,U_1161))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1159,U_1161),U_1160) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1159,U_1161),U_1160)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1159,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1160,U_1161)) ) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
( ! [U_1167,U_1165,U_1163] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1163,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1165,U_1167))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1163,U_1167),U_1165) )
& ! [U_1166,U_1164,U_1162] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1162,U_1166),U_1164)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1162,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1164,U_1166)) ) ),
inference(miniscope,[status(thm)],[f_372_2]) ).
fof(f_372_4,plain,
( ! [U_1165,U_1163,U_1167] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1163,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1165,U_1167))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1163,U_1167),U_1165) )
& ! [U_1166,U_1164,U_1162] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1162,U_1166),U_1164)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1162,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1164,U_1166)) ) ),
inference(definitional_conversion,[status(esa)],[f_372_3]) ).
cnf(f_372_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1162,U_1166),U_1164)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1162,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1164,U_1166)) ),
inference(clausify,[status(thm)],[f_372_4]) ).
cnf(f_372_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1163,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1165,U_1167))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1163,U_1167),U_1165) ),
inference(clausify,[status(thm)],[f_372_4]) ).
fof(f_373_1,plain,
! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_373_2,plain,
! [U_1169,U_1168] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1168,U_1169),U_1169),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
! [U_1168,U_1169] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1168,U_1169),U_1169),
inference(definitional_conversion,[status(esa)],[f_373_2]) ).
cnf(f_373_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1168,U_1169),U_1169),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_1,plain,
! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_374_2,plain,
! [U_1171,U_1170] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1170,U_1171),U_1170),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
! [U_1171,U_1170] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1170,U_1171),U_1170),
inference(definitional_conversion,[status(esa)],[f_374_2]) ).
cnf(f_374_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1170,U_1171),U_1170),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,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_375_2,plain,
! [U_1174,U_1173,U_1172] :
( c_Groups_Ominus__class_Ominus(U_1172,U_1173,U_1174) = c_Groups_Oplus__class_Oplus(U_1172,U_1173,c_Groups_Ouminus__class_Ouminus(U_1172,U_1174))
| ~ class_Groups_Ogroup__add(U_1172) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
! [U_1172,U_1173,U_1174] :
( c_Groups_Ominus__class_Ominus(U_1172,U_1173,U_1174) = c_Groups_Oplus__class_Oplus(U_1172,U_1173,c_Groups_Ouminus__class_Ouminus(U_1172,U_1174))
| ~ class_Groups_Ogroup__add(U_1172) ),
inference(definitional_conversion,[status(esa)],[f_375_2]) ).
cnf(f_375_4,plain,
( c_Groups_Ominus__class_Ominus(U_1172,U_1173,U_1174) = c_Groups_Oplus__class_Oplus(U_1172,U_1173,c_Groups_Ouminus__class_Ouminus(U_1172,U_1174))
| ~ class_Groups_Ogroup__add(U_1172) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,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_376_2,plain,
! [U_1177,U_1176,U_1175] :
( c_Groups_Ominus__class_Ominus(U_1175,U_1176,U_1177) = c_Groups_Oplus__class_Oplus(U_1175,U_1176,c_Groups_Ouminus__class_Ouminus(U_1175,U_1177))
| ~ class_Groups_Oab__group__add(U_1175) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
! [U_1175,U_1176,U_1177] :
( c_Groups_Ominus__class_Ominus(U_1175,U_1176,U_1177) = c_Groups_Oplus__class_Oplus(U_1175,U_1176,c_Groups_Ouminus__class_Ouminus(U_1175,U_1177))
| ~ class_Groups_Oab__group__add(U_1175) ),
inference(definitional_conversion,[status(esa)],[f_376_2]) ).
cnf(f_376_4,plain,
( c_Groups_Ominus__class_Ominus(U_1175,U_1176,U_1177) = c_Groups_Oplus__class_Oplus(U_1175,U_1176,c_Groups_Ouminus__class_Ouminus(U_1175,U_1177))
| ~ class_Groups_Oab__group__add(U_1175) ),
inference(clausify,[status(thm)],[f_376_3]) ).
fof(f_377_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,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_377_2,plain,
! [U_1180,U_1179,U_1178] :
( c_Groups_Ominus__class_Ominus(U_1178,U_1179,U_1180) = c_Groups_Oplus__class_Oplus(U_1178,U_1179,c_Groups_Ouminus__class_Ouminus(U_1178,U_1180))
| ~ class_Rings_Ocomm__ring__1(U_1178) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
! [U_1178,U_1179,U_1180] :
( c_Groups_Ominus__class_Ominus(U_1178,U_1179,U_1180) = c_Groups_Oplus__class_Oplus(U_1178,U_1179,c_Groups_Ouminus__class_Ouminus(U_1178,U_1180))
| ~ class_Rings_Ocomm__ring__1(U_1178) ),
inference(definitional_conversion,[status(esa)],[f_377_2]) ).
cnf(f_377_4,plain,
( c_Groups_Ominus__class_Ominus(U_1178,U_1179,U_1180) = c_Groups_Oplus__class_Oplus(U_1178,U_1179,c_Groups_Ouminus__class_Ouminus(U_1178,U_1180))
| ~ class_Rings_Ocomm__ring__1(U_1178) ),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = 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_378_2,plain,
! [U_1183,U_1182,U_1181] :
( c_Groups_Ominus__class_Ominus(U_1181,U_1182,c_Groups_Ouminus__class_Ouminus(U_1181,U_1183)) = c_Groups_Oplus__class_Oplus(U_1181,U_1182,U_1183)
| ~ class_Groups_Ogroup__add(U_1181) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_1181,U_1182,U_1183] :
( c_Groups_Ominus__class_Ominus(U_1181,U_1182,c_Groups_Ouminus__class_Ouminus(U_1181,U_1183)) = c_Groups_Oplus__class_Oplus(U_1181,U_1182,U_1183)
| ~ class_Groups_Ogroup__add(U_1181) ),
inference(definitional_conversion,[status(esa)],[f_378_2]) ).
cnf(f_378_4,plain,
( c_Groups_Ominus__class_Ominus(U_1181,U_1182,c_Groups_Ouminus__class_Ouminus(U_1181,U_1183)) = c_Groups_Oplus__class_Oplus(U_1181,U_1182,U_1183)
| ~ class_Groups_Ogroup__add(U_1181) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__diff]) ).
fof(f_379_2,plain,
! [U_1187,U_1186,U_1185,U_1184] :
( hAPP(c_Polynomial_Opoly(U_1184,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1184),U_1185,U_1186)),U_1187) = c_Groups_Ominus__class_Ominus(U_1184,hAPP(c_Polynomial_Opoly(U_1184,U_1185),U_1187),hAPP(c_Polynomial_Opoly(U_1184,U_1186),U_1187))
| ~ class_Rings_Ocomm__ring(U_1184) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1184,U_1185,U_1186,U_1187] :
( hAPP(c_Polynomial_Opoly(U_1184,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1184),U_1185,U_1186)),U_1187) = c_Groups_Ominus__class_Ominus(U_1184,hAPP(c_Polynomial_Opoly(U_1184,U_1185),U_1187),hAPP(c_Polynomial_Opoly(U_1184,U_1186),U_1187))
| ~ class_Rings_Ocomm__ring(U_1184) ),
inference(definitional_conversion,[status(esa)],[f_379_2]) ).
cnf(f_379_4,plain,
( hAPP(c_Polynomial_Opoly(U_1184,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1184),U_1185,U_1186)),U_1187) = c_Groups_Ominus__class_Ominus(U_1184,hAPP(c_Polynomial_Opoly(U_1184,U_1185),U_1187),hAPP(c_Polynomial_Opoly(U_1184,U_1186),U_1187))
| ~ class_Rings_Ocomm__ring(U_1184) ),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_1,plain,
! [V_x,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__minus]) ).
fof(f_380_2,plain,
! [U_1190,U_1189,U_1188] :
( hAPP(c_Polynomial_Opoly(U_1188,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1188),U_1189)),U_1190) = c_Groups_Ouminus__class_Ouminus(U_1188,hAPP(c_Polynomial_Opoly(U_1188,U_1189),U_1190))
| ~ class_Rings_Ocomm__ring(U_1188) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
! [U_1188,U_1189,U_1190] :
( hAPP(c_Polynomial_Opoly(U_1188,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1188),U_1189)),U_1190) = c_Groups_Ouminus__class_Ouminus(U_1188,hAPP(c_Polynomial_Opoly(U_1188,U_1189),U_1190))
| ~ class_Rings_Ocomm__ring(U_1188) ),
inference(definitional_conversion,[status(esa)],[f_380_2]) ).
cnf(f_380_4,plain,
( hAPP(c_Polynomial_Opoly(U_1188,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1188),U_1189)),U_1190) = c_Groups_Ouminus__class_Ouminus(U_1188,hAPP(c_Polynomial_Opoly(U_1188,U_1189),U_1190))
| ~ class_Rings_Ocomm__ring(U_1188) ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_1,plain,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
inference(fof_nnf,[status(thm)],[fact_minus__real__def]) ).
fof(f_381_2,plain,
! [U_1192,U_1191] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1191,U_1192) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1191,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1192)),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
! [U_1191,U_1192] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1191,U_1192) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1191,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1192)),
inference(definitional_conversion,[status(esa)],[f_381_2]) ).
cnf(f_381_4,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1191,U_1192) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1191,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1192)),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_1,plain,
! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
inference(fof_nnf,[status(thm)],[fact_real__diff__def]) ).
fof(f_382_2,plain,
! [U_1194,U_1193] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1193,U_1194) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1193,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1194)),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_1194,U_1193] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1193,U_1194) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1193,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1194)),
inference(definitional_conversion,[status(esa)],[f_382_2]) ).
cnf(f_382_4,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1193,U_1194) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1193,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1194)),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_1,plain,
! [V_q_2,V_pa_2,T_a] :
( ( ( V_pa_2 = V_q_2
| ? [B_n] : hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),B_n) != hAPP(c_Polynomial_Ocoeff(T_a,V_q_2),B_n) )
& ( ! [B_n] : hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_a,V_q_2),B_n)
| V_pa_2 != V_q_2 ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_expand__poly__eq]) ).
fof(f_383_2,plain,
! [U_1199,U_1198,U_1197] :
( ( ( U_1198 = U_1199
| ? [U_1196] : hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),U_1196) != hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),U_1196) )
& ( ! [U_1195] : hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),U_1195) = hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),U_1195)
| U_1198 != U_1199 ) )
| ~ class_Groups_Ozero(U_1197) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_1199,U_1198,U_1197] :
( ( ( U_1198 = U_1199
| hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),sK18(U_1199,U_1198,U_1197)) != hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),sK18(U_1199,U_1198,U_1197)) )
& ( ! [U_1195] : hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),U_1195) = hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),U_1195)
| U_1198 != U_1199 ) )
| ~ class_Groups_Ozero(U_1197) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_1196,sK18(U_1199,U_1198,U_1197))],[f_383_2]) ).
fof(f_383_4,plain,
( ! [U_1195,U_1197,U_1198,U_1199] :
( U_1198 = U_1199
| hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),sK18(U_1199,U_1198,U_1197)) != hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),sK18(U_1199,U_1198,U_1197))
| ~ sP122(U_1195,U_1197,U_1198,U_1199) )
& ! [U_1195,U_1197,U_1198,U_1199] :
( hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),U_1195) = hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),U_1195)
| U_1198 != U_1199
| ~ sP122(U_1195,U_1197,U_1198,U_1199) )
& ! [U_1195,U_1197,U_1198,U_1199] :
( sP122(U_1195,U_1197,U_1198,U_1199)
| ~ class_Groups_Ozero(U_1197) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_383_3]) ).
cnf(f_383_5,plain,
( sP122(U_1195,U_1197,U_1198,U_1199)
| ~ class_Groups_Ozero(U_1197) ),
inference(clausify,[status(thm)],[f_383_4]) ).
cnf(f_383_6,plain,
( hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),U_1195) = hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),U_1195)
| U_1198 != U_1199
| ~ sP122(U_1195,U_1197,U_1198,U_1199) ),
inference(clausify,[status(thm)],[f_383_4]) ).
cnf(f_383_7,plain,
( U_1198 = U_1199
| hAPP(c_Polynomial_Ocoeff(U_1197,U_1198),sK18(U_1199,U_1198,U_1197)) != hAPP(c_Polynomial_Ocoeff(U_1197,U_1199),sK18(U_1199,U_1198,U_1197))
| ~ sP122(U_1195,U_1197,U_1198,U_1199) ),
inference(clausify,[status(thm)],[f_383_4]) ).
fof(f_384_1,plain,
! [V_n,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__minus]) ).
fof(f_384_2,plain,
! [U_1202,U_1201,U_1200] :
( hAPP(c_Polynomial_Ocoeff(U_1200,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1200),U_1201)),U_1202) = c_Groups_Ouminus__class_Ouminus(U_1200,hAPP(c_Polynomial_Ocoeff(U_1200,U_1201),U_1202))
| ~ class_Groups_Oab__group__add(U_1200) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
! [U_1201,U_1200,U_1202] :
( hAPP(c_Polynomial_Ocoeff(U_1200,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1200),U_1201)),U_1202) = c_Groups_Ouminus__class_Ouminus(U_1200,hAPP(c_Polynomial_Ocoeff(U_1200,U_1201),U_1202))
| ~ class_Groups_Oab__group__add(U_1200) ),
inference(definitional_conversion,[status(esa)],[f_384_2]) ).
cnf(f_384_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1200,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1200),U_1201)),U_1202) = c_Groups_Ouminus__class_Ouminus(U_1200,hAPP(c_Polynomial_Ocoeff(U_1200,U_1201),U_1202))
| ~ class_Groups_Oab__group__add(U_1200) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Polynomial_Ocoeff(T_a,V_x_2) = c_Polynomial_Ocoeff(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Polynomial_Ocoeff(T_a,V_x_2) != c_Polynomial_Ocoeff(T_a,V_y_2) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__inject]) ).
fof(f_385_2,plain,
! [U_1205,U_1204,U_1203] :
( ( ( c_Polynomial_Ocoeff(U_1203,U_1204) = c_Polynomial_Ocoeff(U_1203,U_1205)
| U_1204 != U_1205 )
& ( U_1204 = U_1205
| c_Polynomial_Ocoeff(U_1203,U_1204) != c_Polynomial_Ocoeff(U_1203,U_1205) ) )
| ~ class_Groups_Ozero(U_1203) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
( ! [U_1203,U_1204,U_1205] :
( c_Polynomial_Ocoeff(U_1203,U_1204) = c_Polynomial_Ocoeff(U_1203,U_1205)
| U_1204 != U_1205
| ~ sP123(U_1203,U_1204,U_1205) )
& ! [U_1203,U_1204,U_1205] :
( U_1204 = U_1205
| c_Polynomial_Ocoeff(U_1203,U_1204) != c_Polynomial_Ocoeff(U_1203,U_1205)
| ~ sP123(U_1203,U_1204,U_1205) )
& ! [U_1203,U_1204,U_1205] :
( sP123(U_1203,U_1204,U_1205)
| ~ class_Groups_Ozero(U_1203) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_385_2]) ).
cnf(f_385_4,plain,
( sP123(U_1203,U_1204,U_1205)
| ~ class_Groups_Ozero(U_1203) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_5,plain,
( U_1204 = U_1205
| c_Polynomial_Ocoeff(U_1203,U_1204) != c_Polynomial_Ocoeff(U_1203,U_1205)
| ~ sP123(U_1203,U_1204,U_1205) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_6,plain,
( c_Polynomial_Ocoeff(U_1203,U_1204) = c_Polynomial_Ocoeff(U_1203,U_1205)
| U_1204 != U_1205
| ~ sP123(U_1203,U_1204,U_1205) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_1,plain,
! [V_n,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__diff]) ).
fof(f_386_2,plain,
! [U_1209,U_1208,U_1207,U_1206] :
( hAPP(c_Polynomial_Ocoeff(U_1206,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1206),U_1207,U_1208)),U_1209) = c_Groups_Ominus__class_Ominus(U_1206,hAPP(c_Polynomial_Ocoeff(U_1206,U_1207),U_1209),hAPP(c_Polynomial_Ocoeff(U_1206,U_1208),U_1209))
| ~ class_Groups_Oab__group__add(U_1206) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
! [U_1207,U_1206,U_1208,U_1209] :
( hAPP(c_Polynomial_Ocoeff(U_1206,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1206),U_1207,U_1208)),U_1209) = c_Groups_Ominus__class_Ominus(U_1206,hAPP(c_Polynomial_Ocoeff(U_1206,U_1207),U_1209),hAPP(c_Polynomial_Ocoeff(U_1206,U_1208),U_1209))
| ~ class_Groups_Oab__group__add(U_1206) ),
inference(definitional_conversion,[status(esa)],[f_386_2]) ).
cnf(f_386_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1206,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1206),U_1207,U_1208)),U_1209) = c_Groups_Ominus__class_Ominus(U_1206,hAPP(c_Polynomial_Ocoeff(U_1206,U_1207),U_1209),hAPP(c_Polynomial_Ocoeff(U_1206,U_1208),U_1209))
| ~ class_Groups_Oab__group__add(U_1206) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_1,plain,
! [V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,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_387_2,plain,
! [U_1211,U_1210] :
( c_Groups_Ouminus__class_Ouminus(U_1210,c_Groups_Ouminus__class_Ouminus(U_1210,U_1211)) = U_1211
| ~ class_Groups_Ogroup__add(U_1210) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
! [U_1211,U_1210] :
( c_Groups_Ouminus__class_Ouminus(U_1210,c_Groups_Ouminus__class_Ouminus(U_1210,U_1211)) = U_1211
| ~ class_Groups_Ogroup__add(U_1210) ),
inference(definitional_conversion,[status(esa)],[f_387_2]) ).
cnf(f_387_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1210,c_Groups_Ouminus__class_Ouminus(U_1210,U_1211)) = U_1211
| ~ class_Groups_Ogroup__add(U_1210) ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = 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_388_2,plain,
! [U_1214,U_1213,U_1212] :
( c_Groups_Ouminus__class_Ouminus(U_1212,c_Groups_Ominus__class_Ominus(U_1212,U_1213,U_1214)) = c_Groups_Ominus__class_Ominus(U_1212,U_1214,U_1213)
| ~ class_Groups_Oab__group__add(U_1212) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
! [U_1212,U_1213,U_1214] :
( c_Groups_Ouminus__class_Ouminus(U_1212,c_Groups_Ominus__class_Ominus(U_1212,U_1213,U_1214)) = c_Groups_Ominus__class_Ominus(U_1212,U_1214,U_1213)
| ~ class_Groups_Oab__group__add(U_1212) ),
inference(definitional_conversion,[status(esa)],[f_388_2]) ).
cnf(f_388_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1212,c_Groups_Ominus__class_Ominus(U_1212,U_1213,U_1214)) = c_Groups_Ominus__class_Ominus(U_1212,U_1214,U_1213)
| ~ class_Groups_Oab__group__add(U_1212) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_b_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) )
& ( V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).
fof(f_389_2,plain,
! [U_1217,U_1216,U_1215] :
( ( ( U_1216 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| U_1217 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1216) )
& ( U_1217 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1216)
| U_1216 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1217) ) )
| ~ class_Groups_Ogroup__add(U_1215) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
( ! [U_1215,U_1216,U_1217] :
( U_1216 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| U_1217 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1216)
| ~ sP124(U_1215,U_1216,U_1217) )
& ! [U_1215,U_1216,U_1217] :
( U_1217 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1216)
| U_1216 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| ~ sP124(U_1215,U_1216,U_1217) )
& ! [U_1215,U_1216,U_1217] :
( sP124(U_1215,U_1216,U_1217)
| ~ class_Groups_Ogroup__add(U_1215) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_389_2]) ).
cnf(f_389_4,plain,
( sP124(U_1215,U_1216,U_1217)
| ~ class_Groups_Ogroup__add(U_1215) ),
inference(clausify,[status(thm)],[f_389_3]) ).
cnf(f_389_5,plain,
( U_1217 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1216)
| U_1216 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| ~ sP124(U_1215,U_1216,U_1217) ),
inference(clausify,[status(thm)],[f_389_3]) ).
cnf(f_389_6,plain,
( U_1216 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| U_1217 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1216)
| ~ sP124(U_1215,U_1216,U_1217) ),
inference(clausify,[status(thm)],[f_389_3]) ).
fof(f_390_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) != V_a_2 )
& ( c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != V_b_2 ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).
fof(f_390_2,plain,
! [U_1220,U_1219,U_1218] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1218,U_1219) = U_1220
| c_Groups_Ouminus__class_Ouminus(U_1218,U_1220) != U_1219 )
& ( c_Groups_Ouminus__class_Ouminus(U_1218,U_1220) = U_1219
| c_Groups_Ouminus__class_Ouminus(U_1218,U_1219) != U_1220 ) )
| ~ class_Groups_Ogroup__add(U_1218) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
( ! [U_1220,U_1218,U_1219] :
( c_Groups_Ouminus__class_Ouminus(U_1218,U_1219) = U_1220
| c_Groups_Ouminus__class_Ouminus(U_1218,U_1220) != U_1219
| ~ sP125(U_1220,U_1218,U_1219) )
& ! [U_1220,U_1218,U_1219] :
( c_Groups_Ouminus__class_Ouminus(U_1218,U_1220) = U_1219
| c_Groups_Ouminus__class_Ouminus(U_1218,U_1219) != U_1220
| ~ sP125(U_1220,U_1218,U_1219) )
& ! [U_1220,U_1218,U_1219] :
( sP125(U_1220,U_1218,U_1219)
| ~ class_Groups_Ogroup__add(U_1218) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_390_2]) ).
cnf(f_390_4,plain,
( sP125(U_1220,U_1218,U_1219)
| ~ class_Groups_Ogroup__add(U_1218) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_5,plain,
( c_Groups_Ouminus__class_Ouminus(U_1218,U_1220) = U_1219
| c_Groups_Ouminus__class_Ouminus(U_1218,U_1219) != U_1220
| ~ sP125(U_1220,U_1218,U_1219) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1218,U_1219) = U_1220
| c_Groups_Ouminus__class_Ouminus(U_1218,U_1220) != U_1219
| ~ sP125(U_1220,U_1218,U_1219) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).
fof(f_391_2,plain,
! [U_1223,U_1222,U_1221] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1221,U_1222) = c_Groups_Ouminus__class_Ouminus(U_1221,U_1223)
| U_1222 != U_1223 )
& ( U_1222 = U_1223
| c_Groups_Ouminus__class_Ouminus(U_1221,U_1222) != c_Groups_Ouminus__class_Ouminus(U_1221,U_1223) ) )
| ~ class_Groups_Ogroup__add(U_1221) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
( ! [U_1223,U_1222,U_1221] :
( c_Groups_Ouminus__class_Ouminus(U_1221,U_1222) = c_Groups_Ouminus__class_Ouminus(U_1221,U_1223)
| U_1222 != U_1223
| ~ sP126(U_1223,U_1222,U_1221) )
& ! [U_1223,U_1222,U_1221] :
( U_1222 = U_1223
| c_Groups_Ouminus__class_Ouminus(U_1221,U_1222) != c_Groups_Ouminus__class_Ouminus(U_1221,U_1223)
| ~ sP126(U_1223,U_1222,U_1221) )
& ! [U_1223,U_1222,U_1221] :
( sP126(U_1223,U_1222,U_1221)
| ~ class_Groups_Ogroup__add(U_1221) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_391_2]) ).
cnf(f_391_4,plain,
( sP126(U_1223,U_1222,U_1221)
| ~ class_Groups_Ogroup__add(U_1221) ),
inference(clausify,[status(thm)],[f_391_3]) ).
cnf(f_391_5,plain,
( U_1222 = U_1223
| c_Groups_Ouminus__class_Ouminus(U_1221,U_1222) != c_Groups_Ouminus__class_Ouminus(U_1221,U_1223)
| ~ sP126(U_1223,U_1222,U_1221) ),
inference(clausify,[status(thm)],[f_391_3]) ).
cnf(f_391_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1221,U_1222) = c_Groups_Ouminus__class_Ouminus(U_1221,U_1223)
| U_1222 != U_1223
| ~ sP126(U_1223,U_1222,U_1221) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = V_b_2
| V_ca_2 != V_d_2 )
& ( V_ca_2 = V_d_2
| V_a_2 != V_b_2 ) )
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_392_2,plain,
! [U_1228,U_1227,U_1226,U_1225,U_1224] :
( ( ( U_1225 = U_1226
| U_1227 != U_1228 )
& ( U_1227 = U_1228
| U_1225 != U_1226 ) )
| c_Groups_Ominus__class_Ominus(U_1224,U_1225,U_1226) != c_Groups_Ominus__class_Ominus(U_1224,U_1227,U_1228)
| ~ class_Groups_Oab__group__add(U_1224) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
( ! [U_1227,U_1226,U_1228,U_1225] :
( U_1225 = U_1226
| U_1227 != U_1228
| ~ sP127(U_1227,U_1226,U_1228,U_1225) )
& ! [U_1227,U_1226,U_1228,U_1225] :
( U_1227 = U_1228
| U_1225 != U_1226
| ~ sP127(U_1227,U_1226,U_1228,U_1225) )
& ! [U_1227,U_1226,U_1228,U_1225,U_1224] :
( sP127(U_1227,U_1226,U_1228,U_1225)
| c_Groups_Ominus__class_Ominus(U_1224,U_1225,U_1226) != c_Groups_Ominus__class_Ominus(U_1224,U_1227,U_1228)
| ~ class_Groups_Oab__group__add(U_1224) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_392_2]) ).
cnf(f_392_4,plain,
( sP127(U_1227,U_1226,U_1228,U_1225)
| c_Groups_Ominus__class_Ominus(U_1224,U_1225,U_1226) != c_Groups_Ominus__class_Ominus(U_1224,U_1227,U_1228)
| ~ class_Groups_Oab__group__add(U_1224) ),
inference(clausify,[status(thm)],[f_392_3]) ).
cnf(f_392_5,plain,
( U_1227 = U_1228
| U_1225 != U_1226
| ~ sP127(U_1227,U_1226,U_1228,U_1225) ),
inference(clausify,[status(thm)],[f_392_3]) ).
cnf(f_392_6,plain,
( U_1225 = U_1226
| U_1227 != U_1228
| ~ sP127(U_1227,U_1226,U_1228,U_1225) ),
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2]) ).
fof(f_393_2,plain,
! [U_1231,U_1230,U_1229] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1229,U_1230),c_RealVector_Onorm__class_Onorm(U_1229,U_1231)),c_RealVector_Onorm__class_Onorm(U_1229,c_Groups_Ominus__class_Ominus(U_1229,U_1230,U_1231)))
| ~ class_RealVector_Oreal__normed__vector(U_1229) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
! [U_1229,U_1230,U_1231] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1229,U_1230),c_RealVector_Onorm__class_Onorm(U_1229,U_1231)),c_RealVector_Onorm__class_Onorm(U_1229,c_Groups_Ominus__class_Ominus(U_1229,U_1230,U_1231)))
| ~ class_RealVector_Oreal__normed__vector(U_1229) ),
inference(definitional_conversion,[status(esa)],[f_393_2]) ).
cnf(f_393_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1229,U_1230),c_RealVector_Onorm__class_Onorm(U_1229,U_1231)),c_RealVector_Onorm__class_Onorm(U_1229,c_Groups_Ominus__class_Ominus(U_1229,U_1230,U_1231)))
| ~ class_RealVector_Oreal__normed__vector(U_1229) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_le__refl]) ).
fof(f_394_2,plain,
! [U_1232] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1232,U_1232),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1232] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1232,U_1232),
inference(definitional_conversion,[status(esa)],[f_394_2]) ).
cnf(f_394_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1232,U_1232),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_1,plain,
! [V_m] : 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_395_2,plain,
! [U_1233] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1233,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1233),U_1233)),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_1233] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1233,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1233),U_1233)),
inference(definitional_conversion,[status(esa)],[f_395_2]) ).
cnf(f_395_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1233,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1233),U_1233)),
inference(clausify,[status(thm)],[f_395_3]) ).
fof(f_396_1,plain,
! [V_m] : 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_396_2,plain,
! [U_1234] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),U_1234))),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
! [U_1234] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),U_1234))),
inference(definitional_conversion,[status(esa)],[f_396_2]) ).
cnf(f_396_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1234,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),U_1234))),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_397_2,plain,
! [U_1236,U_1235] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1235,U_1236),U_1235),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
! [U_1236,U_1235] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1235,U_1236),U_1235),
inference(definitional_conversion,[status(esa)],[f_397_2]) ).
cnf(f_397_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1235,U_1236),U_1235),
inference(clausify,[status(thm)],[f_397_3]) ).
fof(f_398_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).
fof(f_398_2,plain,
! [U_1238,U_1237] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1238,U_1237)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1237,U_1238) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
! [U_1238,U_1237] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1238,U_1237)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1237,U_1238) ),
inference(definitional_conversion,[status(esa)],[f_398_2]) ).
cnf(f_398_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1238,U_1237)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1237,U_1238) ),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [V_n,V_m] :
( 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_399_2,plain,
! [U_1240,U_1239] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1239,U_1240)
| U_1239 != U_1240 ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_1240,U_1239] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1239,U_1240)
| U_1239 != U_1240 ),
inference(definitional_conversion,[status(esa)],[f_399_2]) ).
cnf(f_399_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1239,U_1240)
| U_1239 != U_1240 ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
! [V_k,V_j,V_i] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono1]) ).
fof(f_400_2,plain,
! [U_1243,U_1242,U_1241] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1241),U_1243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1242),U_1243))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1241,U_1242) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
! [U_1241,U_1242,U_1243] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1241),U_1243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1242),U_1243))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1241,U_1242) ),
inference(definitional_conversion,[status(esa)],[f_400_2]) ).
cnf(f_400_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1241),U_1243),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1242),U_1243))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1241,U_1242) ),
inference(clausify,[status(thm)],[f_400_3]) ).
fof(f_401_1,plain,
! [V_k,V_j,V_i] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).
fof(f_401_2,plain,
! [U_1246,U_1245,U_1244] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1246),U_1244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1246),U_1245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1244,U_1245) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
! [U_1244,U_1245,U_1246] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1246),U_1244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1246),U_1245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1244,U_1245) ),
inference(definitional_conversion,[status(esa)],[f_401_2]) ).
cnf(f_401_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1246),U_1244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1246),U_1245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1244,U_1245) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).
fof(f_402_2,plain,
! [U_1249,U_1248,U_1247] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1249,U_1248),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1249,U_1247))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1247,U_1248) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
! [U_1247,U_1248,U_1249] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1249,U_1248),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1249,U_1247))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1247,U_1248) ),
inference(definitional_conversion,[status(esa)],[f_402_2]) ).
cnf(f_402_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1249,U_1248),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1249,U_1247))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1247,U_1248) ),
inference(clausify,[status(thm)],[f_402_3]) ).
fof(f_403_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).
fof(f_403_2,plain,
! [U_1252,U_1251,U_1250] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1250,U_1252),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1251,U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1250,U_1251) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
! [U_1250,U_1251,U_1252] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1250,U_1252),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1251,U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1250,U_1251) ),
inference(definitional_conversion,[status(esa)],[f_403_2]) ).
cnf(f_403_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1250,U_1252),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1251,U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1250,U_1251) ),
inference(clausify,[status(thm)],[f_403_3]) ).
fof(f_404_1,plain,
! [V_n,V_i] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).
fof(f_404_2,plain,
! [U_1254,U_1253] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1254,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1254,U_1253)) = U_1253
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1253,U_1254) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
! [U_1253,U_1254] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1254,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1254,U_1253)) = U_1253
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1253,U_1254) ),
inference(definitional_conversion,[status(esa)],[f_404_2]) ).
cnf(f_404_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1254,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1254,U_1253)) = U_1253
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1253,U_1254) ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_le__trans]) ).
fof(f_405_2,plain,
! [U_1257,U_1256,U_1255] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1255,U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1256,U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1255,U_1256) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
! [U_1256,U_1255,U_1257] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1255,U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1256,U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1255,U_1256) ),
inference(definitional_conversion,[status(esa)],[f_405_2]) ).
cnf(f_405_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1255,U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1256,U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1255,U_1256) ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).
fof(f_406_2,plain,
! [U_1259,U_1258] :
( U_1258 = U_1259
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1259,U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1258,U_1259) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
fof(f_406_3,plain,
! [U_1259,U_1258] :
( U_1258 = U_1259
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1259,U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1258,U_1259) ),
inference(definitional_conversion,[status(esa)],[f_406_2]) ).
cnf(f_406_4,plain,
( U_1258 = U_1259
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1259,U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1258,U_1259) ),
inference(clausify,[status(thm)],[f_406_3]) ).
fof(f_407_1,plain,
! [V_l,V_k,V_j,V_i] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono]) ).
fof(f_407_2,plain,
! [U_1263,U_1262,U_1261,U_1260] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1260),U_1262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1261),U_1263))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1262,U_1263)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1260,U_1261) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_1261,U_1260,U_1262,U_1263] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1260),U_1262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1261),U_1263))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1262,U_1263)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1260,U_1261) ),
inference(definitional_conversion,[status(esa)],[f_407_2]) ).
cnf(f_407_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1260),U_1262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1261),U_1263))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1262,U_1263)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1260,U_1261) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).
fof(f_408_2,plain,
! [U_1266,U_1265,U_1264] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1265,U_1264) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1266,U_1264)
| U_1265 != U_1266 )
& ( U_1265 = U_1266
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1265,U_1264) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1266,U_1264) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1264,U_1266)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1264,U_1265) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
( ! [U_1266,U_1264,U_1265] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1265,U_1264) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1266,U_1264)
| U_1265 != U_1266
| ~ sP128(U_1266,U_1264,U_1265) )
& ! [U_1266,U_1264,U_1265] :
( U_1265 = U_1266
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1265,U_1264) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1266,U_1264)
| ~ sP128(U_1266,U_1264,U_1265) )
& ! [U_1266,U_1264,U_1265] :
( sP128(U_1266,U_1264,U_1265)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1264,U_1266)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1264,U_1265) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_408_2]) ).
cnf(f_408_4,plain,
( sP128(U_1266,U_1264,U_1265)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1264,U_1266)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1264,U_1265) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_5,plain,
( U_1265 = U_1266
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1265,U_1264) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1266,U_1264)
| ~ sP128(U_1266,U_1264,U_1265) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1265,U_1264) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1266,U_1264)
| U_1265 != U_1266
| ~ sP128(U_1266,U_1264,U_1265) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_1,plain,
! [V_n,V_m,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ 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_409_2,plain,
! [U_1269,U_1268,U_1267] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1268,U_1267),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1269,U_1267)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1268,U_1269)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1267,U_1269)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1267,U_1268) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
! [U_1268,U_1269,U_1267] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1268,U_1267),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1269,U_1267)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1268,U_1269)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1267,U_1269)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1267,U_1268) ),
inference(definitional_conversion,[status(esa)],[f_409_2]) ).
cnf(f_409_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1268,U_1267),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1269,U_1267)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1268,U_1269)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1267,U_1269)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1267,U_1268) ),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).
fof(f_410_2,plain,
! [U_1272,U_1271,U_1270] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1271,U_1270),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1272,U_1270))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1271,U_1272) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1271,U_1272)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1271,U_1270),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1272,U_1270)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1270,U_1272)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1270,U_1271) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
( ! [U_1272,U_1270,U_1271] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1271,U_1270),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1272,U_1270))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1271,U_1272)
| ~ sP129(U_1272,U_1270,U_1271) )
& ! [U_1272,U_1270,U_1271] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1271,U_1272)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1271,U_1270),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1272,U_1270))
| ~ sP129(U_1272,U_1270,U_1271) )
& ! [U_1272,U_1270,U_1271] :
( sP129(U_1272,U_1270,U_1271)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1270,U_1272)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1270,U_1271) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_410_2]) ).
cnf(f_410_4,plain,
( sP129(U_1272,U_1270,U_1271)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1270,U_1272)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1270,U_1271) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1271,U_1272)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1271,U_1270),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1272,U_1270))
| ~ sP129(U_1272,U_1270,U_1271) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1271,U_1270),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1272,U_1270))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1271,U_1272)
| ~ sP129(U_1272,U_1270,U_1271) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [V_n,V_k,V_m] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leE]) ).
fof(f_411_2,plain,
! [U_1275,U_1274,U_1273] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1274,U_1275)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1273,U_1275) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1273,U_1274),U_1275) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
fof(f_411_3,plain,
( ! [U_1275,U_1273,U_1274] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1274,U_1275)
| ~ sP130(U_1275,U_1273,U_1274) )
& ! [U_1275,U_1273,U_1274] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1273,U_1275)
| ~ sP130(U_1275,U_1273,U_1274) )
& ! [U_1275,U_1273,U_1274] :
( sP130(U_1275,U_1273,U_1274)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1273,U_1274),U_1275) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_411_2]) ).
cnf(f_411_4,plain,
( sP130(U_1275,U_1273,U_1274)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1273,U_1274),U_1275) ),
inference(clausify,[status(thm)],[f_411_3]) ).
cnf(f_411_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1273,U_1275)
| ~ sP130(U_1275,U_1273,U_1274) ),
inference(clausify,[status(thm)],[f_411_3]) ).
cnf(f_411_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1274,U_1275)
| ~ sP130(U_1275,U_1273,U_1274) ),
inference(clausify,[status(thm)],[f_411_3]) ).
fof(f_412_1,plain,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).
fof(f_412_2,plain,
! [U_1278,U_1277,U_1276] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1276,U_1278)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1276,U_1277),U_1278) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
! [U_1277,U_1278,U_1276] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1276,U_1278)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1276,U_1277),U_1278) ),
inference(definitional_conversion,[status(esa)],[f_412_2]) ).
cnf(f_412_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1276,U_1278)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1276,U_1277),U_1278) ),
inference(clausify,[status(thm)],[f_412_3]) ).
fof(f_413_1,plain,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).
fof(f_413_2,plain,
! [U_1281,U_1280,U_1279] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1280,U_1281)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1279,U_1280),U_1281) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
! [U_1281,U_1280] :
( ! [U_1279] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1279,U_1280),U_1281)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1280,U_1281) ),
inference(miniscope,[status(thm)],[f_413_2]) ).
fof(f_413_4,plain,
! [U_1280,U_1279,U_1281] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1279,U_1280),U_1281)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1280,U_1281) ),
inference(definitional_conversion,[status(esa)],[f_413_3]) ).
cnf(f_413_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1279,U_1280),U_1281)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1280,U_1281) ),
inference(clausify,[status(thm)],[f_413_4]) ).
fof(f_414_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).
fof(f_414_2,plain,
! [U_1285,U_1284,U_1283,U_1282] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1282,U_1284),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1283,U_1285))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1284,U_1285)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1282,U_1283) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
! [U_1283,U_1282,U_1284,U_1285] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1282,U_1284),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1283,U_1285))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1284,U_1285)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1282,U_1283) ),
inference(definitional_conversion,[status(esa)],[f_414_2]) ).
cnf(f_414_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1282,U_1284),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1283,U_1285))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1284,U_1285)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1282,U_1283) ),
inference(clausify,[status(thm)],[f_414_3]) ).
fof(f_415_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).
fof(f_415_2,plain,
! [U_1288,U_1287,U_1286] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1287,U_1288),U_1286) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1287,U_1286),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1286,U_1287) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
! [U_1288,U_1286,U_1287] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1287,U_1288),U_1286) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1287,U_1286),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1286,U_1287) ),
inference(definitional_conversion,[status(esa)],[f_415_2]) ).
cnf(f_415_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1287,U_1288),U_1286) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1287,U_1286),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1286,U_1287) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).
fof(f_416_2,plain,
! [U_1291,U_1290,U_1289] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1290,U_1289),U_1291) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1290,U_1291),U_1289)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1289,U_1290) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
! [U_1290,U_1289,U_1291] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1290,U_1289),U_1291) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1290,U_1291),U_1289)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1289,U_1290) ),
inference(definitional_conversion,[status(esa)],[f_416_2]) ).
cnf(f_416_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1290,U_1289),U_1291) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1290,U_1291),U_1289)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1289,U_1290) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).
fof(f_417_2,plain,
! [U_1294,U_1293,U_1292] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1294,U_1293),U_1292) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1294,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1293,U_1292))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1292,U_1293) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
! [U_1293,U_1292,U_1294] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1294,U_1293),U_1292) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1294,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1293,U_1292))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1292,U_1293) ),
inference(definitional_conversion,[status(esa)],[f_417_2]) ).
cnf(f_417_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1294,U_1293),U_1292) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1294,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1293,U_1292))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1292,U_1293) ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
| V_j_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) )
& ( V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) != V_k_2 ) )
| ~ 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_418_2,plain,
! [U_1297,U_1296,U_1295] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1296,U_1295) = U_1297
| U_1296 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1297,U_1295) )
& ( U_1296 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1297,U_1295)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1296,U_1295) != U_1297 ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1295,U_1296) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
( ! [U_1295,U_1296,U_1297] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1296,U_1295) = U_1297
| U_1296 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1297,U_1295)
| ~ sP131(U_1295,U_1296,U_1297) )
& ! [U_1295,U_1296,U_1297] :
( U_1296 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1297,U_1295)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1296,U_1295) != U_1297
| ~ sP131(U_1295,U_1296,U_1297) )
& ! [U_1295,U_1296,U_1297] :
( sP131(U_1295,U_1296,U_1297)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1295,U_1296) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_418_2]) ).
cnf(f_418_4,plain,
( sP131(U_1295,U_1296,U_1297)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1295,U_1296) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_5,plain,
( U_1296 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1297,U_1295)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1296,U_1295) != U_1297
| ~ sP131(U_1295,U_1296,U_1297) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1296,U_1295) = U_1297
| U_1296 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1297,U_1295)
| ~ sP131(U_1295,U_1296,U_1297) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_1,plain,
! [V_m,V_n] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m
| ~ 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_419_2,plain,
! [U_1299,U_1298] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1299,U_1298),U_1298) = U_1299
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1298,U_1299) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
fof(f_419_3,plain,
! [U_1298,U_1299] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1299,U_1298),U_1298) = U_1299
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1298,U_1299) ),
inference(definitional_conversion,[status(esa)],[f_419_2]) ).
cnf(f_419_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1299,U_1298),U_1298) = U_1299
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1298,U_1299) ),
inference(clausify,[status(thm)],[f_419_3]) ).
fof(f_420_1,plain,
! [V_i_2,V_j_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) )
| ~ 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_420_2,plain,
! [U_1302,U_1301,U_1300] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1302,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1301,U_1300))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1300),U_1301) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1300),U_1301)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1302,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1301,U_1300)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1300,U_1301) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
( ! [U_1301,U_1300,U_1302] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1302,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1301,U_1300))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1300),U_1301)
| ~ sP132(U_1301,U_1300,U_1302) )
& ! [U_1301,U_1300,U_1302] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1300),U_1301)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1302,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1301,U_1300))
| ~ sP132(U_1301,U_1300,U_1302) )
& ! [U_1301,U_1300,U_1302] :
( sP132(U_1301,U_1300,U_1302)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1300,U_1301) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_420_2]) ).
cnf(f_420_4,plain,
( sP132(U_1301,U_1300,U_1302)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1300,U_1301) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1300),U_1301)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1302,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1301,U_1300))
| ~ sP132(U_1301,U_1300,U_1302) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1302,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1301,U_1300))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1300),U_1301)
| ~ sP132(U_1301,U_1300,U_1302) ),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).
fof(f_421_2,plain,
! [U_1305,U_1304,U_1303] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1304,U_1303)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1304),U_1303)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1303,U_1304) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
! [U_1305,U_1303,U_1304] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1304,U_1303)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1304),U_1303)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1303,U_1304) ),
inference(definitional_conversion,[status(esa)],[f_421_2]) ).
cnf(f_421_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1304,U_1303)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1304),U_1303)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1303,U_1304) ),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_1,plain,
! [V_m,V_n] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| ~ 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_422_2,plain,
! [U_1307,U_1306] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1307,U_1306)) = U_1307
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1306,U_1307) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
! [U_1307,U_1306] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1307,U_1306)) = U_1307
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1306,U_1307) ),
inference(definitional_conversion,[status(esa)],[f_422_2]) ).
cnf(f_422_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1307,U_1306)) = U_1307
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1306,U_1307) ),
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).
fof(f_423_2,plain,
! [U_1310,U_1309,U_1308] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1308,U_1310),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1310))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1308,U_1309) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
! [U_1309,U_1308,U_1310] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1308,U_1310),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1310))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1308,U_1309) ),
inference(definitional_conversion,[status(esa)],[f_423_2]) ).
cnf(f_423_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1308,U_1310),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1310))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1308,U_1309) ),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_1,plain,
! [V_m,V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).
fof(f_424_2,plain,
! [U_1313,U_1312,U_1311] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1313,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1312,U_1313),U_1311))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1311,U_1312) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
! [U_1311,U_1312,U_1313] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1313,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1312,U_1313),U_1311))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1311,U_1312) ),
inference(definitional_conversion,[status(esa)],[f_424_2]) ).
cnf(f_424_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1313,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1312,U_1313),U_1311))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1311,U_1312) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).
fof(f_425_2,plain,
! [U_1316,U_1315,U_1314] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1314,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1315))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1314,U_1315) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
! [U_1314,U_1315,U_1316] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1314,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1315))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1314,U_1315) ),
inference(definitional_conversion,[status(esa)],[f_425_2]) ).
cnf(f_425_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1314,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1315))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1314,U_1315) ),
inference(clausify,[status(thm)],[f_425_3]) ).
fof(f_426_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).
fof(f_426_2,plain,
! [U_1319,U_1318,U_1317] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1317,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1318,U_1319))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1317,U_1318) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
! [U_1318,U_1317,U_1319] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1317,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1318,U_1319))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1317,U_1318) ),
inference(definitional_conversion,[status(esa)],[f_426_2]) ).
cnf(f_426_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1317,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1318,U_1319))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1317,U_1318) ),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).
fof(f_427_2,plain,
! [U_1322,U_1321,U_1320] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1320,U_1321),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1320,U_1322))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1321,U_1322) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1321,U_1322)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1320,U_1321),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1320,U_1322)) ) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
( ! [U_1328,U_1326] :
( ! [U_1324] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1326),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1328))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1326,U_1328) )
& ! [U_1327,U_1325] :
( ! [U_1323] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1325),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1327))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1325,U_1327) ) ),
inference(miniscope,[status(thm)],[f_427_2]) ).
fof(f_427_4,plain,
( ! [U_1326,U_1324,U_1328] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1326),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1328))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1326,U_1328) )
& ! [U_1323,U_1325,U_1327] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1325),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1327))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1325,U_1327) ) ),
inference(definitional_conversion,[status(esa)],[f_427_3]) ).
cnf(f_427_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1325),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1327))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1325,U_1327) ),
inference(clausify,[status(thm)],[f_427_4]) ).
cnf(f_427_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1326),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1328))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1326,U_1328) ),
inference(clausify,[status(thm)],[f_427_4]) ).
fof(f_428_1,plain,
! [V_i_2,V_k_2,V_j_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_428_2,plain,
! [U_1331,U_1330,U_1329] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1329,U_1330),U_1331)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1329,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1331,U_1330)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1329,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1331,U_1330))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1329,U_1330),U_1331) ) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
( ! [U_1337,U_1335,U_1333] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1333,U_1335),U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1337,U_1335)) )
& ! [U_1336,U_1334,U_1332] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1332,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1336,U_1334))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1332,U_1334),U_1336) ) ),
inference(miniscope,[status(thm)],[f_428_2]) ).
fof(f_428_4,plain,
( ! [U_1335,U_1333,U_1337] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1333,U_1335),U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1337,U_1335)) )
& ! [U_1332,U_1334,U_1336] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1332,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1336,U_1334))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1332,U_1334),U_1336) ) ),
inference(definitional_conversion,[status(esa)],[f_428_3]) ).
cnf(f_428_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1332,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1336,U_1334))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1332,U_1334),U_1336) ),
inference(clausify,[status(thm)],[f_428_4]) ).
cnf(f_428_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1333,U_1335),U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1337,U_1335)) ),
inference(clausify,[status(thm)],[f_428_4]) ).
fof(f_429_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).
fof(f_429_2,plain,
! [U_1340,U_1339,U_1338] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1340,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1339,U_1338)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1340,U_1338),U_1339)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1338,U_1339) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_1340,U_1338,U_1339] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1340,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1339,U_1338)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1340,U_1338),U_1339)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1338,U_1339) ),
inference(definitional_conversion,[status(esa)],[f_429_2]) ).
cnf(f_429_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1340,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1339,U_1338)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1340,U_1338),U_1339)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1338,U_1339) ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ! [B_k] : V_n_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) )
& ( ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).
fof(f_430_2,plain,
! [U_1344,U_1343] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1343,U_1344)
| ! [U_1342] : U_1344 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1343,U_1342) )
& ( ? [U_1341] : U_1344 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1343,U_1341)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1343,U_1344) ) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
( ! [U_1348,U_1346] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1346,U_1348)
| ! [U_1342] : U_1348 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1346,U_1342) )
& ! [U_1347,U_1345] :
( ? [U_1341] : U_1347 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1345,U_1341)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1345,U_1347) ) ),
inference(miniscope,[status(thm)],[f_430_2]) ).
fof(f_430_4,plain,
( ! [U_1348,U_1346] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1346,U_1348)
| ! [U_1342] : U_1348 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1346,U_1342) )
& ! [U_1347,U_1345] :
( U_1347 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1345,sK19(U_1347,U_1345))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1345,U_1347) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1341,sK19(U_1347,U_1345))],[f_430_3]) ).
fof(f_430_5,plain,
( ! [U_1348,U_1342,U_1346] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1346,U_1348)
| U_1348 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1346,U_1342) )
& ! [U_1345,U_1347] :
( U_1347 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1345,sK19(U_1347,U_1345))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1345,U_1347) ) ),
inference(definitional_conversion,[status(esa)],[f_430_4]) ).
cnf(f_430_6,plain,
( U_1347 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1345,sK19(U_1347,U_1345))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1345,U_1347) ),
inference(clausify,[status(thm)],[f_430_5]) ).
cnf(f_430_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1346,U_1348)
| U_1348 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1346,U_1342) ),
inference(clausify,[status(thm)],[f_430_5]) ).
fof(f_431_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
| ! [B_n] : V_l_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) )
& ( ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__ex__iff]) ).
fof(f_431_2,plain,
! [U_1352,U_1351] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1351,U_1352)
| ! [U_1350] : U_1352 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1351,U_1350) )
& ( ? [U_1349] : U_1352 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1351,U_1349)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1351,U_1352) ) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
( ! [U_1356,U_1354] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1354,U_1356)
| ! [U_1350] : U_1356 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1354,U_1350) )
& ! [U_1355,U_1353] :
( ? [U_1349] : U_1355 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1353,U_1349)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1353,U_1355) ) ),
inference(miniscope,[status(thm)],[f_431_2]) ).
fof(f_431_4,plain,
( ! [U_1356,U_1354] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1354,U_1356)
| ! [U_1350] : U_1356 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1354,U_1350) )
& ! [U_1355,U_1353] :
( U_1355 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1353,sK20(U_1355,U_1353))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1353,U_1355) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1349,sK20(U_1355,U_1353))],[f_431_3]) ).
fof(f_431_5,plain,
( ! [U_1356,U_1350,U_1354] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1354,U_1356)
| U_1356 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1354,U_1350) )
& ! [U_1353,U_1355] :
( U_1355 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1353,sK20(U_1355,U_1353))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1353,U_1355) ) ),
inference(definitional_conversion,[status(esa)],[f_431_4]) ).
cnf(f_431_6,plain,
( U_1355 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1353,sK20(U_1355,U_1353))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1353,U_1355) ),
inference(clausify,[status(thm)],[f_431_5]) ).
cnf(f_431_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1354,U_1356)
| U_1356 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1354,U_1350) ),
inference(clausify,[status(thm)],[f_431_5]) ).
fof(f_432_1,plain,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
inference(fof_nnf,[status(thm)],[fact_le__add1]) ).
fof(f_432_2,plain,
! [U_1358,U_1357] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1357,U_1358)),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_1358,U_1357] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1357,U_1358)),
inference(definitional_conversion,[status(esa)],[f_432_2]) ).
cnf(f_432_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1357,U_1358)),
inference(clausify,[status(thm)],[f_432_3]) ).
fof(f_433_1,plain,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_le__add2]) ).
fof(f_433_2,plain,
! [U_1360,U_1359] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1359,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1360,U_1359)),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_1360,U_1359] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1359,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1360,U_1359)),
inference(definitional_conversion,[status(esa)],[f_433_2]) ).
cnf(f_433_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1359,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1360,U_1359)),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_1,plain,
! [V_a,T_a] :
( 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_434_2,plain,
! [U_1362,U_1361] :
( c_Groups_Ominus__class_Ominus(U_1361,U_1362,c_Groups_Ozero__class_Ozero(U_1361)) = U_1362
| ~ class_Groups_Ogroup__add(U_1361) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1361,U_1362] :
( c_Groups_Ominus__class_Ominus(U_1361,U_1362,c_Groups_Ozero__class_Ozero(U_1361)) = U_1362
| ~ class_Groups_Ogroup__add(U_1361) ),
inference(definitional_conversion,[status(esa)],[f_434_2]) ).
cnf(f_434_4,plain,
( c_Groups_Ominus__class_Ominus(U_1361,U_1362,c_Groups_Ozero__class_Ozero(U_1361)) = U_1362
| ~ class_Groups_Ogroup__add(U_1361) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_1,plain,
! [V_a,T_a] :
( 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_435_2,plain,
! [U_1364,U_1363] :
( c_Groups_Ominus__class_Ominus(U_1363,U_1364,U_1364) = c_Groups_Ozero__class_Ozero(U_1363)
| ~ class_Groups_Ogroup__add(U_1363) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
! [U_1363,U_1364] :
( c_Groups_Ominus__class_Ominus(U_1363,U_1364,U_1364) = c_Groups_Ozero__class_Ozero(U_1363)
| ~ class_Groups_Ogroup__add(U_1363) ),
inference(definitional_conversion,[status(esa)],[f_435_2]) ).
cnf(f_435_4,plain,
( c_Groups_Ominus__class_Ominus(U_1363,U_1364,U_1364) = c_Groups_Ozero__class_Ozero(U_1363)
| ~ class_Groups_Ogroup__add(U_1363) ),
inference(clausify,[status(thm)],[f_435_3]) ).
fof(f_436_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = V_b_2
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != V_b_2 ) )
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).
fof(f_436_2,plain,
! [U_1367,U_1366,U_1365] :
( ( ( U_1366 = U_1367
| c_Groups_Ominus__class_Ominus(U_1365,U_1366,U_1367) != c_Groups_Ozero__class_Ozero(U_1365) )
& ( c_Groups_Ominus__class_Ominus(U_1365,U_1366,U_1367) = c_Groups_Ozero__class_Ozero(U_1365)
| U_1366 != U_1367 ) )
| ~ class_Groups_Oab__group__add(U_1365) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
( ! [U_1365,U_1366,U_1367] :
( U_1366 = U_1367
| c_Groups_Ominus__class_Ominus(U_1365,U_1366,U_1367) != c_Groups_Ozero__class_Ozero(U_1365)
| ~ sP133(U_1365,U_1366,U_1367) )
& ! [U_1365,U_1366,U_1367] :
( c_Groups_Ominus__class_Ominus(U_1365,U_1366,U_1367) = c_Groups_Ozero__class_Ozero(U_1365)
| U_1366 != U_1367
| ~ sP133(U_1365,U_1366,U_1367) )
& ! [U_1365,U_1366,U_1367] :
( sP133(U_1365,U_1366,U_1367)
| ~ class_Groups_Oab__group__add(U_1365) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_436_2]) ).
cnf(f_436_4,plain,
( sP133(U_1365,U_1366,U_1367)
| ~ class_Groups_Oab__group__add(U_1365) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_5,plain,
( c_Groups_Ominus__class_Ominus(U_1365,U_1366,U_1367) = c_Groups_Ozero__class_Ozero(U_1365)
| U_1366 != U_1367
| ~ sP133(U_1365,U_1366,U_1367) ),
inference(clausify,[status(thm)],[f_436_3]) ).
cnf(f_436_6,plain,
( U_1366 = U_1367
| c_Groups_Ominus__class_Ominus(U_1365,U_1366,U_1367) != c_Groups_Ozero__class_Ozero(U_1365)
| ~ sP133(U_1365,U_1366,U_1367) ),
inference(clausify,[status(thm)],[f_436_3]) ).
fof(f_437_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).
fof(f_437_2,plain,
! [U_1370,U_1369,U_1368] :
( ( ( c_Groups_Ominus__class_Ominus(U_1368,U_1369,U_1370) = c_Groups_Ozero__class_Ozero(U_1368)
| U_1369 != U_1370 )
& ( U_1369 = U_1370
| c_Groups_Ominus__class_Ominus(U_1368,U_1369,U_1370) != c_Groups_Ozero__class_Ozero(U_1368) ) )
| ~ class_Groups_Ogroup__add(U_1368) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
( ! [U_1369,U_1370,U_1368] :
( c_Groups_Ominus__class_Ominus(U_1368,U_1369,U_1370) = c_Groups_Ozero__class_Ozero(U_1368)
| U_1369 != U_1370
| ~ sP134(U_1369,U_1370,U_1368) )
& ! [U_1369,U_1370,U_1368] :
( U_1369 = U_1370
| c_Groups_Ominus__class_Ominus(U_1368,U_1369,U_1370) != c_Groups_Ozero__class_Ozero(U_1368)
| ~ sP134(U_1369,U_1370,U_1368) )
& ! [U_1369,U_1370,U_1368] :
( sP134(U_1369,U_1370,U_1368)
| ~ class_Groups_Ogroup__add(U_1368) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_437_2]) ).
cnf(f_437_4,plain,
( sP134(U_1369,U_1370,U_1368)
| ~ class_Groups_Ogroup__add(U_1368) ),
inference(clausify,[status(thm)],[f_437_3]) ).
cnf(f_437_5,plain,
( U_1369 = U_1370
| c_Groups_Ominus__class_Ominus(U_1368,U_1369,U_1370) != c_Groups_Ozero__class_Ozero(U_1368)
| ~ sP134(U_1369,U_1370,U_1368) ),
inference(clausify,[status(thm)],[f_437_3]) ).
cnf(f_437_6,plain,
( c_Groups_Ominus__class_Ominus(U_1368,U_1369,U_1370) = c_Groups_Ozero__class_Ozero(U_1368)
| U_1369 != U_1370
| ~ sP134(U_1369,U_1370,U_1368) ),
inference(clausify,[status(thm)],[f_437_3]) ).
fof(f_438_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_d_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).
fof(f_438_2,plain,
! [U_1375,U_1374,U_1373,U_1372,U_1371] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1371,U_1372,U_1373)
| ~ c_Orderings_Oord__class_Oless__eq(U_1371,U_1374,U_1375) )
& ( c_Orderings_Oord__class_Oless__eq(U_1371,U_1374,U_1375)
| ~ c_Orderings_Oord__class_Oless__eq(U_1371,U_1372,U_1373) ) )
| c_Groups_Ominus__class_Ominus(U_1371,U_1372,U_1373) != c_Groups_Ominus__class_Ominus(U_1371,U_1374,U_1375)
| ~ class_Groups_Oordered__ab__group__add(U_1371) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
( ! [U_1373,U_1372,U_1374,U_1371,U_1375] :
( c_Orderings_Oord__class_Oless__eq(U_1371,U_1372,U_1373)
| ~ c_Orderings_Oord__class_Oless__eq(U_1371,U_1374,U_1375)
| ~ sP135(U_1373,U_1372,U_1374,U_1371,U_1375) )
& ! [U_1373,U_1372,U_1374,U_1371,U_1375] :
( c_Orderings_Oord__class_Oless__eq(U_1371,U_1374,U_1375)
| ~ c_Orderings_Oord__class_Oless__eq(U_1371,U_1372,U_1373)
| ~ sP135(U_1373,U_1372,U_1374,U_1371,U_1375) )
& ! [U_1373,U_1372,U_1374,U_1371,U_1375] :
( sP135(U_1373,U_1372,U_1374,U_1371,U_1375)
| c_Groups_Ominus__class_Ominus(U_1371,U_1372,U_1373) != c_Groups_Ominus__class_Ominus(U_1371,U_1374,U_1375)
| ~ class_Groups_Oordered__ab__group__add(U_1371) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_438_2]) ).
cnf(f_438_4,plain,
( sP135(U_1373,U_1372,U_1374,U_1371,U_1375)
| c_Groups_Ominus__class_Ominus(U_1371,U_1372,U_1373) != c_Groups_Ominus__class_Ominus(U_1371,U_1374,U_1375)
| ~ class_Groups_Oordered__ab__group__add(U_1371) ),
inference(clausify,[status(thm)],[f_438_3]) ).
cnf(f_438_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1371,U_1374,U_1375)
| ~ c_Orderings_Oord__class_Oless__eq(U_1371,U_1372,U_1373)
| ~ sP135(U_1373,U_1372,U_1374,U_1371,U_1375) ),
inference(clausify,[status(thm)],[f_438_3]) ).
cnf(f_438_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1371,U_1372,U_1373)
| ~ c_Orderings_Oord__class_Oless__eq(U_1371,U_1374,U_1375)
| ~ sP135(U_1373,U_1372,U_1374,U_1371,U_1375) ),
inference(clausify,[status(thm)],[f_438_3]) ).
fof(f_439_1,plain,
! [T_a] :
( 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_439_2,plain,
! [U_1376] :
( c_Groups_Ouminus__class_Ouminus(U_1376,c_Groups_Ozero__class_Ozero(U_1376)) = c_Groups_Ozero__class_Ozero(U_1376)
| ~ class_Groups_Ogroup__add(U_1376) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
! [U_1376] :
( c_Groups_Ouminus__class_Ouminus(U_1376,c_Groups_Ozero__class_Ozero(U_1376)) = c_Groups_Ozero__class_Ozero(U_1376)
| ~ class_Groups_Ogroup__add(U_1376) ),
inference(definitional_conversion,[status(esa)],[f_439_2]) ).
cnf(f_439_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1376,c_Groups_Ozero__class_Ozero(U_1376)) = c_Groups_Ozero__class_Ozero(U_1376)
| ~ class_Groups_Ogroup__add(U_1376) ),
inference(clausify,[status(thm)],[f_439_3]) ).
fof(f_440_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| c_Groups_Ozero__class_Ozero(T_a) != V_a_2 )
& ( c_Groups_Ozero__class_Ozero(T_a) = V_a_2
| c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).
fof(f_440_2,plain,
! [U_1378,U_1377] :
( ( ( c_Groups_Ozero__class_Ozero(U_1377) = c_Groups_Ouminus__class_Ouminus(U_1377,U_1378)
| c_Groups_Ozero__class_Ozero(U_1377) != U_1378 )
& ( c_Groups_Ozero__class_Ozero(U_1377) = U_1378
| c_Groups_Ozero__class_Ozero(U_1377) != c_Groups_Ouminus__class_Ouminus(U_1377,U_1378) ) )
| ~ class_Groups_Ogroup__add(U_1377) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
( ! [U_1377,U_1378] :
( c_Groups_Ozero__class_Ozero(U_1377) = c_Groups_Ouminus__class_Ouminus(U_1377,U_1378)
| c_Groups_Ozero__class_Ozero(U_1377) != U_1378
| ~ sP136(U_1377,U_1378) )
& ! [U_1377,U_1378] :
( c_Groups_Ozero__class_Ozero(U_1377) = U_1378
| c_Groups_Ozero__class_Ozero(U_1377) != c_Groups_Ouminus__class_Ouminus(U_1377,U_1378)
| ~ sP136(U_1377,U_1378) )
& ! [U_1377,U_1378] :
( sP136(U_1377,U_1378)
| ~ class_Groups_Ogroup__add(U_1377) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_440_2]) ).
cnf(f_440_4,plain,
( sP136(U_1377,U_1378)
| ~ class_Groups_Ogroup__add(U_1377) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_5,plain,
( c_Groups_Ozero__class_Ozero(U_1377) = U_1378
| c_Groups_Ozero__class_Ozero(U_1377) != c_Groups_Ouminus__class_Ouminus(U_1377,U_1378)
| ~ sP136(U_1377,U_1378) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_6,plain,
( c_Groups_Ozero__class_Ozero(U_1377) = c_Groups_Ouminus__class_Ouminus(U_1377,U_1378)
| c_Groups_Ozero__class_Ozero(U_1377) != U_1378
| ~ sP136(U_1377,U_1378) ),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_1,plain,
! [V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).
fof(f_441_2,plain,
! [U_1380,U_1379] :
( ( ( U_1380 = c_Groups_Ouminus__class_Ouminus(U_1379,U_1380)
| U_1380 != c_Groups_Ozero__class_Ozero(U_1379) )
& ( U_1380 = c_Groups_Ozero__class_Ozero(U_1379)
| U_1380 != c_Groups_Ouminus__class_Ouminus(U_1379,U_1380) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1379) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
( ! [U_1380,U_1379] :
( U_1380 = c_Groups_Ouminus__class_Ouminus(U_1379,U_1380)
| U_1380 != c_Groups_Ozero__class_Ozero(U_1379)
| ~ sP137(U_1380,U_1379) )
& ! [U_1380,U_1379] :
( U_1380 = c_Groups_Ozero__class_Ozero(U_1379)
| U_1380 != c_Groups_Ouminus__class_Ouminus(U_1379,U_1380)
| ~ sP137(U_1380,U_1379) )
& ! [U_1380,U_1379] :
( sP137(U_1380,U_1379)
| ~ class_Groups_Olinordered__ab__group__add(U_1379) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_441_2]) ).
cnf(f_441_4,plain,
( sP137(U_1380,U_1379)
| ~ class_Groups_Olinordered__ab__group__add(U_1379) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_5,plain,
( U_1380 = c_Groups_Ozero__class_Ozero(U_1379)
| U_1380 != c_Groups_Ouminus__class_Ouminus(U_1379,U_1380)
| ~ sP137(U_1380,U_1379) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_6,plain,
( U_1380 = c_Groups_Ouminus__class_Ouminus(U_1379,U_1380)
| U_1380 != c_Groups_Ozero__class_Ozero(U_1379)
| ~ sP137(U_1380,U_1379) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).
fof(f_442_2,plain,
! [U_1382,U_1381] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1381,U_1382) = c_Groups_Ozero__class_Ozero(U_1381)
| U_1382 != c_Groups_Ozero__class_Ozero(U_1381) )
& ( U_1382 = c_Groups_Ozero__class_Ozero(U_1381)
| c_Groups_Ouminus__class_Ouminus(U_1381,U_1382) != c_Groups_Ozero__class_Ozero(U_1381) ) )
| ~ class_Groups_Ogroup__add(U_1381) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
( ! [U_1382,U_1381] :
( c_Groups_Ouminus__class_Ouminus(U_1381,U_1382) = c_Groups_Ozero__class_Ozero(U_1381)
| U_1382 != c_Groups_Ozero__class_Ozero(U_1381)
| ~ sP138(U_1382,U_1381) )
& ! [U_1382,U_1381] :
( U_1382 = c_Groups_Ozero__class_Ozero(U_1381)
| c_Groups_Ouminus__class_Ouminus(U_1381,U_1382) != c_Groups_Ozero__class_Ozero(U_1381)
| ~ sP138(U_1382,U_1381) )
& ! [U_1382,U_1381] :
( sP138(U_1382,U_1381)
| ~ class_Groups_Ogroup__add(U_1381) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_442_2]) ).
cnf(f_442_4,plain,
( sP138(U_1382,U_1381)
| ~ class_Groups_Ogroup__add(U_1381) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_5,plain,
( U_1382 = c_Groups_Ozero__class_Ozero(U_1381)
| c_Groups_Ouminus__class_Ouminus(U_1381,U_1382) != c_Groups_Ozero__class_Ozero(U_1381)
| ~ sP138(U_1382,U_1381) ),
inference(clausify,[status(thm)],[f_442_3]) ).
cnf(f_442_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1381,U_1382) = c_Groups_Ozero__class_Ozero(U_1381)
| U_1382 != c_Groups_Ozero__class_Ozero(U_1381)
| ~ sP138(U_1382,U_1381) ),
inference(clausify,[status(thm)],[f_442_3]) ).
fof(f_443_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != V_a_2 ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).
fof(f_443_2,plain,
! [U_1384,U_1383] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1383,U_1384) = U_1384
| U_1384 != c_Groups_Ozero__class_Ozero(U_1383) )
& ( U_1384 = c_Groups_Ozero__class_Ozero(U_1383)
| c_Groups_Ouminus__class_Ouminus(U_1383,U_1384) != U_1384 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1383) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
( ! [U_1384,U_1383] :
( c_Groups_Ouminus__class_Ouminus(U_1383,U_1384) = U_1384
| U_1384 != c_Groups_Ozero__class_Ozero(U_1383)
| ~ sP139(U_1384,U_1383) )
& ! [U_1384,U_1383] :
( U_1384 = c_Groups_Ozero__class_Ozero(U_1383)
| c_Groups_Ouminus__class_Ouminus(U_1383,U_1384) != U_1384
| ~ sP139(U_1384,U_1383) )
& ! [U_1384,U_1383] :
( sP139(U_1384,U_1383)
| ~ class_Groups_Olinordered__ab__group__add(U_1383) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_443_2]) ).
cnf(f_443_4,plain,
( sP139(U_1384,U_1383)
| ~ class_Groups_Olinordered__ab__group__add(U_1383) ),
inference(clausify,[status(thm)],[f_443_3]) ).
cnf(f_443_5,plain,
( U_1384 = c_Groups_Ozero__class_Ozero(U_1383)
| c_Groups_Ouminus__class_Ouminus(U_1383,U_1384) != U_1384
| ~ sP139(U_1384,U_1383) ),
inference(clausify,[status(thm)],[f_443_3]) ).
cnf(f_443_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1383,U_1384) = U_1384
| U_1384 != c_Groups_Ozero__class_Ozero(U_1383)
| ~ sP139(U_1384,U_1383) ),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) )
| c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_444_2,plain,
! [U_1389,U_1388,U_1387,U_1386,U_1385] :
( ( ( c_Orderings_Oord__class_Oless(U_1385,U_1386,U_1387)
| ~ c_Orderings_Oord__class_Oless(U_1385,U_1388,U_1389) )
& ( c_Orderings_Oord__class_Oless(U_1385,U_1388,U_1389)
| ~ c_Orderings_Oord__class_Oless(U_1385,U_1386,U_1387) ) )
| c_Groups_Ominus__class_Ominus(U_1385,U_1386,U_1387) != c_Groups_Ominus__class_Ominus(U_1385,U_1388,U_1389)
| ~ class_Groups_Oordered__ab__group__add(U_1385) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
( ! [U_1388,U_1389,U_1387,U_1386,U_1385] :
( c_Orderings_Oord__class_Oless(U_1385,U_1386,U_1387)
| ~ c_Orderings_Oord__class_Oless(U_1385,U_1388,U_1389)
| ~ sP140(U_1388,U_1389,U_1387,U_1386,U_1385) )
& ! [U_1388,U_1389,U_1387,U_1386,U_1385] :
( c_Orderings_Oord__class_Oless(U_1385,U_1388,U_1389)
| ~ c_Orderings_Oord__class_Oless(U_1385,U_1386,U_1387)
| ~ sP140(U_1388,U_1389,U_1387,U_1386,U_1385) )
& ! [U_1388,U_1389,U_1387,U_1386,U_1385] :
( sP140(U_1388,U_1389,U_1387,U_1386,U_1385)
| c_Groups_Ominus__class_Ominus(U_1385,U_1386,U_1387) != c_Groups_Ominus__class_Ominus(U_1385,U_1388,U_1389)
| ~ class_Groups_Oordered__ab__group__add(U_1385) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_444_2]) ).
cnf(f_444_4,plain,
( sP140(U_1388,U_1389,U_1387,U_1386,U_1385)
| c_Groups_Ominus__class_Ominus(U_1385,U_1386,U_1387) != c_Groups_Ominus__class_Ominus(U_1385,U_1388,U_1389)
| ~ class_Groups_Oordered__ab__group__add(U_1385) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_5,plain,
( c_Orderings_Oord__class_Oless(U_1385,U_1388,U_1389)
| ~ c_Orderings_Oord__class_Oless(U_1385,U_1386,U_1387)
| ~ sP140(U_1388,U_1389,U_1387,U_1386,U_1385) ),
inference(clausify,[status(thm)],[f_444_3]) ).
cnf(f_444_6,plain,
( c_Orderings_Oord__class_Oless(U_1385,U_1386,U_1387)
| ~ c_Orderings_Oord__class_Oless(U_1385,U_1388,U_1389)
| ~ sP140(U_1388,U_1389,U_1387,U_1386,U_1385) ),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
| ~ 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_445_2,plain,
! [U_1392,U_1391,U_1390] :
( c_Orderings_Oord__class_Oless__eq(U_1390,c_Groups_Ouminus__class_Ouminus(U_1390,U_1392),c_Groups_Ouminus__class_Ouminus(U_1390,U_1391))
| ~ c_Orderings_Oord__class_Oless__eq(U_1390,U_1391,U_1392)
| ~ class_Groups_Oordered__ab__group__add(U_1390) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
! [U_1390,U_1391,U_1392] :
( c_Orderings_Oord__class_Oless__eq(U_1390,c_Groups_Ouminus__class_Ouminus(U_1390,U_1392),c_Groups_Ouminus__class_Ouminus(U_1390,U_1391))
| ~ c_Orderings_Oord__class_Oless__eq(U_1390,U_1391,U_1392)
| ~ class_Groups_Oordered__ab__group__add(U_1390) ),
inference(definitional_conversion,[status(esa)],[f_445_2]) ).
cnf(f_445_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1390,c_Groups_Ouminus__class_Ouminus(U_1390,U_1392),c_Groups_Ouminus__class_Ouminus(U_1390,U_1391))
| ~ c_Orderings_Oord__class_Oless__eq(U_1390,U_1391,U_1392)
| ~ class_Groups_Oordered__ab__group__add(U_1390) ),
inference(clausify,[status(thm)],[f_445_3]) ).
fof(f_446_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).
fof(f_446_2,plain,
! [U_1395,U_1394,U_1393] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1393,c_Groups_Ouminus__class_Ouminus(U_1393,U_1394),c_Groups_Ouminus__class_Ouminus(U_1393,U_1395))
| ~ c_Orderings_Oord__class_Oless__eq(U_1393,U_1395,U_1394) )
& ( c_Orderings_Oord__class_Oless__eq(U_1393,U_1395,U_1394)
| ~ c_Orderings_Oord__class_Oless__eq(U_1393,c_Groups_Ouminus__class_Ouminus(U_1393,U_1394),c_Groups_Ouminus__class_Ouminus(U_1393,U_1395)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1393) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
( ! [U_1395,U_1393,U_1394] :
( c_Orderings_Oord__class_Oless__eq(U_1393,c_Groups_Ouminus__class_Ouminus(U_1393,U_1394),c_Groups_Ouminus__class_Ouminus(U_1393,U_1395))
| ~ c_Orderings_Oord__class_Oless__eq(U_1393,U_1395,U_1394)
| ~ sP141(U_1395,U_1393,U_1394) )
& ! [U_1395,U_1393,U_1394] :
( c_Orderings_Oord__class_Oless__eq(U_1393,U_1395,U_1394)
| ~ c_Orderings_Oord__class_Oless__eq(U_1393,c_Groups_Ouminus__class_Ouminus(U_1393,U_1394),c_Groups_Ouminus__class_Ouminus(U_1393,U_1395))
| ~ sP141(U_1395,U_1393,U_1394) )
& ! [U_1395,U_1393,U_1394] :
( sP141(U_1395,U_1393,U_1394)
| ~ class_Groups_Oordered__ab__group__add(U_1393) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_446_2]) ).
cnf(f_446_4,plain,
( sP141(U_1395,U_1393,U_1394)
| ~ class_Groups_Oordered__ab__group__add(U_1393) ),
inference(clausify,[status(thm)],[f_446_3]) ).
cnf(f_446_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1393,U_1395,U_1394)
| ~ c_Orderings_Oord__class_Oless__eq(U_1393,c_Groups_Ouminus__class_Ouminus(U_1393,U_1394),c_Groups_Ouminus__class_Ouminus(U_1393,U_1395))
| ~ sP141(U_1395,U_1393,U_1394) ),
inference(clausify,[status(thm)],[f_446_3]) ).
cnf(f_446_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1393,c_Groups_Ouminus__class_Ouminus(U_1393,U_1394),c_Groups_Ouminus__class_Ouminus(U_1393,U_1395))
| ~ c_Orderings_Oord__class_Oless__eq(U_1393,U_1395,U_1394)
| ~ sP141(U_1395,U_1393,U_1394) ),
inference(clausify,[status(thm)],[f_446_3]) ).
fof(f_447_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).
fof(f_447_2,plain,
! [U_1398,U_1397,U_1396] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1397),U_1398)
| ~ c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1398),U_1397) )
& ( c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1398),U_1397)
| ~ c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1397),U_1398) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1396) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
( ! [U_1397,U_1398,U_1396] :
( c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1397),U_1398)
| ~ c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1398),U_1397)
| ~ sP142(U_1397,U_1398,U_1396) )
& ! [U_1397,U_1398,U_1396] :
( c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1398),U_1397)
| ~ c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1397),U_1398)
| ~ sP142(U_1397,U_1398,U_1396) )
& ! [U_1397,U_1398,U_1396] :
( sP142(U_1397,U_1398,U_1396)
| ~ class_Groups_Oordered__ab__group__add(U_1396) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142])],[f_447_2]) ).
cnf(f_447_4,plain,
( sP142(U_1397,U_1398,U_1396)
| ~ class_Groups_Oordered__ab__group__add(U_1396) ),
inference(clausify,[status(thm)],[f_447_3]) ).
cnf(f_447_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1398),U_1397)
| ~ c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1397),U_1398)
| ~ sP142(U_1397,U_1398,U_1396) ),
inference(clausify,[status(thm)],[f_447_3]) ).
cnf(f_447_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1397),U_1398)
| ~ c_Orderings_Oord__class_Oless__eq(U_1396,c_Groups_Ouminus__class_Ouminus(U_1396,U_1398),U_1397)
| ~ sP142(U_1397,U_1398,U_1396) ),
inference(clausify,[status(thm)],[f_447_3]) ).
fof(f_448_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).
fof(f_448_2,plain,
! [U_1401,U_1400,U_1399] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1399,U_1400,c_Groups_Ouminus__class_Ouminus(U_1399,U_1401))
| ~ c_Orderings_Oord__class_Oless__eq(U_1399,U_1401,c_Groups_Ouminus__class_Ouminus(U_1399,U_1400)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1399,U_1401,c_Groups_Ouminus__class_Ouminus(U_1399,U_1400))
| ~ c_Orderings_Oord__class_Oless__eq(U_1399,U_1400,c_Groups_Ouminus__class_Ouminus(U_1399,U_1401)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1399) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
( ! [U_1401,U_1400,U_1399] :
( c_Orderings_Oord__class_Oless__eq(U_1399,U_1400,c_Groups_Ouminus__class_Ouminus(U_1399,U_1401))
| ~ c_Orderings_Oord__class_Oless__eq(U_1399,U_1401,c_Groups_Ouminus__class_Ouminus(U_1399,U_1400))
| ~ sP143(U_1401,U_1400,U_1399) )
& ! [U_1401,U_1400,U_1399] :
( c_Orderings_Oord__class_Oless__eq(U_1399,U_1401,c_Groups_Ouminus__class_Ouminus(U_1399,U_1400))
| ~ c_Orderings_Oord__class_Oless__eq(U_1399,U_1400,c_Groups_Ouminus__class_Ouminus(U_1399,U_1401))
| ~ sP143(U_1401,U_1400,U_1399) )
& ! [U_1401,U_1400,U_1399] :
( sP143(U_1401,U_1400,U_1399)
| ~ class_Groups_Oordered__ab__group__add(U_1399) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143])],[f_448_2]) ).
cnf(f_448_4,plain,
( sP143(U_1401,U_1400,U_1399)
| ~ class_Groups_Oordered__ab__group__add(U_1399) ),
inference(clausify,[status(thm)],[f_448_3]) ).
cnf(f_448_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1399,U_1401,c_Groups_Ouminus__class_Ouminus(U_1399,U_1400))
| ~ c_Orderings_Oord__class_Oless__eq(U_1399,U_1400,c_Groups_Ouminus__class_Ouminus(U_1399,U_1401))
| ~ sP143(U_1401,U_1400,U_1399) ),
inference(clausify,[status(thm)],[f_448_3]) ).
cnf(f_448_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1399,U_1400,c_Groups_Ouminus__class_Ouminus(U_1399,U_1401))
| ~ c_Orderings_Oord__class_Oless__eq(U_1399,U_1401,c_Groups_Ouminus__class_Ouminus(U_1399,U_1400))
| ~ sP143(U_1401,U_1400,U_1399) ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).
fof(f_449_2,plain,
! [U_1404,U_1403,U_1402] :
( ( ( c_Orderings_Oord__class_Oless(U_1402,U_1403,c_Groups_Ouminus__class_Ouminus(U_1402,U_1404))
| ~ c_Orderings_Oord__class_Oless(U_1402,U_1404,c_Groups_Ouminus__class_Ouminus(U_1402,U_1403)) )
& ( c_Orderings_Oord__class_Oless(U_1402,U_1404,c_Groups_Ouminus__class_Ouminus(U_1402,U_1403))
| ~ c_Orderings_Oord__class_Oless(U_1402,U_1403,c_Groups_Ouminus__class_Ouminus(U_1402,U_1404)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1402) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
( ! [U_1403,U_1402,U_1404] :
( c_Orderings_Oord__class_Oless(U_1402,U_1403,c_Groups_Ouminus__class_Ouminus(U_1402,U_1404))
| ~ c_Orderings_Oord__class_Oless(U_1402,U_1404,c_Groups_Ouminus__class_Ouminus(U_1402,U_1403))
| ~ sP144(U_1403,U_1402,U_1404) )
& ! [U_1403,U_1402,U_1404] :
( c_Orderings_Oord__class_Oless(U_1402,U_1404,c_Groups_Ouminus__class_Ouminus(U_1402,U_1403))
| ~ c_Orderings_Oord__class_Oless(U_1402,U_1403,c_Groups_Ouminus__class_Ouminus(U_1402,U_1404))
| ~ sP144(U_1403,U_1402,U_1404) )
& ! [U_1403,U_1402,U_1404] :
( sP144(U_1403,U_1402,U_1404)
| ~ class_Groups_Oordered__ab__group__add(U_1402) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144])],[f_449_2]) ).
cnf(f_449_4,plain,
( sP144(U_1403,U_1402,U_1404)
| ~ class_Groups_Oordered__ab__group__add(U_1402) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_5,plain,
( c_Orderings_Oord__class_Oless(U_1402,U_1404,c_Groups_Ouminus__class_Ouminus(U_1402,U_1403))
| ~ c_Orderings_Oord__class_Oless(U_1402,U_1403,c_Groups_Ouminus__class_Ouminus(U_1402,U_1404))
| ~ sP144(U_1403,U_1402,U_1404) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_6,plain,
( c_Orderings_Oord__class_Oless(U_1402,U_1403,c_Groups_Ouminus__class_Ouminus(U_1402,U_1404))
| ~ c_Orderings_Oord__class_Oless(U_1402,U_1404,c_Groups_Ouminus__class_Ouminus(U_1402,U_1403))
| ~ sP144(U_1403,U_1402,U_1404) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).
fof(f_450_2,plain,
! [U_1407,U_1406,U_1405] :
( ( ( c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1406),U_1407)
| ~ c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1407),U_1406) )
& ( c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1407),U_1406)
| ~ c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1406),U_1407) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1405) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
( ! [U_1406,U_1405,U_1407] :
( c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1406),U_1407)
| ~ c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1407),U_1406)
| ~ sP145(U_1406,U_1405,U_1407) )
& ! [U_1406,U_1405,U_1407] :
( c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1407),U_1406)
| ~ c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1406),U_1407)
| ~ sP145(U_1406,U_1405,U_1407) )
& ! [U_1406,U_1405,U_1407] :
( sP145(U_1406,U_1405,U_1407)
| ~ class_Groups_Oordered__ab__group__add(U_1405) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145])],[f_450_2]) ).
cnf(f_450_4,plain,
( sP145(U_1406,U_1405,U_1407)
| ~ class_Groups_Oordered__ab__group__add(U_1405) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_5,plain,
( c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1407),U_1406)
| ~ c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1406),U_1407)
| ~ sP145(U_1406,U_1405,U_1407) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_6,plain,
( c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1406),U_1407)
| ~ c_Orderings_Oord__class_Oless(U_1405,c_Groups_Ouminus__class_Ouminus(U_1405,U_1407),U_1406)
| ~ sP145(U_1406,U_1405,U_1407) ),
inference(clausify,[status(thm)],[f_450_3]) ).
fof(f_451_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).
fof(f_451_2,plain,
! [U_1410,U_1409,U_1408] :
( ( ( c_Orderings_Oord__class_Oless(U_1408,c_Groups_Ouminus__class_Ouminus(U_1408,U_1409),c_Groups_Ouminus__class_Ouminus(U_1408,U_1410))
| ~ c_Orderings_Oord__class_Oless(U_1408,U_1410,U_1409) )
& ( c_Orderings_Oord__class_Oless(U_1408,U_1410,U_1409)
| ~ c_Orderings_Oord__class_Oless(U_1408,c_Groups_Ouminus__class_Ouminus(U_1408,U_1409),c_Groups_Ouminus__class_Ouminus(U_1408,U_1410)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1408) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
( ! [U_1409,U_1410,U_1408] :
( c_Orderings_Oord__class_Oless(U_1408,c_Groups_Ouminus__class_Ouminus(U_1408,U_1409),c_Groups_Ouminus__class_Ouminus(U_1408,U_1410))
| ~ c_Orderings_Oord__class_Oless(U_1408,U_1410,U_1409)
| ~ sP146(U_1409,U_1410,U_1408) )
& ! [U_1409,U_1410,U_1408] :
( c_Orderings_Oord__class_Oless(U_1408,U_1410,U_1409)
| ~ c_Orderings_Oord__class_Oless(U_1408,c_Groups_Ouminus__class_Ouminus(U_1408,U_1409),c_Groups_Ouminus__class_Ouminus(U_1408,U_1410))
| ~ sP146(U_1409,U_1410,U_1408) )
& ! [U_1409,U_1410,U_1408] :
( sP146(U_1409,U_1410,U_1408)
| ~ class_Groups_Oordered__ab__group__add(U_1408) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146])],[f_451_2]) ).
cnf(f_451_4,plain,
( sP146(U_1409,U_1410,U_1408)
| ~ class_Groups_Oordered__ab__group__add(U_1408) ),
inference(clausify,[status(thm)],[f_451_3]) ).
cnf(f_451_5,plain,
( c_Orderings_Oord__class_Oless(U_1408,U_1410,U_1409)
| ~ c_Orderings_Oord__class_Oless(U_1408,c_Groups_Ouminus__class_Ouminus(U_1408,U_1409),c_Groups_Ouminus__class_Ouminus(U_1408,U_1410))
| ~ sP146(U_1409,U_1410,U_1408) ),
inference(clausify,[status(thm)],[f_451_3]) ).
cnf(f_451_6,plain,
( c_Orderings_Oord__class_Oless(U_1408,c_Groups_Ouminus__class_Ouminus(U_1408,U_1409),c_Groups_Ouminus__class_Ouminus(U_1408,U_1410))
| ~ c_Orderings_Oord__class_Oless(U_1408,U_1410,U_1409)
| ~ sP146(U_1409,U_1410,U_1408) ),
inference(clausify,[status(thm)],[f_451_3]) ).
fof(f_452_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(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),V_b_H))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right]) ).
fof(f_452_2,plain,
! [U_1414,U_1413,U_1412,U_1411] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),c_Groups_Ominus__class_Ominus(U_1411,U_1413,U_1414)) = c_Groups_Ominus__class_Ominus(U_1411,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1414))
| ~ class_RealVector_Oreal__normed__algebra(U_1411) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
! [U_1413,U_1412,U_1411,U_1414] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),c_Groups_Ominus__class_Ominus(U_1411,U_1413,U_1414)) = c_Groups_Ominus__class_Ominus(U_1411,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1414))
| ~ class_RealVector_Oreal__normed__algebra(U_1411) ),
inference(definitional_conversion,[status(esa)],[f_452_2]) ).
cnf(f_452_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),c_Groups_Ominus__class_Ominus(U_1411,U_1413,U_1414)) = c_Groups_Ominus__class_Ominus(U_1411,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1414))
| ~ class_RealVector_Oreal__normed__algebra(U_1411) ),
inference(clausify,[status(thm)],[f_452_3]) ).
fof(f_453_1,plain,
! [V_y,V_x,V_xa,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff]) ).
fof(f_453_2,plain,
! [U_1418,U_1417,U_1416,U_1415] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),c_Groups_Ominus__class_Ominus(U_1415,U_1417,U_1418)) = c_Groups_Ominus__class_Ominus(U_1415,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1418))
| ~ class_RealVector_Oreal__normed__algebra(U_1415) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
! [U_1415,U_1416,U_1417,U_1418] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),c_Groups_Ominus__class_Ominus(U_1415,U_1417,U_1418)) = c_Groups_Ominus__class_Ominus(U_1415,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1418))
| ~ class_RealVector_Oreal__normed__algebra(U_1415) ),
inference(definitional_conversion,[status(esa)],[f_453_2]) ).
cnf(f_453_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),c_Groups_Ominus__class_Ominus(U_1415,U_1417,U_1418)) = c_Groups_Ominus__class_Ominus(U_1415,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1418))
| ~ class_RealVector_Oreal__normed__algebra(U_1415) ),
inference(clausify,[status(thm)],[f_453_3]) ).
fof(f_454_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(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_H),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left]) ).
fof(f_454_2,plain,
! [U_1422,U_1421,U_1420,U_1419] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),c_Groups_Ominus__class_Ominus(U_1419,U_1420,U_1421)),U_1422) = c_Groups_Ominus__class_Ominus(U_1419,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),U_1420),U_1422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),U_1421),U_1422))
| ~ class_RealVector_Oreal__normed__algebra(U_1419) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
! [U_1419,U_1420,U_1421,U_1422] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),c_Groups_Ominus__class_Ominus(U_1419,U_1420,U_1421)),U_1422) = c_Groups_Ominus__class_Ominus(U_1419,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),U_1420),U_1422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),U_1421),U_1422))
| ~ class_RealVector_Oreal__normed__algebra(U_1419) ),
inference(definitional_conversion,[status(esa)],[f_454_2]) ).
cnf(f_454_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),c_Groups_Ominus__class_Ominus(U_1419,U_1420,U_1421)),U_1422) = c_Groups_Ominus__class_Ominus(U_1419,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),U_1420),U_1422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1419),U_1421),U_1422))
| ~ class_RealVector_Oreal__normed__algebra(U_1419) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff]) ).
fof(f_455_2,plain,
! [U_1426,U_1425,U_1424,U_1423] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),c_Groups_Ominus__class_Ominus(U_1423,U_1424,U_1425)),U_1426) = c_Groups_Ominus__class_Ominus(U_1423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1424),U_1426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1425),U_1426))
| ~ class_RealVector_Oreal__normed__algebra(U_1423) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
! [U_1423,U_1424,U_1425,U_1426] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),c_Groups_Ominus__class_Ominus(U_1423,U_1424,U_1425)),U_1426) = c_Groups_Ominus__class_Ominus(U_1423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1424),U_1426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1425),U_1426))
| ~ class_RealVector_Oreal__normed__algebra(U_1423) ),
inference(definitional_conversion,[status(esa)],[f_455_2]) ).
cnf(f_455_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),c_Groups_Ominus__class_Ominus(U_1423,U_1424,U_1425)),U_1426) = c_Groups_Ominus__class_Ominus(U_1423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1424),U_1426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1425),U_1426))
| ~ class_RealVector_Oreal__normed__algebra(U_1423) ),
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,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_456_2,plain,
! [U_1429,U_1428,U_1427] :
( c_Groups_Oplus__class_Oplus(U_1427,c_Groups_Ominus__class_Ominus(U_1427,U_1428,U_1429),U_1429) = U_1428
| ~ class_Groups_Ogroup__add(U_1427) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
! [U_1428,U_1429,U_1427] :
( c_Groups_Oplus__class_Oplus(U_1427,c_Groups_Ominus__class_Ominus(U_1427,U_1428,U_1429),U_1429) = U_1428
| ~ class_Groups_Ogroup__add(U_1427) ),
inference(definitional_conversion,[status(esa)],[f_456_2]) ).
cnf(f_456_4,plain,
( c_Groups_Oplus__class_Oplus(U_1427,c_Groups_Ominus__class_Ominus(U_1427,U_1428,U_1429),U_1429) = U_1428
| ~ class_Groups_Ogroup__add(U_1427) ),
inference(clausify,[status(thm)],[f_456_3]) ).
fof(f_457_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,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_457_2,plain,
! [U_1432,U_1431,U_1430] :
( c_Groups_Ominus__class_Ominus(U_1430,c_Groups_Oplus__class_Oplus(U_1430,U_1431,U_1432),U_1432) = U_1431
| ~ class_Groups_Ogroup__add(U_1430) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
! [U_1430,U_1431,U_1432] :
( c_Groups_Ominus__class_Ominus(U_1430,c_Groups_Oplus__class_Oplus(U_1430,U_1431,U_1432),U_1432) = U_1431
| ~ class_Groups_Ogroup__add(U_1430) ),
inference(definitional_conversion,[status(esa)],[f_457_2]) ).
cnf(f_457_4,plain,
( c_Groups_Ominus__class_Ominus(U_1430,c_Groups_Oplus__class_Oplus(U_1430,U_1431,U_1432),U_1432) = U_1431
| ~ class_Groups_Ogroup__add(U_1430) ),
inference(clausify,[status(thm)],[f_457_3]) ).
fof(f_458_1,plain,
! [V_b,V_a,T_a] :
( 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),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_458_2,plain,
! [U_1435,U_1434,U_1433] :
( c_Groups_Ouminus__class_Ouminus(U_1433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1433),U_1434),U_1435)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1433),U_1434),c_Groups_Ouminus__class_Ouminus(U_1433,U_1435))
| ~ class_Rings_Oring(U_1433) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
! [U_1433,U_1434,U_1435] :
( c_Groups_Ouminus__class_Ouminus(U_1433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1433),U_1434),U_1435)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1433),U_1434),c_Groups_Ouminus__class_Ouminus(U_1433,U_1435))
| ~ class_Rings_Oring(U_1433) ),
inference(definitional_conversion,[status(esa)],[f_458_2]) ).
cnf(f_458_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1433),U_1434),U_1435)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1433),U_1434),c_Groups_Ouminus__class_Ouminus(U_1433,U_1435))
| ~ class_Rings_Oring(U_1433) ),
inference(clausify,[status(thm)],[f_458_3]) ).
fof(f_459_1,plain,
! [V_b,V_a,T_a] :
( 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),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_459_2,plain,
! [U_1438,U_1437,U_1436] :
( c_Groups_Ouminus__class_Ouminus(U_1436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1437),U_1438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),c_Groups_Ouminus__class_Ouminus(U_1436,U_1437)),U_1438)
| ~ class_Rings_Oring(U_1436) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
! [U_1436,U_1437,U_1438] :
( c_Groups_Ouminus__class_Ouminus(U_1436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1437),U_1438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),c_Groups_Ouminus__class_Ouminus(U_1436,U_1437)),U_1438)
| ~ class_Rings_Oring(U_1436) ),
inference(definitional_conversion,[status(esa)],[f_459_2]) ).
cnf(f_459_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1437),U_1438)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),c_Groups_Ouminus__class_Ouminus(U_1436,U_1437)),U_1438)
| ~ class_Rings_Oring(U_1436) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right]) ).
fof(f_460_2,plain,
! [U_1441,U_1440,U_1439] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1439),U_1440),c_Groups_Ouminus__class_Ouminus(U_1439,U_1441)) = c_Groups_Ouminus__class_Ouminus(U_1439,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1439),U_1440),U_1441))
| ~ class_RealVector_Oreal__normed__algebra(U_1439) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
! [U_1439,U_1440,U_1441] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1439),U_1440),c_Groups_Ouminus__class_Ouminus(U_1439,U_1441)) = c_Groups_Ouminus__class_Ouminus(U_1439,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1439),U_1440),U_1441))
| ~ class_RealVector_Oreal__normed__algebra(U_1439) ),
inference(definitional_conversion,[status(esa)],[f_460_2]) ).
cnf(f_460_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1439),U_1440),c_Groups_Ouminus__class_Ouminus(U_1439,U_1441)) = c_Groups_Ouminus__class_Ouminus(U_1439,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1439),U_1440),U_1441))
| ~ class_RealVector_Oreal__normed__algebra(U_1439) ),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [V_x,V_xa,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus]) ).
fof(f_461_2,plain,
! [U_1444,U_1443,U_1442] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1442),U_1443),c_Groups_Ouminus__class_Ouminus(U_1442,U_1444)) = c_Groups_Ouminus__class_Ouminus(U_1442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1442),U_1443),U_1444))
| ~ class_RealVector_Oreal__normed__algebra(U_1442) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
! [U_1442,U_1443,U_1444] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1442),U_1443),c_Groups_Ouminus__class_Ouminus(U_1442,U_1444)) = c_Groups_Ouminus__class_Ouminus(U_1442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1442),U_1443),U_1444))
| ~ class_RealVector_Oreal__normed__algebra(U_1442) ),
inference(definitional_conversion,[status(esa)],[f_461_2]) ).
cnf(f_461_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1442),U_1443),c_Groups_Ouminus__class_Ouminus(U_1442,U_1444)) = c_Groups_Ouminus__class_Ouminus(U_1442,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1442),U_1443),U_1444))
| ~ class_RealVector_Oreal__normed__algebra(U_1442) ),
inference(clausify,[status(thm)],[f_461_3]) ).
fof(f_462_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left]) ).
fof(f_462_2,plain,
! [U_1447,U_1446,U_1445] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1445),c_Groups_Ouminus__class_Ouminus(U_1445,U_1446)),U_1447) = c_Groups_Ouminus__class_Ouminus(U_1445,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1445),U_1446),U_1447))
| ~ class_RealVector_Oreal__normed__algebra(U_1445) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_1445,U_1446,U_1447] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1445),c_Groups_Ouminus__class_Ouminus(U_1445,U_1446)),U_1447) = c_Groups_Ouminus__class_Ouminus(U_1445,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1445),U_1446),U_1447))
| ~ class_RealVector_Oreal__normed__algebra(U_1445) ),
inference(definitional_conversion,[status(esa)],[f_462_2]) ).
cnf(f_462_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1445),c_Groups_Ouminus__class_Ouminus(U_1445,U_1446)),U_1447) = c_Groups_Ouminus__class_Ouminus(U_1445,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1445),U_1446),U_1447))
| ~ class_RealVector_Oreal__normed__algebra(U_1445) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus]) ).
fof(f_463_2,plain,
! [U_1450,U_1449,U_1448] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1448),c_Groups_Ouminus__class_Ouminus(U_1448,U_1449)),U_1450) = c_Groups_Ouminus__class_Ouminus(U_1448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1448),U_1449),U_1450))
| ~ class_RealVector_Oreal__normed__algebra(U_1448) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
! [U_1448,U_1449,U_1450] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1448),c_Groups_Ouminus__class_Ouminus(U_1448,U_1449)),U_1450) = c_Groups_Ouminus__class_Ouminus(U_1448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1448),U_1449),U_1450))
| ~ class_RealVector_Oreal__normed__algebra(U_1448) ),
inference(definitional_conversion,[status(esa)],[f_463_2]) ).
cnf(f_463_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1448),c_Groups_Ouminus__class_Ouminus(U_1448,U_1449)),U_1450) = c_Groups_Ouminus__class_Ouminus(U_1448,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1448),U_1449),U_1450))
| ~ class_RealVector_Oreal__normed__algebra(U_1448) ),
inference(clausify,[status(thm)],[f_463_3]) ).
fof(f_464_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),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_464_2,plain,
! [U_1453,U_1452,U_1451] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1451),c_Groups_Ouminus__class_Ouminus(U_1451,U_1452)),U_1453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1451),U_1452),c_Groups_Ouminus__class_Ouminus(U_1451,U_1453))
| ~ class_Rings_Oring(U_1451) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
! [U_1451,U_1452,U_1453] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1451),c_Groups_Ouminus__class_Ouminus(U_1451,U_1452)),U_1453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1451),U_1452),c_Groups_Ouminus__class_Ouminus(U_1451,U_1453))
| ~ class_Rings_Oring(U_1451) ),
inference(definitional_conversion,[status(esa)],[f_464_2]) ).
cnf(f_464_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1451),c_Groups_Ouminus__class_Ouminus(U_1451,U_1452)),U_1453) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1451),U_1452),c_Groups_Ouminus__class_Ouminus(U_1451,U_1453))
| ~ class_Rings_Oring(U_1451) ),
inference(clausify,[status(thm)],[f_464_3]) ).
fof(f_465_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),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_465_2,plain,
! [U_1456,U_1455,U_1454] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1454),c_Groups_Ouminus__class_Ouminus(U_1454,U_1455)),c_Groups_Ouminus__class_Ouminus(U_1454,U_1456)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1454),U_1455),U_1456)
| ~ class_Rings_Oring(U_1454) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
! [U_1454,U_1455,U_1456] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1454),c_Groups_Ouminus__class_Ouminus(U_1454,U_1455)),c_Groups_Ouminus__class_Ouminus(U_1454,U_1456)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1454),U_1455),U_1456)
| ~ class_Rings_Oring(U_1454) ),
inference(definitional_conversion,[status(esa)],[f_465_2]) ).
cnf(f_465_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1454),c_Groups_Ouminus__class_Ouminus(U_1454,U_1455)),c_Groups_Ouminus__class_Ouminus(U_1454,U_1456)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1454),U_1455),U_1456)
| ~ class_Rings_Oring(U_1454) ),
inference(clausify,[status(thm)],[f_465_3]) ).
fof(f_466_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
| ( V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
& V_a_2 != V_b_2 ) )
& ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).
fof(f_466_2,plain,
! [U_1459,U_1458,U_1457] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1458),U_1458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1459),U_1459)
| ( U_1458 != c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)
& U_1458 != U_1459 ) )
& ( U_1458 = c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)
| U_1458 = U_1459
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1458),U_1458) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1459),U_1459) ) )
| ~ class_Rings_Oidom(U_1457) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
( ! [U_1457,U_1458,U_1459] :
( U_1458 != c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)
| ~ sP147(U_1457,U_1458,U_1459) )
& ! [U_1457,U_1458,U_1459] :
( U_1458 != U_1459
| ~ sP147(U_1457,U_1458,U_1459) )
& ! [U_1457,U_1458,U_1459] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1458),U_1458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1459),U_1459)
| sP147(U_1457,U_1458,U_1459)
| ~ sP148(U_1457,U_1458,U_1459) )
& ! [U_1457,U_1458,U_1459] :
( U_1458 = c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)
| U_1458 = U_1459
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1458),U_1458) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1459),U_1459)
| ~ sP148(U_1457,U_1458,U_1459) )
& ! [U_1457,U_1458,U_1459] :
( sP148(U_1457,U_1458,U_1459)
| ~ class_Rings_Oidom(U_1457) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147,sP148])],[f_466_2]) ).
cnf(f_466_4,plain,
( sP148(U_1457,U_1458,U_1459)
| ~ class_Rings_Oidom(U_1457) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_5,plain,
( U_1458 = c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)
| U_1458 = U_1459
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1458),U_1458) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1459),U_1459)
| ~ sP148(U_1457,U_1458,U_1459) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1458),U_1458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1457),U_1459),U_1459)
| sP147(U_1457,U_1458,U_1459)
| ~ sP148(U_1457,U_1458,U_1459) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_7,plain,
( U_1458 != U_1459
| ~ sP147(U_1457,U_1458,U_1459) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_8,plain,
( U_1458 != c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)
| ~ sP147(U_1457,U_1458,U_1459) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),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_467_2,plain,
! [U_1462,U_1461,U_1460] :
( c_Groups_Ouminus__class_Ouminus(U_1460,c_Groups_Oplus__class_Oplus(U_1460,U_1461,U_1462)) = c_Groups_Oplus__class_Oplus(U_1460,c_Groups_Ouminus__class_Ouminus(U_1460,U_1461),c_Groups_Ouminus__class_Ouminus(U_1460,U_1462))
| ~ class_Groups_Oab__group__add(U_1460) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
! [U_1461,U_1462,U_1460] :
( c_Groups_Ouminus__class_Ouminus(U_1460,c_Groups_Oplus__class_Oplus(U_1460,U_1461,U_1462)) = c_Groups_Oplus__class_Oplus(U_1460,c_Groups_Ouminus__class_Ouminus(U_1460,U_1461),c_Groups_Ouminus__class_Ouminus(U_1460,U_1462))
| ~ class_Groups_Oab__group__add(U_1460) ),
inference(definitional_conversion,[status(esa)],[f_467_2]) ).
cnf(f_467_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1460,c_Groups_Oplus__class_Oplus(U_1460,U_1461,U_1462)) = c_Groups_Oplus__class_Oplus(U_1460,c_Groups_Ouminus__class_Ouminus(U_1460,U_1461),c_Groups_Ouminus__class_Ouminus(U_1460,U_1462))
| ~ class_Groups_Oab__group__add(U_1460) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),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_468_2,plain,
! [U_1465,U_1464,U_1463] :
( c_Groups_Ouminus__class_Ouminus(U_1463,c_Groups_Oplus__class_Oplus(U_1463,U_1464,U_1465)) = c_Groups_Oplus__class_Oplus(U_1463,c_Groups_Ouminus__class_Ouminus(U_1463,U_1465),c_Groups_Ouminus__class_Ouminus(U_1463,U_1464))
| ~ class_Groups_Ogroup__add(U_1463) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
! [U_1463,U_1464,U_1465] :
( c_Groups_Ouminus__class_Ouminus(U_1463,c_Groups_Oplus__class_Oplus(U_1463,U_1464,U_1465)) = c_Groups_Oplus__class_Oplus(U_1463,c_Groups_Ouminus__class_Ouminus(U_1463,U_1465),c_Groups_Ouminus__class_Ouminus(U_1463,U_1464))
| ~ class_Groups_Ogroup__add(U_1463) ),
inference(definitional_conversion,[status(esa)],[f_468_2]) ).
cnf(f_468_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1463,c_Groups_Oplus__class_Oplus(U_1463,U_1464,U_1465)) = c_Groups_Oplus__class_Oplus(U_1463,c_Groups_Ouminus__class_Ouminus(U_1463,U_1465),c_Groups_Ouminus__class_Ouminus(U_1463,U_1464))
| ~ class_Groups_Ogroup__add(U_1463) ),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,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_469_2,plain,
! [U_1468,U_1467,U_1466] :
( c_Groups_Oplus__class_Oplus(U_1466,U_1467,c_Groups_Oplus__class_Oplus(U_1466,c_Groups_Ouminus__class_Ouminus(U_1466,U_1467),U_1468)) = U_1468
| ~ class_Groups_Ogroup__add(U_1466) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
! [U_1467,U_1466,U_1468] :
( c_Groups_Oplus__class_Oplus(U_1466,U_1467,c_Groups_Oplus__class_Oplus(U_1466,c_Groups_Ouminus__class_Ouminus(U_1466,U_1467),U_1468)) = U_1468
| ~ class_Groups_Ogroup__add(U_1466) ),
inference(definitional_conversion,[status(esa)],[f_469_2]) ).
cnf(f_469_4,plain,
( c_Groups_Oplus__class_Oplus(U_1466,U_1467,c_Groups_Oplus__class_Oplus(U_1466,c_Groups_Ouminus__class_Ouminus(U_1466,U_1467),U_1468)) = U_1468
| ~ class_Groups_Ogroup__add(U_1466) ),
inference(clausify,[status(thm)],[f_469_3]) ).
fof(f_470_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),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_470_2,plain,
! [U_1471,U_1470,U_1469] :
( c_Groups_Oplus__class_Oplus(U_1469,c_Groups_Ouminus__class_Ouminus(U_1469,U_1470),c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1471)) = U_1471
| ~ class_Groups_Ogroup__add(U_1469) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
! [U_1469,U_1470,U_1471] :
( c_Groups_Oplus__class_Oplus(U_1469,c_Groups_Ouminus__class_Ouminus(U_1469,U_1470),c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1471)) = U_1471
| ~ class_Groups_Ogroup__add(U_1469) ),
inference(definitional_conversion,[status(esa)],[f_470_2]) ).
cnf(f_470_4,plain,
( c_Groups_Oplus__class_Oplus(U_1469,c_Groups_Ouminus__class_Ouminus(U_1469,U_1470),c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1471)) = U_1471
| ~ class_Groups_Ogroup__add(U_1469) ),
inference(clausify,[status(thm)],[f_470_3]) ).
fof(f_471_1,plain,
! [V_n,V_m] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_471_2,plain,
! [U_1473,U_1472] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1472),U_1473) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1473,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1472,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1473))
| U_1472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1472),U_1473) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
( ! [U_1477,U_1475] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1475),U_1477) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1475,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1477))
| U_1475 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1476,U_1474] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1474),U_1476) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1474 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_471_2]) ).
fof(f_471_4,plain,
( ! [U_1475,U_1477] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1475),U_1477) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1475,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1477))
| U_1475 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1474,U_1476] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1474),U_1476) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1474 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_471_3]) ).
cnf(f_471_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1474),U_1476) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1474 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_471_4]) ).
cnf(f_471_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1475),U_1477) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1475,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1477))
| U_1475 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_471_4]) ).
fof(f_472_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,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_472_2,plain,
! [U_1480,U_1479,U_1478] :
( c_Groups_Oabs__class_Oabs(U_1478,c_Groups_Ominus__class_Ominus(U_1478,U_1479,U_1480)) = c_Groups_Oabs__class_Oabs(U_1478,c_Groups_Ominus__class_Ominus(U_1478,U_1480,U_1479))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1478) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
! [U_1479,U_1478,U_1480] :
( c_Groups_Oabs__class_Oabs(U_1478,c_Groups_Ominus__class_Ominus(U_1478,U_1479,U_1480)) = c_Groups_Oabs__class_Oabs(U_1478,c_Groups_Ominus__class_Ominus(U_1478,U_1480,U_1479))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1478) ),
inference(definitional_conversion,[status(esa)],[f_472_2]) ).
cnf(f_472_4,plain,
( c_Groups_Oabs__class_Oabs(U_1478,c_Groups_Ominus__class_Ominus(U_1478,U_1479,U_1480)) = c_Groups_Oabs__class_Oabs(U_1478,c_Groups_Ominus__class_Ominus(U_1478,U_1480,U_1479))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1478) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_1,plain,
! [V_b,V_a,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__minus__commute]) ).
fof(f_473_2,plain,
! [U_1483,U_1482,U_1481] :
( c_RealVector_Onorm__class_Onorm(U_1481,c_Groups_Ominus__class_Ominus(U_1481,U_1482,U_1483)) = c_RealVector_Onorm__class_Onorm(U_1481,c_Groups_Ominus__class_Ominus(U_1481,U_1483,U_1482))
| ~ class_RealVector_Oreal__normed__vector(U_1481) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_1481,U_1482,U_1483] :
( c_RealVector_Onorm__class_Onorm(U_1481,c_Groups_Ominus__class_Ominus(U_1481,U_1482,U_1483)) = c_RealVector_Onorm__class_Onorm(U_1481,c_Groups_Ominus__class_Ominus(U_1481,U_1483,U_1482))
| ~ class_RealVector_Oreal__normed__vector(U_1481) ),
inference(definitional_conversion,[status(esa)],[f_473_2]) ).
cnf(f_473_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1481,c_Groups_Ominus__class_Ominus(U_1481,U_1482,U_1483)) = c_RealVector_Onorm__class_Onorm(U_1481,c_Groups_Ominus__class_Ominus(U_1481,U_1483,U_1482))
| ~ class_RealVector_Oreal__normed__vector(U_1481) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = 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_474_2,plain,
! [U_1485,U_1484] :
( c_Groups_Oabs__class_Oabs(U_1484,c_Groups_Ouminus__class_Ouminus(U_1484,U_1485)) = c_Groups_Oabs__class_Oabs(U_1484,U_1485)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1484) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
! [U_1484,U_1485] :
( c_Groups_Oabs__class_Oabs(U_1484,c_Groups_Ouminus__class_Ouminus(U_1484,U_1485)) = c_Groups_Oabs__class_Oabs(U_1484,U_1485)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1484) ),
inference(definitional_conversion,[status(esa)],[f_474_2]) ).
cnf(f_474_4,plain,
( c_Groups_Oabs__class_Oabs(U_1484,c_Groups_Ouminus__class_Ouminus(U_1484,U_1485)) = c_Groups_Oabs__class_Oabs(U_1484,U_1485)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1484) ),
inference(clausify,[status(thm)],[f_474_3]) ).
fof(f_475_1,plain,
! [V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel]) ).
fof(f_475_2,plain,
! [U_1487,U_1486] :
( c_RealVector_Onorm__class_Onorm(U_1486,c_Groups_Ouminus__class_Ouminus(U_1486,U_1487)) = c_RealVector_Onorm__class_Onorm(U_1486,U_1487)
| ~ class_RealVector_Oreal__normed__vector(U_1486) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
! [U_1486,U_1487] :
( c_RealVector_Onorm__class_Onorm(U_1486,c_Groups_Ouminus__class_Ouminus(U_1486,U_1487)) = c_RealVector_Onorm__class_Onorm(U_1486,U_1487)
| ~ class_RealVector_Oreal__normed__vector(U_1486) ),
inference(definitional_conversion,[status(esa)],[f_475_2]) ).
cnf(f_475_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1486,c_Groups_Ouminus__class_Ouminus(U_1486,U_1487)) = c_RealVector_Onorm__class_Onorm(U_1486,U_1487)
| ~ class_RealVector_Oreal__normed__vector(U_1486) ),
inference(clausify,[status(thm)],[f_475_3]) ).
fof(f_476_1,plain,
! [V_p,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J]) ).
fof(f_476_2,plain,
! [U_1489,U_1488] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1488),U_1489,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1488))) = U_1489
| ~ class_Groups_Oab__group__add(U_1488) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_1488,U_1489] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1488),U_1489,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1488))) = U_1489
| ~ class_Groups_Oab__group__add(U_1488) ),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1488),U_1489,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1488))) = U_1489
| ~ class_Groups_Oab__group__add(U_1488) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [V_x,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) )
& ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__poly__def]) ).
fof(f_477_2,plain,
! [U_1491,U_1490] :
( ( ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1490),U_1491) = U_1491
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1490),U_1491,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1490))) )
& ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1490),U_1491) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1490),U_1491)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1490),U_1491,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1490))) ) )
| ~ class_Rings_Olinordered__idom(U_1490) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
( ! [U_1490,U_1491] :
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1490),U_1491) = U_1491
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1490),U_1491,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1490)))
| ~ sP149(U_1490,U_1491) )
& ! [U_1490,U_1491] :
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1490),U_1491) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1490),U_1491)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1490),U_1491,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1490)))
| ~ sP149(U_1490,U_1491) )
& ! [U_1490,U_1491] :
( sP149(U_1490,U_1491)
| ~ class_Rings_Olinordered__idom(U_1490) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_477_2]) ).
cnf(f_477_4,plain,
( sP149(U_1490,U_1491)
| ~ class_Rings_Olinordered__idom(U_1490) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_5,plain,
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1490),U_1491) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1490),U_1491)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1490),U_1491,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1490)))
| ~ sP149(U_1490,U_1491) ),
inference(clausify,[status(thm)],[f_477_3]) ).
cnf(f_477_6,plain,
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1490),U_1491) = U_1491
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1490),U_1491,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1490)))
| ~ sP149(U_1490,U_1491) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [T_a] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J]) ).
fof(f_478_2,plain,
! [U_1492] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1492),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1492))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1492))
| ~ class_Groups_Oab__group__add(U_1492) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_1492] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1492),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1492))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1492))
| ~ class_Groups_Oab__group__add(U_1492) ),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1492),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1492))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1492))
| ~ class_Groups_Oab__group__add(U_1492) ),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [V_x,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__minus]) ).
fof(f_479_2,plain,
! [U_1494,U_1493] :
( c_Groups_Osgn__class_Osgn(U_1493,c_Groups_Ouminus__class_Ouminus(U_1493,U_1494)) = c_Groups_Ouminus__class_Ouminus(U_1493,c_Groups_Osgn__class_Osgn(U_1493,U_1494))
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
! [U_1494,U_1493] :
( c_Groups_Osgn__class_Osgn(U_1493,c_Groups_Ouminus__class_Ouminus(U_1493,U_1494)) = c_Groups_Ouminus__class_Ouminus(U_1493,c_Groups_Osgn__class_Osgn(U_1493,U_1494))
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(definitional_conversion,[status(esa)],[f_479_2]) ).
cnf(f_479_4,plain,
( c_Groups_Osgn__class_Osgn(U_1493,c_Groups_Ouminus__class_Ouminus(U_1493,U_1494)) = c_Groups_Ouminus__class_Ouminus(U_1493,c_Groups_Osgn__class_Osgn(U_1493,U_1494))
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3]) ).
fof(f_480_2,plain,
! [U_1497,U_1496,U_1495] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1495,U_1496),c_RealVector_Onorm__class_Onorm(U_1495,U_1497))),c_RealVector_Onorm__class_Onorm(U_1495,c_Groups_Ominus__class_Ominus(U_1495,U_1496,U_1497)))
| ~ class_RealVector_Oreal__normed__vector(U_1495) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
! [U_1495,U_1496,U_1497] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1495,U_1496),c_RealVector_Onorm__class_Onorm(U_1495,U_1497))),c_RealVector_Onorm__class_Onorm(U_1495,c_Groups_Ominus__class_Ominus(U_1495,U_1496,U_1497)))
| ~ class_RealVector_Oreal__normed__vector(U_1495) ),
inference(definitional_conversion,[status(esa)],[f_480_2]) ).
cnf(f_480_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1495,U_1496),c_RealVector_Onorm__class_Onorm(U_1495,U_1497))),c_RealVector_Onorm__class_Onorm(U_1495,c_Groups_Ominus__class_Ominus(U_1495,U_1496,U_1497)))
| ~ class_RealVector_Oreal__normed__vector(U_1495) ),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).
fof(f_481_2,plain,
! [U_1500,U_1499,U_1498] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1498,U_1499,U_1500)
| ~ c_Orderings_Oord__class_Oless__eq(U_1498,c_Groups_Ominus__class_Ominus(U_1498,U_1499,U_1500),c_Groups_Ozero__class_Ozero(U_1498)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1498,c_Groups_Ominus__class_Ominus(U_1498,U_1499,U_1500),c_Groups_Ozero__class_Ozero(U_1498))
| ~ c_Orderings_Oord__class_Oless__eq(U_1498,U_1499,U_1500) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1498) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
( ! [U_1498,U_1499,U_1500] :
( c_Orderings_Oord__class_Oless__eq(U_1498,U_1499,U_1500)
| ~ c_Orderings_Oord__class_Oless__eq(U_1498,c_Groups_Ominus__class_Ominus(U_1498,U_1499,U_1500),c_Groups_Ozero__class_Ozero(U_1498))
| ~ sP150(U_1498,U_1499,U_1500) )
& ! [U_1498,U_1499,U_1500] :
( c_Orderings_Oord__class_Oless__eq(U_1498,c_Groups_Ominus__class_Ominus(U_1498,U_1499,U_1500),c_Groups_Ozero__class_Ozero(U_1498))
| ~ c_Orderings_Oord__class_Oless__eq(U_1498,U_1499,U_1500)
| ~ sP150(U_1498,U_1499,U_1500) )
& ! [U_1498,U_1499,U_1500] :
( sP150(U_1498,U_1499,U_1500)
| ~ class_Groups_Oordered__ab__group__add(U_1498) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_481_2]) ).
cnf(f_481_4,plain,
( sP150(U_1498,U_1499,U_1500)
| ~ class_Groups_Oordered__ab__group__add(U_1498) ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1498,c_Groups_Ominus__class_Ominus(U_1498,U_1499,U_1500),c_Groups_Ozero__class_Ozero(U_1498))
| ~ c_Orderings_Oord__class_Oless__eq(U_1498,U_1499,U_1500)
| ~ sP150(U_1498,U_1499,U_1500) ),
inference(clausify,[status(thm)],[f_481_3]) ).
cnf(f_481_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1498,U_1499,U_1500)
| ~ c_Orderings_Oord__class_Oless__eq(U_1498,c_Groups_Ominus__class_Ominus(U_1498,U_1499,U_1500),c_Groups_Ozero__class_Ozero(U_1498))
| ~ sP150(U_1498,U_1499,U_1500) ),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).
fof(f_482_2,plain,
! [U_1503,U_1502,U_1501] :
( ( ( c_Orderings_Oord__class_Oless(U_1501,U_1502,U_1503)
| ~ c_Orderings_Oord__class_Oless(U_1501,c_Groups_Ominus__class_Ominus(U_1501,U_1502,U_1503),c_Groups_Ozero__class_Ozero(U_1501)) )
& ( c_Orderings_Oord__class_Oless(U_1501,c_Groups_Ominus__class_Ominus(U_1501,U_1502,U_1503),c_Groups_Ozero__class_Ozero(U_1501))
| ~ c_Orderings_Oord__class_Oless(U_1501,U_1502,U_1503) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1501) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
( ! [U_1503,U_1502,U_1501] :
( c_Orderings_Oord__class_Oless(U_1501,U_1502,U_1503)
| ~ c_Orderings_Oord__class_Oless(U_1501,c_Groups_Ominus__class_Ominus(U_1501,U_1502,U_1503),c_Groups_Ozero__class_Ozero(U_1501))
| ~ sP151(U_1503,U_1502,U_1501) )
& ! [U_1503,U_1502,U_1501] :
( c_Orderings_Oord__class_Oless(U_1501,c_Groups_Ominus__class_Ominus(U_1501,U_1502,U_1503),c_Groups_Ozero__class_Ozero(U_1501))
| ~ c_Orderings_Oord__class_Oless(U_1501,U_1502,U_1503)
| ~ sP151(U_1503,U_1502,U_1501) )
& ! [U_1503,U_1502,U_1501] :
( sP151(U_1503,U_1502,U_1501)
| ~ class_Groups_Oordered__ab__group__add(U_1501) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_482_2]) ).
cnf(f_482_4,plain,
( sP151(U_1503,U_1502,U_1501)
| ~ class_Groups_Oordered__ab__group__add(U_1501) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_5,plain,
( c_Orderings_Oord__class_Oless(U_1501,c_Groups_Ominus__class_Ominus(U_1501,U_1502,U_1503),c_Groups_Ozero__class_Ozero(U_1501))
| ~ c_Orderings_Oord__class_Oless(U_1501,U_1502,U_1503)
| ~ sP151(U_1503,U_1502,U_1501) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_6,plain,
( c_Orderings_Oord__class_Oless(U_1501,U_1502,U_1503)
| ~ c_Orderings_Oord__class_Oless(U_1501,c_Groups_Ominus__class_Ominus(U_1501,U_1502,U_1503),c_Groups_Ozero__class_Ozero(U_1501))
| ~ sP151(U_1503,U_1502,U_1501) ),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).
fof(f_483_2,plain,
! [U_1505,U_1504] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ouminus__class_Ouminus(U_1504,U_1505),U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ozero__class_Ozero(U_1504),U_1505) )
& ( c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ozero__class_Ozero(U_1504),U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ouminus__class_Ouminus(U_1504,U_1505),U_1505) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1504) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
( ! [U_1505,U_1504] :
( c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ouminus__class_Ouminus(U_1504,U_1505),U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ozero__class_Ozero(U_1504),U_1505)
| ~ sP152(U_1505,U_1504) )
& ! [U_1505,U_1504] :
( c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ozero__class_Ozero(U_1504),U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ouminus__class_Ouminus(U_1504,U_1505),U_1505)
| ~ sP152(U_1505,U_1504) )
& ! [U_1505,U_1504] :
( sP152(U_1505,U_1504)
| ~ class_Groups_Olinordered__ab__group__add(U_1504) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_483_2]) ).
cnf(f_483_4,plain,
( sP152(U_1505,U_1504)
| ~ class_Groups_Olinordered__ab__group__add(U_1504) ),
inference(clausify,[status(thm)],[f_483_3]) ).
cnf(f_483_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ozero__class_Ozero(U_1504),U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ouminus__class_Ouminus(U_1504,U_1505),U_1505)
| ~ sP152(U_1505,U_1504) ),
inference(clausify,[status(thm)],[f_483_3]) ).
cnf(f_483_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ouminus__class_Ouminus(U_1504,U_1505),U_1505)
| ~ c_Orderings_Oord__class_Oless__eq(U_1504,c_Groups_Ozero__class_Ozero(U_1504),U_1505)
| ~ sP152(U_1505,U_1504) ),
inference(clausify,[status(thm)],[f_483_3]) ).
fof(f_484_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).
fof(f_484_2,plain,
! [U_1507,U_1506] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ouminus__class_Ouminus(U_1506,U_1507),c_Groups_Ozero__class_Ozero(U_1506))
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507) )
& ( c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507)
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ouminus__class_Ouminus(U_1506,U_1507),c_Groups_Ozero__class_Ozero(U_1506)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1506) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
( ! [U_1507,U_1506] :
( c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ouminus__class_Ouminus(U_1506,U_1507),c_Groups_Ozero__class_Ozero(U_1506))
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507)
| ~ sP153(U_1507,U_1506) )
& ! [U_1507,U_1506] :
( c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507)
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ouminus__class_Ouminus(U_1506,U_1507),c_Groups_Ozero__class_Ozero(U_1506))
| ~ sP153(U_1507,U_1506) )
& ! [U_1507,U_1506] :
( sP153(U_1507,U_1506)
| ~ class_Groups_Oordered__ab__group__add(U_1506) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153])],[f_484_2]) ).
cnf(f_484_4,plain,
( sP153(U_1507,U_1506)
| ~ class_Groups_Oordered__ab__group__add(U_1506) ),
inference(clausify,[status(thm)],[f_484_3]) ).
cnf(f_484_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507)
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ouminus__class_Ouminus(U_1506,U_1507),c_Groups_Ozero__class_Ozero(U_1506))
| ~ sP153(U_1507,U_1506) ),
inference(clausify,[status(thm)],[f_484_3]) ).
cnf(f_484_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ouminus__class_Ouminus(U_1506,U_1507),c_Groups_Ozero__class_Ozero(U_1506))
| ~ c_Orderings_Oord__class_Oless__eq(U_1506,c_Groups_Ozero__class_Ozero(U_1506),U_1507)
| ~ sP153(U_1507,U_1506) ),
inference(clausify,[status(thm)],[f_484_3]) ).
fof(f_485_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).
fof(f_485_2,plain,
! [U_1509,U_1508] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ouminus__class_Ouminus(U_1508,U_1509))
| ~ c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ozero__class_Ozero(U_1508)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ozero__class_Ozero(U_1508))
| ~ c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ouminus__class_Ouminus(U_1508,U_1509)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1508) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
fof(f_485_3,plain,
( ! [U_1509,U_1508] :
( c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ouminus__class_Ouminus(U_1508,U_1509))
| ~ c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ozero__class_Ozero(U_1508))
| ~ sP154(U_1509,U_1508) )
& ! [U_1509,U_1508] :
( c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ozero__class_Ozero(U_1508))
| ~ c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ouminus__class_Ouminus(U_1508,U_1509))
| ~ sP154(U_1509,U_1508) )
& ! [U_1509,U_1508] :
( sP154(U_1509,U_1508)
| ~ class_Groups_Olinordered__ab__group__add(U_1508) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154])],[f_485_2]) ).
cnf(f_485_4,plain,
( sP154(U_1509,U_1508)
| ~ class_Groups_Olinordered__ab__group__add(U_1508) ),
inference(clausify,[status(thm)],[f_485_3]) ).
cnf(f_485_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ozero__class_Ozero(U_1508))
| ~ c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ouminus__class_Ouminus(U_1508,U_1509))
| ~ sP154(U_1509,U_1508) ),
inference(clausify,[status(thm)],[f_485_3]) ).
cnf(f_485_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ouminus__class_Ouminus(U_1508,U_1509))
| ~ c_Orderings_Oord__class_Oless__eq(U_1508,U_1509,c_Groups_Ozero__class_Ozero(U_1508))
| ~ sP154(U_1509,U_1508) ),
inference(clausify,[status(thm)],[f_485_3]) ).
fof(f_486_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).
fof(f_486_2,plain,
! [U_1511,U_1510] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),c_Groups_Ouminus__class_Ouminus(U_1510,U_1511))
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,U_1511,c_Groups_Ozero__class_Ozero(U_1510)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1510,U_1511,c_Groups_Ozero__class_Ozero(U_1510))
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),c_Groups_Ouminus__class_Ouminus(U_1510,U_1511)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1510) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
( ! [U_1511,U_1510] :
( c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),c_Groups_Ouminus__class_Ouminus(U_1510,U_1511))
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,U_1511,c_Groups_Ozero__class_Ozero(U_1510))
| ~ sP155(U_1511,U_1510) )
& ! [U_1511,U_1510] :
( c_Orderings_Oord__class_Oless__eq(U_1510,U_1511,c_Groups_Ozero__class_Ozero(U_1510))
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),c_Groups_Ouminus__class_Ouminus(U_1510,U_1511))
| ~ sP155(U_1511,U_1510) )
& ! [U_1511,U_1510] :
( sP155(U_1511,U_1510)
| ~ class_Groups_Oordered__ab__group__add(U_1510) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_486_2]) ).
cnf(f_486_4,plain,
( sP155(U_1511,U_1510)
| ~ class_Groups_Oordered__ab__group__add(U_1510) ),
inference(clausify,[status(thm)],[f_486_3]) ).
cnf(f_486_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1510,U_1511,c_Groups_Ozero__class_Ozero(U_1510))
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),c_Groups_Ouminus__class_Ouminus(U_1510,U_1511))
| ~ sP155(U_1511,U_1510) ),
inference(clausify,[status(thm)],[f_486_3]) ).
cnf(f_486_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1510,c_Groups_Ozero__class_Ozero(U_1510),c_Groups_Ouminus__class_Ouminus(U_1510,U_1511))
| ~ c_Orderings_Oord__class_Oless__eq(U_1510,U_1511,c_Groups_Ozero__class_Ozero(U_1510))
| ~ sP155(U_1511,U_1510) ),
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).
fof(f_487_2,plain,
! [U_1513,U_1512] :
( ( ( c_Orderings_Oord__class_Oless(U_1512,c_Groups_Ozero__class_Ozero(U_1512),c_Groups_Ouminus__class_Ouminus(U_1512,U_1513))
| ~ c_Orderings_Oord__class_Oless(U_1512,U_1513,c_Groups_Ozero__class_Ozero(U_1512)) )
& ( c_Orderings_Oord__class_Oless(U_1512,U_1513,c_Groups_Ozero__class_Ozero(U_1512))
| ~ c_Orderings_Oord__class_Oless(U_1512,c_Groups_Ozero__class_Ozero(U_1512),c_Groups_Ouminus__class_Ouminus(U_1512,U_1513)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1512) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
( ! [U_1513,U_1512] :
( c_Orderings_Oord__class_Oless(U_1512,c_Groups_Ozero__class_Ozero(U_1512),c_Groups_Ouminus__class_Ouminus(U_1512,U_1513))
| ~ c_Orderings_Oord__class_Oless(U_1512,U_1513,c_Groups_Ozero__class_Ozero(U_1512))
| ~ sP156(U_1513,U_1512) )
& ! [U_1513,U_1512] :
( c_Orderings_Oord__class_Oless(U_1512,U_1513,c_Groups_Ozero__class_Ozero(U_1512))
| ~ c_Orderings_Oord__class_Oless(U_1512,c_Groups_Ozero__class_Ozero(U_1512),c_Groups_Ouminus__class_Ouminus(U_1512,U_1513))
| ~ sP156(U_1513,U_1512) )
& ! [U_1513,U_1512] :
( sP156(U_1513,U_1512)
| ~ class_Groups_Oordered__ab__group__add(U_1512) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156])],[f_487_2]) ).
cnf(f_487_4,plain,
( sP156(U_1513,U_1512)
| ~ class_Groups_Oordered__ab__group__add(U_1512) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_5,plain,
( c_Orderings_Oord__class_Oless(U_1512,U_1513,c_Groups_Ozero__class_Ozero(U_1512))
| ~ c_Orderings_Oord__class_Oless(U_1512,c_Groups_Ozero__class_Ozero(U_1512),c_Groups_Ouminus__class_Ouminus(U_1512,U_1513))
| ~ sP156(U_1513,U_1512) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_6,plain,
( c_Orderings_Oord__class_Oless(U_1512,c_Groups_Ozero__class_Ozero(U_1512),c_Groups_Ouminus__class_Ouminus(U_1512,U_1513))
| ~ c_Orderings_Oord__class_Oless(U_1512,U_1513,c_Groups_Ozero__class_Ozero(U_1512))
| ~ sP156(U_1513,U_1512) ),
inference(clausify,[status(thm)],[f_487_3]) ).
fof(f_488_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).
fof(f_488_2,plain,
! [U_1515,U_1514] :
( ( ( c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ouminus__class_Ouminus(U_1514,U_1515),c_Groups_Ozero__class_Ozero(U_1514))
| ~ c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ozero__class_Ozero(U_1514),U_1515) )
& ( c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ozero__class_Ozero(U_1514),U_1515)
| ~ c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ouminus__class_Ouminus(U_1514,U_1515),c_Groups_Ozero__class_Ozero(U_1514)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1514) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
( ! [U_1515,U_1514] :
( c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ouminus__class_Ouminus(U_1514,U_1515),c_Groups_Ozero__class_Ozero(U_1514))
| ~ c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ozero__class_Ozero(U_1514),U_1515)
| ~ sP157(U_1515,U_1514) )
& ! [U_1515,U_1514] :
( c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ozero__class_Ozero(U_1514),U_1515)
| ~ c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ouminus__class_Ouminus(U_1514,U_1515),c_Groups_Ozero__class_Ozero(U_1514))
| ~ sP157(U_1515,U_1514) )
& ! [U_1515,U_1514] :
( sP157(U_1515,U_1514)
| ~ class_Groups_Oordered__ab__group__add(U_1514) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157])],[f_488_2]) ).
cnf(f_488_4,plain,
( sP157(U_1515,U_1514)
| ~ class_Groups_Oordered__ab__group__add(U_1514) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_5,plain,
( c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ozero__class_Ozero(U_1514),U_1515)
| ~ c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ouminus__class_Ouminus(U_1514,U_1515),c_Groups_Ozero__class_Ozero(U_1514))
| ~ sP157(U_1515,U_1514) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_6,plain,
( c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ouminus__class_Ouminus(U_1514,U_1515),c_Groups_Ozero__class_Ozero(U_1514))
| ~ c_Orderings_Oord__class_Oless(U_1514,c_Groups_Ozero__class_Ozero(U_1514),U_1515)
| ~ sP157(U_1515,U_1514) ),
inference(clausify,[status(thm)],[f_488_3]) ).
fof(f_489_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).
fof(f_489_2,plain,
! [U_1517,U_1516] :
( ( ( c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ouminus__class_Ouminus(U_1516,U_1517),U_1517)
| ~ c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ozero__class_Ozero(U_1516),U_1517) )
& ( c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ozero__class_Ozero(U_1516),U_1517)
| ~ c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ouminus__class_Ouminus(U_1516,U_1517),U_1517) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1516) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
( ! [U_1517,U_1516] :
( c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ouminus__class_Ouminus(U_1516,U_1517),U_1517)
| ~ c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ozero__class_Ozero(U_1516),U_1517)
| ~ sP158(U_1517,U_1516) )
& ! [U_1517,U_1516] :
( c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ozero__class_Ozero(U_1516),U_1517)
| ~ c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ouminus__class_Ouminus(U_1516,U_1517),U_1517)
| ~ sP158(U_1517,U_1516) )
& ! [U_1517,U_1516] :
( sP158(U_1517,U_1516)
| ~ class_Groups_Olinordered__ab__group__add(U_1516) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158])],[f_489_2]) ).
cnf(f_489_4,plain,
( sP158(U_1517,U_1516)
| ~ class_Groups_Olinordered__ab__group__add(U_1516) ),
inference(clausify,[status(thm)],[f_489_3]) ).
cnf(f_489_5,plain,
( c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ozero__class_Ozero(U_1516),U_1517)
| ~ c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ouminus__class_Ouminus(U_1516,U_1517),U_1517)
| ~ sP158(U_1517,U_1516) ),
inference(clausify,[status(thm)],[f_489_3]) ).
cnf(f_489_6,plain,
( c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ouminus__class_Ouminus(U_1516,U_1517),U_1517)
| ~ c_Orderings_Oord__class_Oless(U_1516,c_Groups_Ozero__class_Ozero(U_1516),U_1517)
| ~ sP158(U_1517,U_1516) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).
fof(f_490_2,plain,
! [U_1519,U_1518] :
( ( ( c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ouminus__class_Ouminus(U_1518,U_1519))
| ~ c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ozero__class_Ozero(U_1518)) )
& ( c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ozero__class_Ozero(U_1518))
| ~ c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ouminus__class_Ouminus(U_1518,U_1519)) ) )
| ~ class_Rings_Olinordered__idom(U_1518) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
( ! [U_1519,U_1518] :
( c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ouminus__class_Ouminus(U_1518,U_1519))
| ~ c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ozero__class_Ozero(U_1518))
| ~ sP159(U_1519,U_1518) )
& ! [U_1519,U_1518] :
( c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ozero__class_Ozero(U_1518))
| ~ c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ouminus__class_Ouminus(U_1518,U_1519))
| ~ sP159(U_1519,U_1518) )
& ! [U_1519,U_1518] :
( sP159(U_1519,U_1518)
| ~ class_Rings_Olinordered__idom(U_1518) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_490_2]) ).
cnf(f_490_4,plain,
( sP159(U_1519,U_1518)
| ~ class_Rings_Olinordered__idom(U_1518) ),
inference(clausify,[status(thm)],[f_490_3]) ).
cnf(f_490_5,plain,
( c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ozero__class_Ozero(U_1518))
| ~ c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ouminus__class_Ouminus(U_1518,U_1519))
| ~ sP159(U_1519,U_1518) ),
inference(clausify,[status(thm)],[f_490_3]) ).
cnf(f_490_6,plain,
( c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ouminus__class_Ouminus(U_1518,U_1519))
| ~ c_Orderings_Oord__class_Oless(U_1518,U_1519,c_Groups_Ozero__class_Ozero(U_1518))
| ~ sP159(U_1519,U_1518) ),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,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_491_2,plain,
! [U_1521,U_1520] :
( c_Groups_Oplus__class_Oplus(U_1520,U_1521,c_Groups_Ouminus__class_Ouminus(U_1520,U_1521)) = c_Groups_Ozero__class_Ozero(U_1520)
| ~ class_Groups_Ogroup__add(U_1520) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
! [U_1521,U_1520] :
( c_Groups_Oplus__class_Oplus(U_1520,U_1521,c_Groups_Ouminus__class_Ouminus(U_1520,U_1521)) = c_Groups_Ozero__class_Ozero(U_1520)
| ~ class_Groups_Ogroup__add(U_1520) ),
inference(definitional_conversion,[status(esa)],[f_491_2]) ).
cnf(f_491_4,plain,
( c_Groups_Oplus__class_Oplus(U_1520,U_1521,c_Groups_Ouminus__class_Ouminus(U_1520,U_1521)) = c_Groups_Ozero__class_Ozero(U_1520)
| ~ class_Groups_Ogroup__add(U_1520) ),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).
fof(f_492_2,plain,
! [U_1524,U_1523,U_1522] :
( ( ( U_1523 = c_Groups_Ouminus__class_Ouminus(U_1522,U_1524)
| c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1524) != c_Groups_Ozero__class_Ozero(U_1522) )
& ( c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1524) = c_Groups_Ozero__class_Ozero(U_1522)
| U_1523 != c_Groups_Ouminus__class_Ouminus(U_1522,U_1524) ) )
| ~ class_Groups_Ogroup__add(U_1522) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
( ! [U_1522,U_1523,U_1524] :
( U_1523 = c_Groups_Ouminus__class_Ouminus(U_1522,U_1524)
| c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1524) != c_Groups_Ozero__class_Ozero(U_1522)
| ~ sP160(U_1522,U_1523,U_1524) )
& ! [U_1522,U_1523,U_1524] :
( c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1524) = c_Groups_Ozero__class_Ozero(U_1522)
| U_1523 != c_Groups_Ouminus__class_Ouminus(U_1522,U_1524)
| ~ sP160(U_1522,U_1523,U_1524) )
& ! [U_1522,U_1523,U_1524] :
( sP160(U_1522,U_1523,U_1524)
| ~ class_Groups_Ogroup__add(U_1522) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_492_2]) ).
cnf(f_492_4,plain,
( sP160(U_1522,U_1523,U_1524)
| ~ class_Groups_Ogroup__add(U_1522) ),
inference(clausify,[status(thm)],[f_492_3]) ).
cnf(f_492_5,plain,
( c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1524) = c_Groups_Ozero__class_Ozero(U_1522)
| U_1523 != c_Groups_Ouminus__class_Ouminus(U_1522,U_1524)
| ~ sP160(U_1522,U_1523,U_1524) ),
inference(clausify,[status(thm)],[f_492_3]) ).
cnf(f_492_6,plain,
( U_1523 = c_Groups_Ouminus__class_Ouminus(U_1522,U_1524)
| c_Groups_Oplus__class_Oplus(U_1522,U_1523,U_1524) != c_Groups_Ozero__class_Ozero(U_1522)
| ~ sP160(U_1522,U_1523,U_1524) ),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,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_493_2,plain,
! [U_1526,U_1525] :
( c_Groups_Oplus__class_Oplus(U_1525,c_Groups_Ouminus__class_Ouminus(U_1525,U_1526),U_1526) = c_Groups_Ozero__class_Ozero(U_1525)
| ~ class_Groups_Ogroup__add(U_1525) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
! [U_1526,U_1525] :
( c_Groups_Oplus__class_Oplus(U_1525,c_Groups_Ouminus__class_Ouminus(U_1525,U_1526),U_1526) = c_Groups_Ozero__class_Ozero(U_1525)
| ~ class_Groups_Ogroup__add(U_1525) ),
inference(definitional_conversion,[status(esa)],[f_493_2]) ).
cnf(f_493_4,plain,
( c_Groups_Oplus__class_Oplus(U_1525,c_Groups_Ouminus__class_Ouminus(U_1525,U_1526),U_1526) = c_Groups_Ozero__class_Ozero(U_1525)
| ~ class_Groups_Ogroup__add(U_1525) ),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,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_494_2,plain,
! [U_1528,U_1527] :
( c_Groups_Oplus__class_Oplus(U_1527,c_Groups_Ouminus__class_Ouminus(U_1527,U_1528),U_1528) = c_Groups_Ozero__class_Ozero(U_1527)
| ~ class_Groups_Oab__group__add(U_1527) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
! [U_1528,U_1527] :
( c_Groups_Oplus__class_Oplus(U_1527,c_Groups_Ouminus__class_Ouminus(U_1527,U_1528),U_1528) = c_Groups_Ozero__class_Ozero(U_1527)
| ~ class_Groups_Oab__group__add(U_1527) ),
inference(definitional_conversion,[status(esa)],[f_494_2]) ).
cnf(f_494_4,plain,
( c_Groups_Oplus__class_Oplus(U_1527,c_Groups_Ouminus__class_Ouminus(U_1527,U_1528),U_1528) = c_Groups_Ozero__class_Ozero(U_1527)
| ~ class_Groups_Oab__group__add(U_1527) ),
inference(clausify,[status(thm)],[f_494_3]) ).
fof(f_495_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b
| 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_495_2,plain,
! [U_1531,U_1530,U_1529] :
( c_Groups_Ouminus__class_Ouminus(U_1529,U_1530) = U_1531
| c_Groups_Oplus__class_Oplus(U_1529,U_1530,U_1531) != c_Groups_Ozero__class_Ozero(U_1529)
| ~ class_Groups_Ogroup__add(U_1529) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
! [U_1529,U_1530,U_1531] :
( c_Groups_Ouminus__class_Ouminus(U_1529,U_1530) = U_1531
| c_Groups_Oplus__class_Oplus(U_1529,U_1530,U_1531) != c_Groups_Ozero__class_Ozero(U_1529)
| ~ class_Groups_Ogroup__add(U_1529) ),
inference(definitional_conversion,[status(esa)],[f_495_2]) ).
cnf(f_495_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1529,U_1530) = U_1531
| c_Groups_Oplus__class_Oplus(U_1529,U_1530,U_1531) != c_Groups_Ozero__class_Ozero(U_1529)
| ~ class_Groups_Ogroup__add(U_1529) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) )
& ( V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff]) ).
fof(f_496_2,plain,
! [U_1534,U_1533,U_1532] :
( ( ( c_Groups_Oplus__class_Oplus(U_1532,U_1533,U_1534) = c_Groups_Ozero__class_Ozero(U_1532)
| U_1534 != c_Groups_Ouminus__class_Ouminus(U_1532,U_1533) )
& ( U_1534 = c_Groups_Ouminus__class_Ouminus(U_1532,U_1533)
| c_Groups_Oplus__class_Oplus(U_1532,U_1533,U_1534) != c_Groups_Ozero__class_Ozero(U_1532) ) )
| ~ class_Groups_Ogroup__add(U_1532) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
( ! [U_1533,U_1532,U_1534] :
( c_Groups_Oplus__class_Oplus(U_1532,U_1533,U_1534) = c_Groups_Ozero__class_Ozero(U_1532)
| U_1534 != c_Groups_Ouminus__class_Ouminus(U_1532,U_1533)
| ~ sP161(U_1533,U_1532,U_1534) )
& ! [U_1533,U_1532,U_1534] :
( U_1534 = c_Groups_Ouminus__class_Ouminus(U_1532,U_1533)
| c_Groups_Oplus__class_Oplus(U_1532,U_1533,U_1534) != c_Groups_Ozero__class_Ozero(U_1532)
| ~ sP161(U_1533,U_1532,U_1534) )
& ! [U_1533,U_1532,U_1534] :
( sP161(U_1533,U_1532,U_1534)
| ~ class_Groups_Ogroup__add(U_1532) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_496_2]) ).
cnf(f_496_4,plain,
( sP161(U_1533,U_1532,U_1534)
| ~ class_Groups_Ogroup__add(U_1532) ),
inference(clausify,[status(thm)],[f_496_3]) ).
cnf(f_496_5,plain,
( U_1534 = c_Groups_Ouminus__class_Ouminus(U_1532,U_1533)
| c_Groups_Oplus__class_Oplus(U_1532,U_1533,U_1534) != c_Groups_Ozero__class_Ozero(U_1532)
| ~ sP161(U_1533,U_1532,U_1534) ),
inference(clausify,[status(thm)],[f_496_3]) ).
cnf(f_496_6,plain,
( c_Groups_Oplus__class_Oplus(U_1532,U_1533,U_1534) = c_Groups_Ozero__class_Ozero(U_1532)
| U_1534 != c_Groups_Ouminus__class_Ouminus(U_1532,U_1533)
| ~ sP161(U_1533,U_1532,U_1534) ),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(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_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__diff__mult]) ).
fof(f_497_2,plain,
! [U_1539,U_1538,U_1537,U_1536,U_1535] :
( c_Groups_Ominus__class_Ominus(U_1535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),U_1537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1538),U_1539)) = c_Groups_Oplus__class_Oplus(U_1535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),c_Groups_Ominus__class_Ominus(U_1535,U_1537,U_1539)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),c_Groups_Ominus__class_Ominus(U_1535,U_1536,U_1538)),U_1539))
| ~ class_Rings_Oring(U_1535) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
! [U_1535,U_1536,U_1537,U_1538,U_1539] :
( c_Groups_Ominus__class_Ominus(U_1535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),U_1537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1538),U_1539)) = c_Groups_Oplus__class_Oplus(U_1535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),c_Groups_Ominus__class_Ominus(U_1535,U_1537,U_1539)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),c_Groups_Ominus__class_Ominus(U_1535,U_1536,U_1538)),U_1539))
| ~ class_Rings_Oring(U_1535) ),
inference(definitional_conversion,[status(esa)],[f_497_2]) ).
cnf(f_497_4,plain,
( c_Groups_Ominus__class_Ominus(U_1535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),U_1537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1538),U_1539)) = c_Groups_Oplus__class_Oplus(U_1535,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),c_Groups_Ominus__class_Ominus(U_1535,U_1537,U_1539)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),c_Groups_Ominus__class_Ominus(U_1535,U_1536,U_1538)),U_1539))
| ~ class_Rings_Oring(U_1535) ),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(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_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod]) ).
fof(f_498_2,plain,
! [U_1544,U_1543,U_1542,U_1541,U_1540] :
( c_Groups_Ominus__class_Ominus(U_1540,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1543),U_1544)) = c_Groups_Oplus__class_Oplus(U_1540,c_Groups_Oplus__class_Oplus(U_1540,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),c_Groups_Ominus__class_Ominus(U_1540,U_1541,U_1543)),c_Groups_Ominus__class_Ominus(U_1540,U_1542,U_1544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),c_Groups_Ominus__class_Ominus(U_1540,U_1541,U_1543)),U_1544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1543),c_Groups_Ominus__class_Ominus(U_1540,U_1542,U_1544)))
| ~ class_RealVector_Oreal__normed__algebra(U_1540) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
! [U_1541,U_1540,U_1542,U_1543,U_1544] :
( c_Groups_Ominus__class_Ominus(U_1540,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1543),U_1544)) = c_Groups_Oplus__class_Oplus(U_1540,c_Groups_Oplus__class_Oplus(U_1540,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),c_Groups_Ominus__class_Ominus(U_1540,U_1541,U_1543)),c_Groups_Ominus__class_Ominus(U_1540,U_1542,U_1544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),c_Groups_Ominus__class_Ominus(U_1540,U_1541,U_1543)),U_1544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1543),c_Groups_Ominus__class_Ominus(U_1540,U_1542,U_1544)))
| ~ class_RealVector_Oreal__normed__algebra(U_1540) ),
inference(definitional_conversion,[status(esa)],[f_498_2]) ).
cnf(f_498_4,plain,
( c_Groups_Ominus__class_Ominus(U_1540,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1543),U_1544)) = c_Groups_Oplus__class_Oplus(U_1540,c_Groups_Oplus__class_Oplus(U_1540,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),c_Groups_Ominus__class_Ominus(U_1540,U_1541,U_1543)),c_Groups_Ominus__class_Ominus(U_1540,U_1542,U_1544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),c_Groups_Ominus__class_Ominus(U_1540,U_1541,U_1543)),U_1544)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1540),U_1543),c_Groups_Ominus__class_Ominus(U_1540,U_1542,U_1544)))
| ~ class_RealVector_Oreal__normed__algebra(U_1540) ),
inference(clausify,[status(thm)],[f_498_3]) ).
fof(f_499_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
| V_ca_2 != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2) )
& ( V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2) ) )
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).
fof(f_499_2,plain,
! [U_1550,U_1549,U_1548,U_1547,U_1546,U_1545] :
( ( ( c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547),U_1548) = c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1549),U_1547),U_1550)
| U_1548 != c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),c_Groups_Ominus__class_Ominus(U_1545,U_1549,U_1546)),U_1547),U_1550) )
& ( U_1548 = c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),c_Groups_Ominus__class_Ominus(U_1545,U_1549,U_1546)),U_1547),U_1550)
| c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547),U_1548) != c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1549),U_1547),U_1550) ) )
| ~ class_Rings_Oring(U_1545) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
( ! [U_1545,U_1546,U_1547,U_1548,U_1549,U_1550] :
( c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547),U_1548) = c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1549),U_1547),U_1550)
| U_1548 != c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),c_Groups_Ominus__class_Ominus(U_1545,U_1549,U_1546)),U_1547),U_1550)
| ~ sP162(U_1545,U_1546,U_1547,U_1548,U_1549,U_1550) )
& ! [U_1545,U_1546,U_1547,U_1548,U_1549,U_1550] :
( U_1548 = c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),c_Groups_Ominus__class_Ominus(U_1545,U_1549,U_1546)),U_1547),U_1550)
| c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547),U_1548) != c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1549),U_1547),U_1550)
| ~ sP162(U_1545,U_1546,U_1547,U_1548,U_1549,U_1550) )
& ! [U_1545,U_1546,U_1547,U_1548,U_1549,U_1550] :
( sP162(U_1545,U_1546,U_1547,U_1548,U_1549,U_1550)
| ~ class_Rings_Oring(U_1545) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_499_2]) ).
cnf(f_499_4,plain,
( sP162(U_1545,U_1546,U_1547,U_1548,U_1549,U_1550)
| ~ class_Rings_Oring(U_1545) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_5,plain,
( U_1548 = c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),c_Groups_Ominus__class_Ominus(U_1545,U_1549,U_1546)),U_1547),U_1550)
| c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547),U_1548) != c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1549),U_1547),U_1550)
| ~ sP162(U_1545,U_1546,U_1547,U_1548,U_1549,U_1550) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_6,plain,
( c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547),U_1548) = c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1549),U_1547),U_1550)
| U_1548 != c_Groups_Oplus__class_Oplus(U_1545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),c_Groups_Ominus__class_Ominus(U_1545,U_1549,U_1546)),U_1547),U_1550)
| ~ sP162(U_1545,U_1546,U_1547,U_1548,U_1549,U_1550) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2) != V_d_2 )
& ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2) = V_d_2
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2) ) )
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).
fof(f_500_2,plain,
! [U_1556,U_1555,U_1554,U_1553,U_1552,U_1551] :
( ( ( c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1552),U_1553),U_1554) = c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1555),U_1553),U_1556)
| c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),c_Groups_Ominus__class_Ominus(U_1551,U_1552,U_1555)),U_1553),U_1554) != U_1556 )
& ( c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),c_Groups_Ominus__class_Ominus(U_1551,U_1552,U_1555)),U_1553),U_1554) = U_1556
| c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1552),U_1553),U_1554) != c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1555),U_1553),U_1556) ) )
| ~ class_Rings_Oring(U_1551) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
( ! [U_1553,U_1551,U_1554,U_1555,U_1552,U_1556] :
( c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1552),U_1553),U_1554) = c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1555),U_1553),U_1556)
| c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),c_Groups_Ominus__class_Ominus(U_1551,U_1552,U_1555)),U_1553),U_1554) != U_1556
| ~ sP163(U_1553,U_1551,U_1554,U_1555,U_1552,U_1556) )
& ! [U_1553,U_1551,U_1554,U_1555,U_1552,U_1556] :
( c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),c_Groups_Ominus__class_Ominus(U_1551,U_1552,U_1555)),U_1553),U_1554) = U_1556
| c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1552),U_1553),U_1554) != c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1555),U_1553),U_1556)
| ~ sP163(U_1553,U_1551,U_1554,U_1555,U_1552,U_1556) )
& ! [U_1553,U_1551,U_1554,U_1555,U_1552,U_1556] :
( sP163(U_1553,U_1551,U_1554,U_1555,U_1552,U_1556)
| ~ class_Rings_Oring(U_1551) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_500_2]) ).
cnf(f_500_4,plain,
( sP163(U_1553,U_1551,U_1554,U_1555,U_1552,U_1556)
| ~ class_Rings_Oring(U_1551) ),
inference(clausify,[status(thm)],[f_500_3]) ).
cnf(f_500_5,plain,
( c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),c_Groups_Ominus__class_Ominus(U_1551,U_1552,U_1555)),U_1553),U_1554) = U_1556
| c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1552),U_1553),U_1554) != c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1555),U_1553),U_1556)
| ~ sP163(U_1553,U_1551,U_1554,U_1555,U_1552,U_1556) ),
inference(clausify,[status(thm)],[f_500_3]) ).
cnf(f_500_6,plain,
( c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1552),U_1553),U_1554) = c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),U_1555),U_1553),U_1556)
| c_Groups_Oplus__class_Oplus(U_1551,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1551),c_Groups_Ominus__class_Ominus(U_1551,U_1552,U_1555)),U_1553),U_1554) != U_1556
| ~ sP163(U_1553,U_1551,U_1554,U_1555,U_1552,U_1556) ),
inference(clausify,[status(thm)],[f_500_3]) ).
fof(f_501_1,plain,
! [V_x_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
& V_x_2 != c_Groups_Oone__class_Oone(T_a) ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).
fof(f_501_2,plain,
! [U_1558,U_1557] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1557),U_1558),U_1558) = c_Groups_Oone__class_Oone(U_1557)
| ( U_1558 != c_Groups_Ouminus__class_Ouminus(U_1557,c_Groups_Oone__class_Oone(U_1557))
& U_1558 != c_Groups_Oone__class_Oone(U_1557) ) )
& ( U_1558 = c_Groups_Ouminus__class_Ouminus(U_1557,c_Groups_Oone__class_Oone(U_1557))
| U_1558 = c_Groups_Oone__class_Oone(U_1557)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1557),U_1558),U_1558) != c_Groups_Oone__class_Oone(U_1557) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_1557) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
( ! [U_1558,U_1557] :
( U_1558 != c_Groups_Ouminus__class_Ouminus(U_1557,c_Groups_Oone__class_Oone(U_1557))
| ~ sP164(U_1558,U_1557) )
& ! [U_1558,U_1557] :
( U_1558 != c_Groups_Oone__class_Oone(U_1557)
| ~ sP164(U_1558,U_1557) )
& ! [U_1558,U_1557] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1557),U_1558),U_1558) = c_Groups_Oone__class_Oone(U_1557)
| sP164(U_1558,U_1557)
| ~ sP165(U_1558,U_1557) )
& ! [U_1558,U_1557] :
( U_1558 = c_Groups_Ouminus__class_Ouminus(U_1557,c_Groups_Oone__class_Oone(U_1557))
| U_1558 = c_Groups_Oone__class_Oone(U_1557)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1557),U_1558),U_1558) != c_Groups_Oone__class_Oone(U_1557)
| ~ sP165(U_1558,U_1557) )
& ! [U_1558,U_1557] :
( sP165(U_1558,U_1557)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1557) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164,sP165])],[f_501_2]) ).
cnf(f_501_4,plain,
( sP165(U_1558,U_1557)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1557) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_5,plain,
( U_1558 = c_Groups_Ouminus__class_Ouminus(U_1557,c_Groups_Oone__class_Oone(U_1557))
| U_1558 = c_Groups_Oone__class_Oone(U_1557)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1557),U_1558),U_1558) != c_Groups_Oone__class_Oone(U_1557)
| ~ sP165(U_1558,U_1557) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1557),U_1558),U_1558) = c_Groups_Oone__class_Oone(U_1557)
| sP164(U_1558,U_1557)
| ~ sP165(U_1558,U_1557) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_7,plain,
( U_1558 != c_Groups_Oone__class_Oone(U_1557)
| ~ sP164(U_1558,U_1557) ),
inference(clausify,[status(thm)],[f_501_3]) ).
cnf(f_501_8,plain,
( U_1558 != c_Groups_Ouminus__class_Ouminus(U_1557,c_Groups_Oone__class_Oone(U_1557))
| ~ sP164(U_1558,U_1557) ),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_502_2,plain,
! [U_1560,U_1559] :
( c_Groups_Ouminus__class_Ouminus(U_1559,U_1560) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1559),c_Groups_Ouminus__class_Ouminus(U_1559,c_Groups_Oone__class_Oone(U_1559))),U_1560)
| ~ class_Rings_Ocomm__ring__1(U_1559) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
! [U_1560,U_1559] :
( c_Groups_Ouminus__class_Ouminus(U_1559,U_1560) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1559),c_Groups_Ouminus__class_Ouminus(U_1559,c_Groups_Oone__class_Oone(U_1559))),U_1560)
| ~ class_Rings_Ocomm__ring__1(U_1559) ),
inference(definitional_conversion,[status(esa)],[f_502_2]) ).
cnf(f_502_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1559,U_1560) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1559),c_Groups_Ouminus__class_Ouminus(U_1559,c_Groups_Oone__class_Oone(U_1559))),U_1560)
| ~ class_Rings_Ocomm__ring__1(U_1559) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,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_503_2,plain,
! [U_1563,U_1562,U_1561] :
( c_Orderings_Oord__class_Oless__eq(U_1561,c_Groups_Ominus__class_Ominus(U_1561,c_Groups_Oabs__class_Oabs(U_1561,U_1562),c_Groups_Oabs__class_Oabs(U_1561,U_1563)),c_Groups_Oabs__class_Oabs(U_1561,c_Groups_Ominus__class_Ominus(U_1561,U_1563,U_1562)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1561) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
! [U_1563,U_1561,U_1562] :
( c_Orderings_Oord__class_Oless__eq(U_1561,c_Groups_Ominus__class_Ominus(U_1561,c_Groups_Oabs__class_Oabs(U_1561,U_1562),c_Groups_Oabs__class_Oabs(U_1561,U_1563)),c_Groups_Oabs__class_Oabs(U_1561,c_Groups_Ominus__class_Ominus(U_1561,U_1563,U_1562)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1561) ),
inference(definitional_conversion,[status(esa)],[f_503_2]) ).
cnf(f_503_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1561,c_Groups_Ominus__class_Ominus(U_1561,c_Groups_Oabs__class_Oabs(U_1561,U_1562),c_Groups_Oabs__class_Oabs(U_1561,U_1563)),c_Groups_Oabs__class_Oabs(U_1561,c_Groups_Ominus__class_Ominus(U_1561,U_1563,U_1562)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1561) ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,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_504_2,plain,
! [U_1566,U_1565,U_1564] :
( c_Orderings_Oord__class_Oless__eq(U_1564,c_Groups_Ominus__class_Ominus(U_1564,c_Groups_Oabs__class_Oabs(U_1564,U_1565),c_Groups_Oabs__class_Oabs(U_1564,U_1566)),c_Groups_Oabs__class_Oabs(U_1564,c_Groups_Ominus__class_Ominus(U_1564,U_1565,U_1566)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1564) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
! [U_1564,U_1565,U_1566] :
( c_Orderings_Oord__class_Oless__eq(U_1564,c_Groups_Ominus__class_Ominus(U_1564,c_Groups_Oabs__class_Oabs(U_1564,U_1565),c_Groups_Oabs__class_Oabs(U_1564,U_1566)),c_Groups_Oabs__class_Oabs(U_1564,c_Groups_Ominus__class_Ominus(U_1564,U_1565,U_1566)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1564) ),
inference(definitional_conversion,[status(esa)],[f_504_2]) ).
cnf(f_504_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1564,c_Groups_Ominus__class_Ominus(U_1564,c_Groups_Oabs__class_Oabs(U_1564,U_1565),c_Groups_Oabs__class_Oabs(U_1564,U_1566)),c_Groups_Oabs__class_Oabs(U_1564,c_Groups_Ominus__class_Ominus(U_1564,U_1565,U_1566)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1564) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,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_505_2,plain,
! [U_1569,U_1568,U_1567] :
( c_Orderings_Oord__class_Oless__eq(U_1567,c_Groups_Oabs__class_Oabs(U_1567,c_Groups_Ominus__class_Ominus(U_1567,c_Groups_Oabs__class_Oabs(U_1567,U_1568),c_Groups_Oabs__class_Oabs(U_1567,U_1569))),c_Groups_Oabs__class_Oabs(U_1567,c_Groups_Ominus__class_Ominus(U_1567,U_1568,U_1569)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1567) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
! [U_1567,U_1568,U_1569] :
( c_Orderings_Oord__class_Oless__eq(U_1567,c_Groups_Oabs__class_Oabs(U_1567,c_Groups_Ominus__class_Ominus(U_1567,c_Groups_Oabs__class_Oabs(U_1567,U_1568),c_Groups_Oabs__class_Oabs(U_1567,U_1569))),c_Groups_Oabs__class_Oabs(U_1567,c_Groups_Ominus__class_Ominus(U_1567,U_1568,U_1569)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1567) ),
inference(definitional_conversion,[status(esa)],[f_505_2]) ).
cnf(f_505_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1567,c_Groups_Oabs__class_Oabs(U_1567,c_Groups_Ominus__class_Ominus(U_1567,c_Groups_Oabs__class_Oabs(U_1567,U_1568),c_Groups_Oabs__class_Oabs(U_1567,U_1569))),c_Groups_Oabs__class_Oabs(U_1567,c_Groups_Ominus__class_Ominus(U_1567,U_1568,U_1569)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1567) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,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_506_2,plain,
! [U_1572,U_1571,U_1570] :
( c_Orderings_Oord__class_Oless__eq(U_1570,c_Groups_Ouminus__class_Ouminus(U_1570,U_1571),U_1572)
| ~ c_Orderings_Oord__class_Oless__eq(U_1570,c_Groups_Oabs__class_Oabs(U_1570,U_1571),U_1572)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1570) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_1571,U_1570,U_1572] :
( c_Orderings_Oord__class_Oless__eq(U_1570,c_Groups_Ouminus__class_Ouminus(U_1570,U_1571),U_1572)
| ~ c_Orderings_Oord__class_Oless__eq(U_1570,c_Groups_Oabs__class_Oabs(U_1570,U_1571),U_1572)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1570) ),
inference(definitional_conversion,[status(esa)],[f_506_2]) ).
cnf(f_506_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1570,c_Groups_Ouminus__class_Ouminus(U_1570,U_1571),U_1572)
| ~ c_Orderings_Oord__class_Oless__eq(U_1570,c_Groups_Oabs__class_Oabs(U_1570,U_1571),U_1572)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1570) ),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ 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_507_2,plain,
! [U_1575,U_1574,U_1573] :
( c_Orderings_Oord__class_Oless__eq(U_1573,c_Groups_Oabs__class_Oabs(U_1573,U_1574),U_1575)
| ~ c_Orderings_Oord__class_Oless__eq(U_1573,c_Groups_Ouminus__class_Ouminus(U_1573,U_1574),U_1575)
| ~ c_Orderings_Oord__class_Oless__eq(U_1573,U_1574,U_1575)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1573) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
! [U_1574,U_1573,U_1575] :
( c_Orderings_Oord__class_Oless__eq(U_1573,c_Groups_Oabs__class_Oabs(U_1573,U_1574),U_1575)
| ~ c_Orderings_Oord__class_Oless__eq(U_1573,c_Groups_Ouminus__class_Ouminus(U_1573,U_1574),U_1575)
| ~ c_Orderings_Oord__class_Oless__eq(U_1573,U_1574,U_1575)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1573) ),
inference(definitional_conversion,[status(esa)],[f_507_2]) ).
cnf(f_507_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1573,c_Groups_Oabs__class_Oabs(U_1573,U_1574),U_1575)
| ~ c_Orderings_Oord__class_Oless__eq(U_1573,c_Groups_Ouminus__class_Ouminus(U_1573,U_1574),U_1575)
| ~ c_Orderings_Oord__class_Oless__eq(U_1573,U_1574,U_1575)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1573) ),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).
fof(f_508_2,plain,
! [U_1578,U_1577,U_1576] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Oabs__class_Oabs(U_1576,U_1577),U_1578)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Ouminus__class_Ouminus(U_1576,U_1577),U_1578)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,U_1577,U_1578) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Ouminus__class_Ouminus(U_1576,U_1577),U_1578)
& c_Orderings_Oord__class_Oless__eq(U_1576,U_1577,U_1578) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Oabs__class_Oabs(U_1576,U_1577),U_1578) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_1576) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
fof(f_508_3,plain,
( ! [U_1577,U_1578,U_1576] :
( c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Ouminus__class_Ouminus(U_1576,U_1577),U_1578)
| ~ sP166(U_1577,U_1578,U_1576) )
& ! [U_1577,U_1578,U_1576] :
( c_Orderings_Oord__class_Oless__eq(U_1576,U_1577,U_1578)
| ~ sP166(U_1577,U_1578,U_1576) )
& ! [U_1577,U_1578,U_1576] :
( c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Oabs__class_Oabs(U_1576,U_1577),U_1578)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Ouminus__class_Ouminus(U_1576,U_1577),U_1578)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,U_1577,U_1578)
| ~ sP167(U_1577,U_1578,U_1576) )
& ! [U_1577,U_1578,U_1576] :
( sP166(U_1577,U_1578,U_1576)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Oabs__class_Oabs(U_1576,U_1577),U_1578)
| ~ sP167(U_1577,U_1578,U_1576) )
& ! [U_1577,U_1578,U_1576] :
( sP167(U_1577,U_1578,U_1576)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1576) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166,sP167])],[f_508_2]) ).
cnf(f_508_4,plain,
( sP167(U_1577,U_1578,U_1576)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1576) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_5,plain,
( sP166(U_1577,U_1578,U_1576)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Oabs__class_Oabs(U_1576,U_1577),U_1578)
| ~ sP167(U_1577,U_1578,U_1576) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Oabs__class_Oabs(U_1576,U_1577),U_1578)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Ouminus__class_Ouminus(U_1576,U_1577),U_1578)
| ~ c_Orderings_Oord__class_Oless__eq(U_1576,U_1577,U_1578)
| ~ sP167(U_1577,U_1578,U_1576) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1576,U_1577,U_1578)
| ~ sP166(U_1577,U_1578,U_1576) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_1576,c_Groups_Ouminus__class_Ouminus(U_1576,U_1577),U_1578)
| ~ sP166(U_1577,U_1578,U_1576) ),
inference(clausify,[status(thm)],[f_508_3]) ).
fof(f_509_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),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_509_2,plain,
! [U_1580,U_1579] :
( c_Orderings_Oord__class_Oless__eq(U_1579,c_Groups_Ouminus__class_Ouminus(U_1579,U_1580),c_Groups_Oabs__class_Oabs(U_1579,U_1580))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1579) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
! [U_1579,U_1580] :
( c_Orderings_Oord__class_Oless__eq(U_1579,c_Groups_Ouminus__class_Ouminus(U_1579,U_1580),c_Groups_Oabs__class_Oabs(U_1579,U_1580))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1579) ),
inference(definitional_conversion,[status(esa)],[f_509_2]) ).
cnf(f_509_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1579,c_Groups_Ouminus__class_Ouminus(U_1579,U_1580),c_Groups_Oabs__class_Oabs(U_1579,U_1580))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1579) ),
inference(clausify,[status(thm)],[f_509_3]) ).
fof(f_510_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).
fof(f_510_2,plain,
! [U_1583,U_1582,U_1581] :
( ( ( c_Orderings_Oord__class_Oless(U_1581,c_Groups_Oabs__class_Oabs(U_1581,U_1582),U_1583)
| ~ c_Orderings_Oord__class_Oless(U_1581,c_Groups_Ouminus__class_Ouminus(U_1581,U_1582),U_1583)
| ~ c_Orderings_Oord__class_Oless(U_1581,U_1582,U_1583) )
& ( ( c_Orderings_Oord__class_Oless(U_1581,c_Groups_Ouminus__class_Ouminus(U_1581,U_1582),U_1583)
& c_Orderings_Oord__class_Oless(U_1581,U_1582,U_1583) )
| ~ c_Orderings_Oord__class_Oless(U_1581,c_Groups_Oabs__class_Oabs(U_1581,U_1582),U_1583) ) )
| ~ class_Rings_Olinordered__idom(U_1581) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
( ! [U_1583,U_1582,U_1581] :
( c_Orderings_Oord__class_Oless(U_1581,c_Groups_Ouminus__class_Ouminus(U_1581,U_1582),U_1583)
| ~ sP168(U_1583,U_1582,U_1581) )
& ! [U_1583,U_1582,U_1581] :
( c_Orderings_Oord__class_Oless(U_1581,U_1582,U_1583)
| ~ sP168(U_1583,U_1582,U_1581) )
& ! [U_1583,U_1582,U_1581] :
( c_Orderings_Oord__class_Oless(U_1581,c_Groups_Oabs__class_Oabs(U_1581,U_1582),U_1583)
| ~ c_Orderings_Oord__class_Oless(U_1581,c_Groups_Ouminus__class_Ouminus(U_1581,U_1582),U_1583)
| ~ c_Orderings_Oord__class_Oless(U_1581,U_1582,U_1583)
| ~ sP169(U_1583,U_1582,U_1581) )
& ! [U_1583,U_1582,U_1581] :
( sP168(U_1583,U_1582,U_1581)
| ~ c_Orderings_Oord__class_Oless(U_1581,c_Groups_Oabs__class_Oabs(U_1581,U_1582),U_1583)
| ~ sP169(U_1583,U_1582,U_1581) )
& ! [U_1583,U_1582,U_1581] :
( sP169(U_1583,U_1582,U_1581)
| ~ class_Rings_Olinordered__idom(U_1581) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169])],[f_510_2]) ).
cnf(f_510_4,plain,
( sP169(U_1583,U_1582,U_1581)
| ~ class_Rings_Olinordered__idom(U_1581) ),
inference(clausify,[status(thm)],[f_510_3]) ).
cnf(f_510_5,plain,
( sP168(U_1583,U_1582,U_1581)
| ~ c_Orderings_Oord__class_Oless(U_1581,c_Groups_Oabs__class_Oabs(U_1581,U_1582),U_1583)
| ~ sP169(U_1583,U_1582,U_1581) ),
inference(clausify,[status(thm)],[f_510_3]) ).
cnf(f_510_6,plain,
( c_Orderings_Oord__class_Oless(U_1581,c_Groups_Oabs__class_Oabs(U_1581,U_1582),U_1583)
| ~ c_Orderings_Oord__class_Oless(U_1581,c_Groups_Ouminus__class_Ouminus(U_1581,U_1582),U_1583)
| ~ c_Orderings_Oord__class_Oless(U_1581,U_1582,U_1583)
| ~ sP169(U_1583,U_1582,U_1581) ),
inference(clausify,[status(thm)],[f_510_3]) ).
cnf(f_510_7,plain,
( c_Orderings_Oord__class_Oless(U_1581,U_1582,U_1583)
| ~ sP168(U_1583,U_1582,U_1581) ),
inference(clausify,[status(thm)],[f_510_3]) ).
cnf(f_510_8,plain,
( c_Orderings_Oord__class_Oless(U_1581,c_Groups_Ouminus__class_Ouminus(U_1581,U_1582),U_1583)
| ~ sP168(U_1583,U_1582,U_1581) ),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff]) ).
fof(f_511_2,plain,
! [U_1585,U_1584] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1584,U_1585)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1584,U_1585),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1584,U_1585),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1584,U_1585) ) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
( ! [U_1589,U_1587] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1587,U_1589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1587,U_1589),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1588,U_1586] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1586,U_1588),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1586,U_1588) ) ),
inference(miniscope,[status(thm)],[f_511_2]) ).
fof(f_511_4,plain,
( ! [U_1589,U_1587] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1587,U_1589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1587,U_1589),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1586,U_1588] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1586,U_1588),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1586,U_1588) ) ),
inference(definitional_conversion,[status(esa)],[f_511_3]) ).
cnf(f_511_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1586,U_1588),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1586,U_1588) ),
inference(clausify,[status(thm)],[f_511_4]) ).
cnf(f_511_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1587,U_1589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1587,U_1589),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_511_4]) ).
fof(f_512_1,plain,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)),
inference(fof_nnf,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(f_512_2,plain,
! [U_1591,U_1590] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1590),U_1590)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1591),U_1591)),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_1591,U_1590] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1590),U_1590)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1591),U_1591)),
inference(definitional_conversion,[status(esa)],[f_512_2]) ).
cnf(f_512_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1590),U_1590)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1591),U_1591)),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) )
& ( V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff]) ).
fof(f_513_2,plain,
! [U_1593,U_1592] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1592,U_1593) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1593 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1592) )
& ( U_1593 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1592)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1592,U_1593) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
( ! [U_1597,U_1595] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1595,U_1597) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1597 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1595) )
& ! [U_1596,U_1594] :
( U_1596 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1594)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1594,U_1596) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_513_2]) ).
fof(f_513_4,plain,
( ! [U_1597,U_1595] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1595,U_1597) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1597 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1595) )
& ! [U_1594,U_1596] :
( U_1596 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1594)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1594,U_1596) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_513_3]) ).
cnf(f_513_5,plain,
( U_1596 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1594)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1594,U_1596) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_513_4]) ).
cnf(f_513_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1595,U_1597) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1597 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1595) ),
inference(clausify,[status(thm)],[f_513_4]) ).
fof(f_514_1,plain,
! [V_a_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != V_a_2 )
& ( V_x_2 = V_a_2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff]) ).
fof(f_514_2,plain,
! [U_1599,U_1598] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1599)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1598 != U_1599 )
& ( U_1598 = U_1599
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1598,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1599)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
( ! [U_1603,U_1601] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1601,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1603)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1601 != U_1603 )
& ! [U_1602,U_1600] :
( U_1600 = U_1602
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1600,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1602)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_514_2]) ).
fof(f_514_4,plain,
( ! [U_1601,U_1603] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1601,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1603)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1601 != U_1603 )
& ! [U_1602,U_1600] :
( U_1600 = U_1602
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1600,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1602)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_514_3]) ).
cnf(f_514_5,plain,
( U_1600 = U_1602
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1600,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1602)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_514_4]) ).
cnf(f_514_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1601,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1603)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1601 != U_1603 ),
inference(clausify,[status(thm)],[f_514_4]) ).
fof(f_515_1,plain,
! [V_n,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__0]) ).
fof(f_515_2,plain,
! [U_1605,U_1604] :
( hAPP(c_Polynomial_Ocoeff(U_1604,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1604))),U_1605) = c_Groups_Ozero__class_Ozero(U_1604)
| ~ class_Groups_Ozero(U_1604) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_1604,U_1605] :
( hAPP(c_Polynomial_Ocoeff(U_1604,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1604))),U_1605) = c_Groups_Ozero__class_Ozero(U_1604)
| ~ class_Groups_Ozero(U_1604) ),
inference(definitional_conversion,[status(esa)],[f_515_2]) ).
cnf(f_515_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1604,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1604))),U_1605) = c_Groups_Ozero__class_Ozero(U_1604)
| ~ class_Groups_Ozero(U_1604) ),
inference(clausify,[status(thm)],[f_515_3]) ).
fof(f_516_1,plain,
! [V_ra_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2) ) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff]) ).
fof(f_516_2,plain,
! [U_1607,U_1606] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1606),U_1607)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1606,U_1607)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1607),U_1606) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1606,U_1607)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1607),U_1606) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1606),U_1607) ) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
( ! [U_1611,U_1609] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1609),U_1611)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1609,U_1611)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1611),U_1609) )
& ! [U_1610,U_1608] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1608,U_1610)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1610),U_1608) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1608),U_1610) ) ),
inference(miniscope,[status(thm)],[f_516_2]) ).
fof(f_516_4,plain,
( ! [U_1610,U_1608] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1608,U_1610)
| ~ sP170(U_1610,U_1608) )
& ! [U_1610,U_1608] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1610),U_1608)
| ~ sP170(U_1610,U_1608) )
& ! [U_1611,U_1609] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1609),U_1611)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1609,U_1611)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1611),U_1609) )
& ! [U_1610,U_1608] :
( sP170(U_1610,U_1608)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1608),U_1610) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_516_3]) ).
cnf(f_516_5,plain,
( sP170(U_1610,U_1608)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1608),U_1610) ),
inference(clausify,[status(thm)],[f_516_4]) ).
cnf(f_516_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1609),U_1611)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1609,U_1611)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1611),U_1609) ),
inference(clausify,[status(thm)],[f_516_4]) ).
cnf(f_516_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1610),U_1608)
| ~ sP170(U_1610,U_1608) ),
inference(clausify,[status(thm)],[f_516_4]) ).
cnf(f_516_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1608,U_1610)
| ~ sP170(U_1610,U_1608) ),
inference(clausify,[status(thm)],[f_516_4]) ).
fof(f_517_1,plain,
! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))),
inference(fof_nnf,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(f_517_2,plain,
! [U_1613,U_1612] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1612,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1613))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1613,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1612))),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
! [U_1612,U_1613] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1612,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1613))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1613,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1612))),
inference(definitional_conversion,[status(esa)],[f_517_2]) ).
cnf(f_517_4,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1612,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1613))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1613,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1612))),
inference(clausify,[status(thm)],[f_517_3]) ).
fof(f_518_1,plain,
! [V_n,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__add]) ).
fof(f_518_2,plain,
! [U_1617,U_1616,U_1615,U_1614] :
( hAPP(c_Polynomial_Ocoeff(U_1614,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1614),U_1615,U_1616)),U_1617) = c_Groups_Oplus__class_Oplus(U_1614,hAPP(c_Polynomial_Ocoeff(U_1614,U_1615),U_1617),hAPP(c_Polynomial_Ocoeff(U_1614,U_1616),U_1617))
| ~ class_Groups_Ocomm__monoid__add(U_1614) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
! [U_1614,U_1615,U_1616,U_1617] :
( hAPP(c_Polynomial_Ocoeff(U_1614,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1614),U_1615,U_1616)),U_1617) = c_Groups_Oplus__class_Oplus(U_1614,hAPP(c_Polynomial_Ocoeff(U_1614,U_1615),U_1617),hAPP(c_Polynomial_Ocoeff(U_1614,U_1616),U_1617))
| ~ class_Groups_Ocomm__monoid__add(U_1614) ),
inference(definitional_conversion,[status(esa)],[f_518_2]) ).
cnf(f_518_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1614,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1614),U_1615,U_1616)),U_1617) = c_Groups_Oplus__class_Oplus(U_1614,hAPP(c_Polynomial_Ocoeff(U_1614,U_1615),U_1617),hAPP(c_Polynomial_Ocoeff(U_1614,U_1616),U_1617))
| ~ class_Groups_Ocomm__monoid__add(U_1614) ),
inference(clausify,[status(thm)],[f_518_3]) ).
fof(f_519_1,plain,
! [V_x,T_a] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) ) )
| V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__poly__def]) ).
fof(f_519_2,plain,
! [U_1619,U_1618] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1618),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1618)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1618),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)),U_1619) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1618))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1618),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)),U_1619) ) )
| U_1619 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618))
| U_1619 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)) ) )
| ~ class_Rings_Olinordered__idom(U_1618) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
( ! [U_1619,U_1618] :
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1618),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1618)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1618),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)),U_1619)
| ~ sP171(U_1619,U_1618) )
& ! [U_1619,U_1618] :
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1618))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1618),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)),U_1619)
| ~ sP171(U_1619,U_1618) )
& ! [U_1619,U_1618] :
( sP171(U_1619,U_1618)
| U_1619 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618))
| ~ sP172(U_1619,U_1618) )
& ! [U_1619,U_1618] :
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618))
| U_1619 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618))
| ~ sP172(U_1619,U_1618) )
& ! [U_1619,U_1618] :
( sP172(U_1619,U_1618)
| ~ class_Rings_Olinordered__idom(U_1618) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171,sP172])],[f_519_2]) ).
cnf(f_519_4,plain,
( sP172(U_1619,U_1618)
| ~ class_Rings_Olinordered__idom(U_1618) ),
inference(clausify,[status(thm)],[f_519_3]) ).
cnf(f_519_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618))
| U_1619 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618))
| ~ sP172(U_1619,U_1618) ),
inference(clausify,[status(thm)],[f_519_3]) ).
cnf(f_519_6,plain,
( sP171(U_1619,U_1618)
| U_1619 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618))
| ~ sP172(U_1619,U_1618) ),
inference(clausify,[status(thm)],[f_519_3]) ).
cnf(f_519_7,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1618))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1618),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)),U_1619)
| ~ sP171(U_1619,U_1618) ),
inference(clausify,[status(thm)],[f_519_3]) ).
cnf(f_519_8,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1618),U_1619) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1618),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1618)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1618),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1618)),U_1619)
| ~ sP171(U_1619,U_1618) ),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).
fof(f_520_2,plain,
! [U_1625,U_1624,U_1623,U_1622,U_1621,U_1620] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1620,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),U_1622),U_1623),c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1624),U_1622),U_1625))
| ~ c_Orderings_Oord__class_Oless__eq(U_1620,U_1623,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),c_Groups_Ominus__class_Ominus(U_1620,U_1624,U_1621)),U_1622),U_1625)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1620,U_1623,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),c_Groups_Ominus__class_Ominus(U_1620,U_1624,U_1621)),U_1622),U_1625))
| ~ c_Orderings_Oord__class_Oless__eq(U_1620,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),U_1622),U_1623),c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1624),U_1622),U_1625)) ) )
| ~ class_Rings_Oordered__ring(U_1620) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
( ! [U_1621,U_1622,U_1625,U_1623,U_1620,U_1624] :
( c_Orderings_Oord__class_Oless__eq(U_1620,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),U_1622),U_1623),c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1624),U_1622),U_1625))
| ~ c_Orderings_Oord__class_Oless__eq(U_1620,U_1623,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),c_Groups_Ominus__class_Ominus(U_1620,U_1624,U_1621)),U_1622),U_1625))
| ~ sP173(U_1621,U_1622,U_1625,U_1623,U_1620,U_1624) )
& ! [U_1621,U_1622,U_1625,U_1623,U_1620,U_1624] :
( c_Orderings_Oord__class_Oless__eq(U_1620,U_1623,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),c_Groups_Ominus__class_Ominus(U_1620,U_1624,U_1621)),U_1622),U_1625))
| ~ c_Orderings_Oord__class_Oless__eq(U_1620,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),U_1622),U_1623),c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1624),U_1622),U_1625))
| ~ sP173(U_1621,U_1622,U_1625,U_1623,U_1620,U_1624) )
& ! [U_1621,U_1622,U_1625,U_1623,U_1620,U_1624] :
( sP173(U_1621,U_1622,U_1625,U_1623,U_1620,U_1624)
| ~ class_Rings_Oordered__ring(U_1620) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_520_2]) ).
cnf(f_520_4,plain,
( sP173(U_1621,U_1622,U_1625,U_1623,U_1620,U_1624)
| ~ class_Rings_Oordered__ring(U_1620) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1620,U_1623,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),c_Groups_Ominus__class_Ominus(U_1620,U_1624,U_1621)),U_1622),U_1625))
| ~ c_Orderings_Oord__class_Oless__eq(U_1620,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),U_1622),U_1623),c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1624),U_1622),U_1625))
| ~ sP173(U_1621,U_1622,U_1625,U_1623,U_1620,U_1624) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1620,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1621),U_1622),U_1623),c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),U_1624),U_1622),U_1625))
| ~ c_Orderings_Oord__class_Oless__eq(U_1620,U_1623,c_Groups_Oplus__class_Oplus(U_1620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1620),c_Groups_Ominus__class_Ominus(U_1620,U_1624,U_1621)),U_1622),U_1625))
| ~ sP173(U_1621,U_1622,U_1625,U_1623,U_1620,U_1624) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).
fof(f_521_2,plain,
! [U_1631,U_1630,U_1629,U_1628,U_1627,U_1626] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),U_1628),U_1629),c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1630),U_1628),U_1631))
| ~ c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),c_Groups_Ominus__class_Ominus(U_1626,U_1627,U_1630)),U_1628),U_1629),U_1631) )
& ( c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),c_Groups_Ominus__class_Ominus(U_1626,U_1627,U_1630)),U_1628),U_1629),U_1631)
| ~ c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),U_1628),U_1629),c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1630),U_1628),U_1631)) ) )
| ~ class_Rings_Oordered__ring(U_1626) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
( ! [U_1628,U_1626,U_1627,U_1629,U_1630,U_1631] :
( c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),U_1628),U_1629),c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1630),U_1628),U_1631))
| ~ c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),c_Groups_Ominus__class_Ominus(U_1626,U_1627,U_1630)),U_1628),U_1629),U_1631)
| ~ sP174(U_1628,U_1626,U_1627,U_1629,U_1630,U_1631) )
& ! [U_1628,U_1626,U_1627,U_1629,U_1630,U_1631] :
( c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),c_Groups_Ominus__class_Ominus(U_1626,U_1627,U_1630)),U_1628),U_1629),U_1631)
| ~ c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),U_1628),U_1629),c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1630),U_1628),U_1631))
| ~ sP174(U_1628,U_1626,U_1627,U_1629,U_1630,U_1631) )
& ! [U_1628,U_1626,U_1627,U_1629,U_1630,U_1631] :
( sP174(U_1628,U_1626,U_1627,U_1629,U_1630,U_1631)
| ~ class_Rings_Oordered__ring(U_1626) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_521_2]) ).
cnf(f_521_4,plain,
( sP174(U_1628,U_1626,U_1627,U_1629,U_1630,U_1631)
| ~ class_Rings_Oordered__ring(U_1626) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),c_Groups_Ominus__class_Ominus(U_1626,U_1627,U_1630)),U_1628),U_1629),U_1631)
| ~ c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),U_1628),U_1629),c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1630),U_1628),U_1631))
| ~ sP174(U_1628,U_1626,U_1627,U_1629,U_1630,U_1631) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1627),U_1628),U_1629),c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),U_1630),U_1628),U_1631))
| ~ c_Orderings_Oord__class_Oless__eq(U_1626,c_Groups_Oplus__class_Oplus(U_1626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1626),c_Groups_Ominus__class_Ominus(U_1626,U_1627,U_1630)),U_1628),U_1629),U_1631)
| ~ sP174(U_1628,U_1626,U_1627,U_1629,U_1630,U_1631) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).
fof(f_522_2,plain,
! [U_1637,U_1636,U_1635,U_1634,U_1633,U_1632] :
( ( ( c_Orderings_Oord__class_Oless(U_1632,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634),U_1635),c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1636),U_1634),U_1637))
| ~ c_Orderings_Oord__class_Oless(U_1632,U_1635,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ominus__class_Ominus(U_1632,U_1636,U_1633)),U_1634),U_1637)) )
& ( c_Orderings_Oord__class_Oless(U_1632,U_1635,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ominus__class_Ominus(U_1632,U_1636,U_1633)),U_1634),U_1637))
| ~ c_Orderings_Oord__class_Oless(U_1632,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634),U_1635),c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1636),U_1634),U_1637)) ) )
| ~ class_Rings_Oordered__ring(U_1632) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
( ! [U_1632,U_1633,U_1634,U_1635,U_1636,U_1637] :
( c_Orderings_Oord__class_Oless(U_1632,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634),U_1635),c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1636),U_1634),U_1637))
| ~ c_Orderings_Oord__class_Oless(U_1632,U_1635,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ominus__class_Ominus(U_1632,U_1636,U_1633)),U_1634),U_1637))
| ~ sP175(U_1632,U_1633,U_1634,U_1635,U_1636,U_1637) )
& ! [U_1632,U_1633,U_1634,U_1635,U_1636,U_1637] :
( c_Orderings_Oord__class_Oless(U_1632,U_1635,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ominus__class_Ominus(U_1632,U_1636,U_1633)),U_1634),U_1637))
| ~ c_Orderings_Oord__class_Oless(U_1632,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634),U_1635),c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1636),U_1634),U_1637))
| ~ sP175(U_1632,U_1633,U_1634,U_1635,U_1636,U_1637) )
& ! [U_1632,U_1633,U_1634,U_1635,U_1636,U_1637] :
( sP175(U_1632,U_1633,U_1634,U_1635,U_1636,U_1637)
| ~ class_Rings_Oordered__ring(U_1632) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_522_2]) ).
cnf(f_522_4,plain,
( sP175(U_1632,U_1633,U_1634,U_1635,U_1636,U_1637)
| ~ class_Rings_Oordered__ring(U_1632) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_5,plain,
( c_Orderings_Oord__class_Oless(U_1632,U_1635,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ominus__class_Ominus(U_1632,U_1636,U_1633)),U_1634),U_1637))
| ~ c_Orderings_Oord__class_Oless(U_1632,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634),U_1635),c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1636),U_1634),U_1637))
| ~ sP175(U_1632,U_1633,U_1634,U_1635,U_1636,U_1637) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_6,plain,
( c_Orderings_Oord__class_Oless(U_1632,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1633),U_1634),U_1635),c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),U_1636),U_1634),U_1637))
| ~ c_Orderings_Oord__class_Oless(U_1632,U_1635,c_Groups_Oplus__class_Oplus(U_1632,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1632),c_Groups_Ominus__class_Ominus(U_1632,U_1636,U_1633)),U_1634),U_1637))
| ~ sP175(U_1632,U_1633,U_1634,U_1635,U_1636,U_1637) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_1,plain,
! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).
fof(f_523_2,plain,
! [U_1643,U_1642,U_1641,U_1640,U_1639,U_1638] :
( ( ( c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),U_1640),U_1641),c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1642),U_1640),U_1643))
| ~ c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),c_Groups_Ominus__class_Ominus(U_1638,U_1639,U_1642)),U_1640),U_1641),U_1643) )
& ( c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),c_Groups_Ominus__class_Ominus(U_1638,U_1639,U_1642)),U_1640),U_1641),U_1643)
| ~ c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),U_1640),U_1641),c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1642),U_1640),U_1643)) ) )
| ~ class_Rings_Oordered__ring(U_1638) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
( ! [U_1638,U_1640,U_1639,U_1641,U_1642,U_1643] :
( c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),U_1640),U_1641),c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1642),U_1640),U_1643))
| ~ c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),c_Groups_Ominus__class_Ominus(U_1638,U_1639,U_1642)),U_1640),U_1641),U_1643)
| ~ sP176(U_1638,U_1640,U_1639,U_1641,U_1642,U_1643) )
& ! [U_1638,U_1640,U_1639,U_1641,U_1642,U_1643] :
( c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),c_Groups_Ominus__class_Ominus(U_1638,U_1639,U_1642)),U_1640),U_1641),U_1643)
| ~ c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),U_1640),U_1641),c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1642),U_1640),U_1643))
| ~ sP176(U_1638,U_1640,U_1639,U_1641,U_1642,U_1643) )
& ! [U_1638,U_1640,U_1639,U_1641,U_1642,U_1643] :
( sP176(U_1638,U_1640,U_1639,U_1641,U_1642,U_1643)
| ~ class_Rings_Oordered__ring(U_1638) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_523_2]) ).
cnf(f_523_4,plain,
( sP176(U_1638,U_1640,U_1639,U_1641,U_1642,U_1643)
| ~ class_Rings_Oordered__ring(U_1638) ),
inference(clausify,[status(thm)],[f_523_3]) ).
cnf(f_523_5,plain,
( c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),c_Groups_Ominus__class_Ominus(U_1638,U_1639,U_1642)),U_1640),U_1641),U_1643)
| ~ c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),U_1640),U_1641),c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1642),U_1640),U_1643))
| ~ sP176(U_1638,U_1640,U_1639,U_1641,U_1642,U_1643) ),
inference(clausify,[status(thm)],[f_523_3]) ).
cnf(f_523_6,plain,
( c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1639),U_1640),U_1641),c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),U_1642),U_1640),U_1643))
| ~ c_Orderings_Oord__class_Oless(U_1638,c_Groups_Oplus__class_Oplus(U_1638,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1638),c_Groups_Ominus__class_Ominus(U_1638,U_1639,U_1642)),U_1640),U_1641),U_1643)
| ~ sP176(U_1638,U_1640,U_1639,U_1641,U_1642,U_1643) ),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_1,plain,
! [V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored]) ).
fof(f_524_2,plain,
! [U_1645,U_1644] :
( c_Groups_Ominus__class_Ominus(U_1644,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1644),U_1645),U_1645),c_Groups_Oone__class_Oone(U_1644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1644),c_Groups_Oplus__class_Oplus(U_1644,U_1645,c_Groups_Oone__class_Oone(U_1644))),c_Groups_Ominus__class_Ominus(U_1644,U_1645,c_Groups_Oone__class_Oone(U_1644)))
| ~ class_Rings_Oring__1(U_1644) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
! [U_1644,U_1645] :
( c_Groups_Ominus__class_Ominus(U_1644,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1644),U_1645),U_1645),c_Groups_Oone__class_Oone(U_1644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1644),c_Groups_Oplus__class_Oplus(U_1644,U_1645,c_Groups_Oone__class_Oone(U_1644))),c_Groups_Ominus__class_Ominus(U_1644,U_1645,c_Groups_Oone__class_Oone(U_1644)))
| ~ class_Rings_Oring__1(U_1644) ),
inference(definitional_conversion,[status(esa)],[f_524_2]) ).
cnf(f_524_4,plain,
( c_Groups_Ominus__class_Ominus(U_1644,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1644),U_1645),U_1645),c_Groups_Oone__class_Oone(U_1644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1644),c_Groups_Oplus__class_Oplus(U_1644,U_1645,c_Groups_Oone__class_Oone(U_1644))),c_Groups_Ominus__class_Ominus(U_1644,U_1645,c_Groups_Oone__class_Oone(U_1644)))
| ~ class_Rings_Oring__1(U_1644) ),
inference(clausify,[status(thm)],[f_524_3]) ).
fof(f_525_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,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_525_2,plain,
! [U_1647,U_1646] :
( c_Orderings_Oord__class_Oless__eq(U_1646,c_Groups_Ouminus__class_Ouminus(U_1646,c_Groups_Oabs__class_Oabs(U_1646,U_1647)),c_Groups_Ozero__class_Ozero(U_1646))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1646) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
fof(f_525_3,plain,
! [U_1647,U_1646] :
( c_Orderings_Oord__class_Oless__eq(U_1646,c_Groups_Ouminus__class_Ouminus(U_1646,c_Groups_Oabs__class_Oabs(U_1646,U_1647)),c_Groups_Ozero__class_Ozero(U_1646))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1646) ),
inference(definitional_conversion,[status(esa)],[f_525_2]) ).
cnf(f_525_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1646,c_Groups_Ouminus__class_Ouminus(U_1646,c_Groups_Oabs__class_Oabs(U_1646,U_1647)),c_Groups_Ozero__class_Ozero(U_1646))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1646) ),
inference(clausify,[status(thm)],[f_525_3]) ).
fof(f_526_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ 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_526_2,plain,
! [U_1649,U_1648] :
( c_Groups_Oabs__class_Oabs(U_1648,U_1649) = c_Groups_Ouminus__class_Ouminus(U_1648,U_1649)
| ~ c_Orderings_Oord__class_Oless__eq(U_1648,U_1649,c_Groups_Ozero__class_Ozero(U_1648))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1648) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
! [U_1648,U_1649] :
( c_Groups_Oabs__class_Oabs(U_1648,U_1649) = c_Groups_Ouminus__class_Ouminus(U_1648,U_1649)
| ~ c_Orderings_Oord__class_Oless__eq(U_1648,U_1649,c_Groups_Ozero__class_Ozero(U_1648))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1648) ),
inference(definitional_conversion,[status(esa)],[f_526_2]) ).
cnf(f_526_4,plain,
( c_Groups_Oabs__class_Oabs(U_1648,U_1649) = c_Groups_Ouminus__class_Ouminus(U_1648,U_1649)
| ~ c_Orderings_Oord__class_Oless__eq(U_1648,U_1649,c_Groups_Ozero__class_Ozero(U_1648))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1648) ),
inference(clausify,[status(thm)],[f_526_3]) ).
fof(f_527_1,plain,
! [V_a,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ 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_527_2,plain,
! [U_1651,U_1650] :
( ( ( c_Groups_Oabs__class_Oabs(U_1650,U_1651) = U_1651
| c_Orderings_Oord__class_Oless(U_1650,U_1651,c_Groups_Ozero__class_Ozero(U_1650)) )
& ( c_Groups_Oabs__class_Oabs(U_1650,U_1651) = c_Groups_Ouminus__class_Ouminus(U_1650,U_1651)
| ~ c_Orderings_Oord__class_Oless(U_1650,U_1651,c_Groups_Ozero__class_Ozero(U_1650)) ) )
| ~ class_Groups_Oabs__if(U_1650) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
fof(f_527_3,plain,
( ! [U_1651,U_1650] :
( c_Groups_Oabs__class_Oabs(U_1650,U_1651) = U_1651
| c_Orderings_Oord__class_Oless(U_1650,U_1651,c_Groups_Ozero__class_Ozero(U_1650))
| ~ sP177(U_1651,U_1650) )
& ! [U_1651,U_1650] :
( c_Groups_Oabs__class_Oabs(U_1650,U_1651) = c_Groups_Ouminus__class_Ouminus(U_1650,U_1651)
| ~ c_Orderings_Oord__class_Oless(U_1650,U_1651,c_Groups_Ozero__class_Ozero(U_1650))
| ~ sP177(U_1651,U_1650) )
& ! [U_1651,U_1650] :
( sP177(U_1651,U_1650)
| ~ class_Groups_Oabs__if(U_1650) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_527_2]) ).
cnf(f_527_4,plain,
( sP177(U_1651,U_1650)
| ~ class_Groups_Oabs__if(U_1650) ),
inference(clausify,[status(thm)],[f_527_3]) ).
cnf(f_527_5,plain,
( c_Groups_Oabs__class_Oabs(U_1650,U_1651) = c_Groups_Ouminus__class_Ouminus(U_1650,U_1651)
| ~ c_Orderings_Oord__class_Oless(U_1650,U_1651,c_Groups_Ozero__class_Ozero(U_1650))
| ~ sP177(U_1651,U_1650) ),
inference(clausify,[status(thm)],[f_527_3]) ).
cnf(f_527_6,plain,
( c_Groups_Oabs__class_Oabs(U_1650,U_1651) = U_1651
| c_Orderings_Oord__class_Oless(U_1650,U_1651,c_Groups_Ozero__class_Ozero(U_1650))
| ~ sP177(U_1651,U_1650) ),
inference(clausify,[status(thm)],[f_527_3]) ).
fof(f_528_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ 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_528_2,plain,
! [U_1653,U_1652] :
( c_Groups_Oabs__class_Oabs(U_1652,U_1653) = c_Groups_Ouminus__class_Ouminus(U_1652,U_1653)
| ~ c_Orderings_Oord__class_Oless(U_1652,U_1653,c_Groups_Ozero__class_Ozero(U_1652))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1652) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
! [U_1653,U_1652] :
( c_Groups_Oabs__class_Oabs(U_1652,U_1653) = c_Groups_Ouminus__class_Ouminus(U_1652,U_1653)
| ~ c_Orderings_Oord__class_Oless(U_1652,U_1653,c_Groups_Ozero__class_Ozero(U_1652))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1652) ),
inference(definitional_conversion,[status(esa)],[f_528_2]) ).
cnf(f_528_4,plain,
( c_Groups_Oabs__class_Oabs(U_1652,U_1653) = c_Groups_Ouminus__class_Ouminus(U_1652,U_1653)
| ~ c_Orderings_Oord__class_Oless(U_1652,U_1653,c_Groups_Ozero__class_Ozero(U_1652))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1652) ),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),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_529_2,plain,
! [U_1656,U_1655,U_1654] :
( c_Orderings_Oord__class_Oless__eq(U_1654,c_Groups_Oabs__class_Oabs(U_1654,c_Groups_Ominus__class_Ominus(U_1654,U_1655,U_1656)),c_Groups_Oplus__class_Oplus(U_1654,c_Groups_Oabs__class_Oabs(U_1654,U_1655),c_Groups_Oabs__class_Oabs(U_1654,U_1656)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1654) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
! [U_1655,U_1654,U_1656] :
( c_Orderings_Oord__class_Oless__eq(U_1654,c_Groups_Oabs__class_Oabs(U_1654,c_Groups_Ominus__class_Ominus(U_1654,U_1655,U_1656)),c_Groups_Oplus__class_Oplus(U_1654,c_Groups_Oabs__class_Oabs(U_1654,U_1655),c_Groups_Oabs__class_Oabs(U_1654,U_1656)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1654) ),
inference(definitional_conversion,[status(esa)],[f_529_2]) ).
cnf(f_529_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1654,c_Groups_Oabs__class_Oabs(U_1654,c_Groups_Ominus__class_Ominus(U_1654,U_1655,U_1656)),c_Groups_Oplus__class_Oplus(U_1654,c_Groups_Oabs__class_Oabs(U_1654,U_1655),c_Groups_Oabs__class_Oabs(U_1654,U_1656)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1654) ),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,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_530_2,plain,
! [U_1661,U_1660,U_1659,U_1658,U_1657] :
( c_Orderings_Oord__class_Oless__eq(U_1657,c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,c_Groups_Oplus__class_Oplus(U_1657,U_1658,U_1659),c_Groups_Oplus__class_Oplus(U_1657,U_1660,U_1661))),c_Groups_Oplus__class_Oplus(U_1657,c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,U_1658,U_1660)),c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,U_1659,U_1661))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1657) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
! [U_1657,U_1658,U_1659,U_1660,U_1661] :
( c_Orderings_Oord__class_Oless__eq(U_1657,c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,c_Groups_Oplus__class_Oplus(U_1657,U_1658,U_1659),c_Groups_Oplus__class_Oplus(U_1657,U_1660,U_1661))),c_Groups_Oplus__class_Oplus(U_1657,c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,U_1658,U_1660)),c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,U_1659,U_1661))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1657) ),
inference(definitional_conversion,[status(esa)],[f_530_2]) ).
cnf(f_530_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1657,c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,c_Groups_Oplus__class_Oplus(U_1657,U_1658,U_1659),c_Groups_Oplus__class_Oplus(U_1657,U_1660,U_1661))),c_Groups_Oplus__class_Oplus(U_1657,c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,U_1658,U_1660)),c_Groups_Oabs__class_Oabs(U_1657,c_Groups_Ominus__class_Ominus(U_1657,U_1659,U_1661))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1657) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq]) ).
fof(f_531_2,plain,
! [U_1664,U_1663,U_1662] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1662,U_1663),c_RealVector_Onorm__class_Onorm(U_1662,U_1664)),c_RealVector_Onorm__class_Onorm(U_1662,c_Groups_Oplus__class_Oplus(U_1662,U_1663,U_1664)))
| ~ class_RealVector_Oreal__normed__vector(U_1662) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
! [U_1663,U_1662,U_1664] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1662,U_1663),c_RealVector_Onorm__class_Onorm(U_1662,U_1664)),c_RealVector_Onorm__class_Onorm(U_1662,c_Groups_Oplus__class_Oplus(U_1662,U_1663,U_1664)))
| ~ class_RealVector_Oreal__normed__vector(U_1662) ),
inference(definitional_conversion,[status(esa)],[f_531_2]) ).
cnf(f_531_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1662,U_1663),c_RealVector_Onorm__class_Onorm(U_1662,U_1664)),c_RealVector_Onorm__class_Onorm(U_1662,c_Groups_Oplus__class_Oplus(U_1662,U_1663,U_1664)))
| ~ class_RealVector_Oreal__normed__vector(U_1662) ),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4]) ).
fof(f_532_2,plain,
! [U_1667,U_1666,U_1665] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1665,c_Groups_Ominus__class_Ominus(U_1665,U_1666,U_1667)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1665,U_1666),c_RealVector_Onorm__class_Onorm(U_1665,U_1667)))
| ~ class_RealVector_Oreal__normed__vector(U_1665) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
! [U_1665,U_1666,U_1667] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1665,c_Groups_Ominus__class_Ominus(U_1665,U_1666,U_1667)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1665,U_1666),c_RealVector_Onorm__class_Onorm(U_1665,U_1667)))
| ~ class_RealVector_Oreal__normed__vector(U_1665) ),
inference(definitional_conversion,[status(esa)],[f_532_2]) ).
cnf(f_532_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1665,c_Groups_Ominus__class_Ominus(U_1665,U_1666,U_1667)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1665,U_1666),c_RealVector_Onorm__class_Onorm(U_1665,U_1667)))
| ~ class_RealVector_Oreal__normed__vector(U_1665) ),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff]) ).
fof(f_533_2,plain,
! [U_1669,U_1668] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1668,U_1669))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1668),U_1669) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1668),U_1669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1668,U_1669)) ) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
( ! [U_1673,U_1671] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1671,U_1673))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1671),U_1673) )
& ! [U_1672,U_1670] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1670),U_1672)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1670,U_1672)) ) ),
inference(miniscope,[status(thm)],[f_533_2]) ).
fof(f_533_4,plain,
( ! [U_1673,U_1671] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1671,U_1673))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1671),U_1673) )
& ! [U_1670,U_1672] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1670),U_1672)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1670,U_1672)) ) ),
inference(definitional_conversion,[status(esa)],[f_533_3]) ).
cnf(f_533_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1670),U_1672)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1670,U_1672)) ),
inference(clausify,[status(thm)],[f_533_4]) ).
cnf(f_533_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1671,U_1673))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1671),U_1673) ),
inference(clausify,[status(thm)],[f_533_4]) ).
fof(f_534_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff]) ).
fof(f_534_2,plain,
! [U_1675,U_1674] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1674,U_1675),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1675,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1674)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1675,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1674))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1674,U_1675),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
( ! [U_1679,U_1677] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1677,U_1679),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1679,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1677)) )
& ! [U_1678,U_1676] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1678,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1676))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1676,U_1678),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_534_2]) ).
fof(f_534_4,plain,
( ! [U_1679,U_1677] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1677,U_1679),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1679,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1677)) )
& ! [U_1678,U_1676] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1678,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1676))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1676,U_1678),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_534_3]) ).
cnf(f_534_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1678,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1676))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1676,U_1678),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_534_4]) ).
cnf(f_534_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1677,U_1679),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1679,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1677)) ),
inference(clausify,[status(thm)],[f_534_4]) ).
fof(f_535_1,plain,
! [V_a] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) ) )
| V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_sgn__real__def]) ).
fof(f_535_2,plain,
! [U_1680] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1680) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1680) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1680) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1680) ) )
| U_1680 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1680) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1680 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
fof(f_535_3,plain,
( ! [U_1682] :
( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1682) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1682) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1682) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1682) ) )
| U_1682 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1681] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1681) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1681 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_535_2]) ).
fof(f_535_4,plain,
( ! [U_1682] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1682) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1682)
| ~ sP178(U_1682) )
& ! [U_1682] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1682) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1682)
| ~ sP178(U_1682) )
& ! [U_1682] :
( sP178(U_1682)
| U_1682 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1681] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1681) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1681 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_535_3]) ).
cnf(f_535_5,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1681) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1681 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_535_4]) ).
cnf(f_535_6,plain,
( sP178(U_1682)
| U_1682 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_535_4]) ).
cnf(f_535_7,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1682) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1682)
| ~ sP178(U_1682) ),
inference(clausify,[status(thm)],[f_535_4]) ).
cnf(f_535_8,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1682) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1682)
| ~ sP178(U_1682) ),
inference(clausify,[status(thm)],[f_535_4]) ).
fof(f_536_1,plain,
! [V_x] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ) )
| V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sgn__def]) ).
fof(f_536_2,plain,
! [U_1683] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1683) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1683) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1683) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1683) ) )
| U_1683 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1683) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1683 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
fof(f_536_3,plain,
( ! [U_1685] :
( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1685) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1685) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1685) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1685) ) )
| U_1685 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1684] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1684) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1684 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_536_2]) ).
fof(f_536_4,plain,
( ! [U_1685] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1685) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1685)
| ~ sP179(U_1685) )
& ! [U_1685] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1685) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1685)
| ~ sP179(U_1685) )
& ! [U_1685] :
( sP179(U_1685)
| U_1685 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1684] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1684) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1684 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_536_3]) ).
cnf(f_536_5,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1684) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1684 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_536_4]) ).
cnf(f_536_6,plain,
( sP179(U_1685)
| U_1685 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_536_4]) ).
cnf(f_536_7,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1685) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1685)
| ~ sP179(U_1685) ),
inference(clausify,[status(thm)],[f_536_4]) ).
cnf(f_536_8,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1685) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1685)
| ~ sP179(U_1685) ),
inference(clausify,[status(thm)],[f_536_4]) ).
fof(f_537_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff]) ).
fof(f_537_2,plain,
! [U_1687,U_1686] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1686,U_1687))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1686),U_1687) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1686),U_1687)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1686,U_1687)) ) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
( ! [U_1691,U_1689] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1689,U_1691))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1689),U_1691) )
& ! [U_1690,U_1688] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1688),U_1690)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1688,U_1690)) ) ),
inference(miniscope,[status(thm)],[f_537_2]) ).
fof(f_537_4,plain,
( ! [U_1689,U_1691] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1689,U_1691))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1689),U_1691) )
& ! [U_1690,U_1688] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1688),U_1690)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1688,U_1690)) ) ),
inference(definitional_conversion,[status(esa)],[f_537_3]) ).
cnf(f_537_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1688),U_1690)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1688,U_1690)) ),
inference(clausify,[status(thm)],[f_537_4]) ).
cnf(f_537_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1689,U_1691))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1689),U_1691) ),
inference(clausify,[status(thm)],[f_537_4]) ).
fof(f_538_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff]) ).
fof(f_538_2,plain,
! [U_1693,U_1692] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1692,U_1693),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1693,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1692)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1693,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1692))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1692,U_1693),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
( ! [U_1697,U_1695] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1695,U_1697),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1697,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1695)) )
& ! [U_1696,U_1694] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1696,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1694))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1694,U_1696),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_538_2]) ).
fof(f_538_4,plain,
( ! [U_1695,U_1697] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1695,U_1697),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1697,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1695)) )
& ! [U_1696,U_1694] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1696,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1694))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1694,U_1696),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_538_3]) ).
cnf(f_538_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1696,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1694))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1694,U_1696),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_538_4]) ).
cnf(f_538_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1695,U_1697),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1697,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1695)) ),
inference(clausify,[status(thm)],[f_538_4]) ).
fof(f_539_1,plain,
! [V_a] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_abs__real__def]) ).
fof(f_539_2,plain,
! [U_1698] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1698) = U_1698
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1698,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1698) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1698)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1698,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
fof(f_539_3,plain,
( ! [U_1700] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1700) = U_1700
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1700,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1699] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1699) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1699)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1699,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_539_2]) ).
fof(f_539_4,plain,
( ! [U_1700] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1700) = U_1700
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1700,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1699] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1699) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1699)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1699,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_539_3]) ).
cnf(f_539_5,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1699) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1699)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1699,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_539_4]) ).
cnf(f_539_6,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1700) = U_1700
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1700,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_539_4]) ).
fof(f_540_1,plain,
! [V_r] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__abs__def]) ).
fof(f_540_2,plain,
! [U_1701] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1701) = U_1701
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1701,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1701) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1701)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1701,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
fof(f_540_3,plain,
( ! [U_1703] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1703) = U_1703
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1703,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1702] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1702) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1702)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1702,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_540_2]) ).
fof(f_540_4,plain,
( ! [U_1703] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1703) = U_1703
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1703,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1702] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1702) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1702)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1702,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_540_3]) ).
cnf(f_540_5,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1702) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1702)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1702,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_540_4]) ).
cnf(f_540_6,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1703) = U_1703
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1703,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_540_4]) ).
fof(f_541_1,plain,
! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))),
inference(fof_nnf,[status(thm)],[fact_abs__sum__triangle__ineq]) ).
fof(f_541_2,plain,
! [U_1707,U_1706,U_1705,U_1704] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1704,U_1705),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1706),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1707)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1704,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1706))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1705,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1707))))),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
! [U_1704,U_1705,U_1706,U_1707] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1704,U_1705),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1706),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1707)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1704,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1706))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1705,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1707))))),
inference(definitional_conversion,[status(esa)],[f_541_2]) ).
cnf(f_541_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1704,U_1705),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1706),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1707)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1704,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1706))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1705,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1707))))),
inference(clausify,[status(thm)],[f_541_3]) ).
fof(f_542_1,plain,
! [V_n] : 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_542_2,plain,
! [U_1708] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1708),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
! [U_1708] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1708),
inference(definitional_conversion,[status(esa)],[f_542_2]) ).
cnf(f_542_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1708),
inference(clausify,[status(thm)],[f_542_3]) ).
fof(f_543_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).
fof(f_543_2,plain,
! [U_1709] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
fof(f_543_3,plain,
( ! [U_1711] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1711,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1711 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1710] :
( U_1710 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1710,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_543_2]) ).
fof(f_543_4,plain,
( ! [U_1711] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1711,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1711 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1710] :
( U_1710 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1710,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa)],[f_543_3]) ).
cnf(f_543_5,plain,
( U_1710 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1710,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_543_4]) ).
cnf(f_543_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1711,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1711 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_543_4]) ).
fof(f_544_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).
fof(f_544_2,plain,
! [U_1714,U_1713,U_1712] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1712),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1712),U_1714))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1713,U_1714)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1712) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1713,U_1714)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1712)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1712),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1712),U_1714)) ) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
fof(f_544_3,plain,
( ! [U_1720,U_1718,U_1716] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1716),U_1718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1716),U_1720))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1718,U_1720)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1716) ) )
& ! [U_1719,U_1717,U_1715] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1717,U_1719)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1715)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1715),U_1717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1715),U_1719)) ) ),
inference(miniscope,[status(thm)],[f_544_2]) ).
fof(f_544_4,plain,
( ! [U_1718,U_1716,U_1720] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1718,U_1720)
| ~ sP180(U_1718,U_1716,U_1720) )
& ! [U_1718,U_1716,U_1720] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1716)
| ~ sP180(U_1718,U_1716,U_1720) )
& ! [U_1718,U_1716,U_1720] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1716),U_1718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1716),U_1720))
| sP180(U_1718,U_1716,U_1720) )
& ! [U_1715,U_1717,U_1719] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1717,U_1719)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1715)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1715),U_1717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1715),U_1719)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_544_3]) ).
cnf(f_544_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1717,U_1719)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1715)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1715),U_1717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1715),U_1719)) ),
inference(clausify,[status(thm)],[f_544_4]) ).
cnf(f_544_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1716),U_1718),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1716),U_1720))
| sP180(U_1718,U_1716,U_1720) ),
inference(clausify,[status(thm)],[f_544_4]) ).
cnf(f_544_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1716)
| ~ sP180(U_1718,U_1716,U_1720) ),
inference(clausify,[status(thm)],[f_544_4]) ).
cnf(f_544_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1718,U_1720)
| ~ sP180(U_1718,U_1716,U_1720) ),
inference(clausify,[status(thm)],[f_544_4]) ).
fof(f_545_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).
fof(f_545_2,plain,
! [U_1723,U_1722,U_1721] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1721),U_1722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1723),U_1722))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1721,U_1723)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1722) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1721,U_1723)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1722)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1721),U_1722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1723),U_1722)) ) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
fof(f_545_3,plain,
( ! [U_1729,U_1727,U_1725] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1725),U_1727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1729),U_1727))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1725,U_1729)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1727) ) )
& ! [U_1728,U_1726,U_1724] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1724,U_1728)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1724),U_1726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1728),U_1726)) ) ),
inference(miniscope,[status(thm)],[f_545_2]) ).
fof(f_545_4,plain,
( ! [U_1725,U_1727,U_1729] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1725,U_1729)
| ~ sP181(U_1725,U_1727,U_1729) )
& ! [U_1725,U_1727,U_1729] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1727)
| ~ sP181(U_1725,U_1727,U_1729) )
& ! [U_1725,U_1727,U_1729] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1725),U_1727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1729),U_1727))
| sP181(U_1725,U_1727,U_1729) )
& ! [U_1728,U_1724,U_1726] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1724,U_1728)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1724),U_1726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1728),U_1726)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_545_3]) ).
cnf(f_545_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1724,U_1728)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1724),U_1726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1728),U_1726)) ),
inference(clausify,[status(thm)],[f_545_4]) ).
cnf(f_545_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1725),U_1727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1729),U_1727))
| sP181(U_1725,U_1727,U_1729) ),
inference(clausify,[status(thm)],[f_545_4]) ).
cnf(f_545_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1727)
| ~ sP181(U_1725,U_1727,U_1729) ),
inference(clausify,[status(thm)],[f_545_4]) ).
cnf(f_545_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1725,U_1729)
| ~ sP181(U_1725,U_1727,U_1729) ),
inference(clausify,[status(thm)],[f_545_4]) ).
fof(f_546_1,plain,
! [V_n] :
( 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_546_2,plain,
! [U_1730] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1730)
| U_1730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
fof(f_546_3,plain,
! [U_1730] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1730)
| U_1730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_546_2]) ).
cnf(f_546_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1730)
| U_1730 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_546_3]) ).
fof(f_547_1,plain,
! [V_k,V_j,V_i] :
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).
fof(f_547_2,plain,
! [U_1733,U_1732,U_1731] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1733),U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1733),U_1732))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1733)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1731,U_1732) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
fof(f_547_3,plain,
! [U_1731,U_1733,U_1732] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1733),U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1733),U_1732))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1733)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1731,U_1732) ),
inference(definitional_conversion,[status(esa)],[f_547_2]) ).
cnf(f_547_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1733),U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1733),U_1732))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1733)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1731,U_1732) ),
inference(clausify,[status(thm)],[f_547_3]) ).
fof(f_548_1,plain,
! [V_k,V_j,V_i] :
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).
fof(f_548_2,plain,
! [U_1736,U_1735,U_1734] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1734),U_1736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1735),U_1736))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1736)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1734,U_1735) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
! [U_1736,U_1734,U_1735] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1734),U_1736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1735),U_1736))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1736)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1734,U_1735) ),
inference(definitional_conversion,[status(esa)],[f_548_2]) ).
cnf(f_548_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1734),U_1736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1735),U_1736))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1736)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1734,U_1735) ),
inference(clausify,[status(thm)],[f_548_3]) ).
fof(f_549_1,plain,
! [V_n,V_m] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).
fof(f_549_2,plain,
! [U_1738,U_1737] :
( U_1738 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1737,U_1738) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
! [U_1738] :
( ! [U_1737] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1737,U_1738)
| U_1738 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_549_2]) ).
fof(f_549_4,plain,
! [U_1738,U_1737] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1737,U_1738)
| U_1738 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_549_3]) ).
cnf(f_549_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1737,U_1738)
| U_1738 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_549_4]) ).
fof(f_550_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).
fof(f_550_2,plain,
! [U_1741,U_1740,U_1739] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1739),U_1740) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1741),U_1740)
| ( U_1740 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1739 != U_1741 ) )
& ( U_1740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1739 = U_1741
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1739),U_1740) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1741),U_1740) ) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
( ! [U_1747,U_1745,U_1743] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1743),U_1745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1747),U_1745)
| ( U_1745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1743 != U_1747 ) )
& ! [U_1746,U_1744,U_1742] :
( U_1744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1742 = U_1746
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1742),U_1744) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1746),U_1744) ) ),
inference(miniscope,[status(thm)],[f_550_2]) ).
fof(f_550_4,plain,
( ! [U_1743,U_1745,U_1747] :
( U_1745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP182(U_1743,U_1745,U_1747) )
& ! [U_1743,U_1745,U_1747] :
( U_1743 != U_1747
| ~ sP182(U_1743,U_1745,U_1747) )
& ! [U_1743,U_1745,U_1747] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1743),U_1745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1747),U_1745)
| sP182(U_1743,U_1745,U_1747) )
& ! [U_1744,U_1742,U_1746] :
( U_1744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1742 = U_1746
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1742),U_1744) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1746),U_1744) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_550_3]) ).
cnf(f_550_5,plain,
( U_1744 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1742 = U_1746
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1742),U_1744) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1746),U_1744) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1743),U_1745) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1747),U_1745)
| sP182(U_1743,U_1745,U_1747) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_7,plain,
( U_1743 != U_1747
| ~ sP182(U_1743,U_1745,U_1747) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_8,plain,
( U_1745 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP182(U_1743,U_1745,U_1747) ),
inference(clausify,[status(thm)],[f_550_4]) ).
fof(f_551_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).
fof(f_551_2,plain,
! [U_1750,U_1749,U_1748] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1748),U_1749) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1748),U_1750)
| ( U_1748 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1749 != U_1750 ) )
& ( U_1748 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1749 = U_1750
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1748),U_1749) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1748),U_1750) ) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
( ! [U_1756,U_1754,U_1752] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1752),U_1754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1752),U_1756)
| ( U_1752 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1754 != U_1756 ) )
& ! [U_1755,U_1753,U_1751] :
( U_1751 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1753 = U_1755
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1751),U_1753) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1751),U_1755) ) ),
inference(miniscope,[status(thm)],[f_551_2]) ).
fof(f_551_4,plain,
( ! [U_1756,U_1754,U_1752] :
( U_1752 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP183(U_1756,U_1754,U_1752) )
& ! [U_1756,U_1754,U_1752] :
( U_1754 != U_1756
| ~ sP183(U_1756,U_1754,U_1752) )
& ! [U_1756,U_1754,U_1752] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1752),U_1754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1752),U_1756)
| sP183(U_1756,U_1754,U_1752) )
& ! [U_1753,U_1751,U_1755] :
( U_1751 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1753 = U_1755
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1751),U_1753) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1751),U_1755) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_551_3]) ).
cnf(f_551_5,plain,
( U_1751 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1753 = U_1755
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1751),U_1753) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1751),U_1755) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1752),U_1754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1752),U_1756)
| sP183(U_1756,U_1754,U_1752) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_7,plain,
( U_1754 != U_1756
| ~ sP183(U_1756,U_1754,U_1752) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_8,plain,
( U_1752 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP183(U_1756,U_1754,U_1752) ),
inference(clausify,[status(thm)],[f_551_4]) ).
fof(f_552_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).
fof(f_552_2,plain,
! [U_1759,U_1758,U_1757] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1757),U_1758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1759),U_1758))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1757,U_1759)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1758) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1757,U_1759)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1758) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1757),U_1758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1759),U_1758)) ) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
( ! [U_1765,U_1763,U_1761] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1761),U_1763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1765),U_1763))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1761,U_1765)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1763) )
& ! [U_1764,U_1762,U_1760] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1760,U_1764)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1762) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1760),U_1762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1764),U_1762)) ) ),
inference(miniscope,[status(thm)],[f_552_2]) ).
fof(f_552_4,plain,
( ! [U_1760,U_1762,U_1764] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1760,U_1764)
| ~ sP184(U_1760,U_1762,U_1764) )
& ! [U_1760,U_1762,U_1764] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1762)
| ~ sP184(U_1760,U_1762,U_1764) )
& ! [U_1761,U_1763,U_1765] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1761),U_1763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1765),U_1763))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1761,U_1765)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1763) )
& ! [U_1760,U_1762,U_1764] :
( sP184(U_1760,U_1762,U_1764)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1760),U_1762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1764),U_1762)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_552_3]) ).
cnf(f_552_5,plain,
( sP184(U_1760,U_1762,U_1764)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1760),U_1762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1764),U_1762)) ),
inference(clausify,[status(thm)],[f_552_4]) ).
cnf(f_552_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1761),U_1763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1765),U_1763))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1761,U_1765)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1763) ),
inference(clausify,[status(thm)],[f_552_4]) ).
cnf(f_552_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1762)
| ~ sP184(U_1760,U_1762,U_1764) ),
inference(clausify,[status(thm)],[f_552_4]) ).
cnf(f_552_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1760,U_1764)
| ~ sP184(U_1760,U_1762,U_1764) ),
inference(clausify,[status(thm)],[f_552_4]) ).
fof(f_553_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).
fof(f_553_2,plain,
! [U_1768,U_1767,U_1766] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1766),U_1767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1766),U_1768))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1767,U_1768)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1766) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1767,U_1768)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1766) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1766),U_1767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1766),U_1768)) ) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
( ! [U_1774,U_1772,U_1770] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1770),U_1772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1770),U_1774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1772,U_1774)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1770) )
& ! [U_1773,U_1771,U_1769] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1771,U_1773)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1769) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1769),U_1771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1769),U_1773)) ) ),
inference(miniscope,[status(thm)],[f_553_2]) ).
fof(f_553_4,plain,
( ! [U_1773,U_1769,U_1771] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1771,U_1773)
| ~ sP185(U_1773,U_1769,U_1771) )
& ! [U_1773,U_1769,U_1771] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1769)
| ~ sP185(U_1773,U_1769,U_1771) )
& ! [U_1772,U_1770,U_1774] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1770),U_1772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1770),U_1774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1772,U_1774)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1770) )
& ! [U_1773,U_1769,U_1771] :
( sP185(U_1773,U_1769,U_1771)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1769),U_1771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1769),U_1773)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_553_3]) ).
cnf(f_553_5,plain,
( sP185(U_1773,U_1769,U_1771)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1769),U_1771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1769),U_1773)) ),
inference(clausify,[status(thm)],[f_553_4]) ).
cnf(f_553_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1770),U_1772),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1770),U_1774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1772,U_1774)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1770) ),
inference(clausify,[status(thm)],[f_553_4]) ).
cnf(f_553_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1769)
| ~ sP185(U_1773,U_1769,U_1771) ),
inference(clausify,[status(thm)],[f_553_4]) ).
cnf(f_553_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1771,U_1773)
| ~ sP185(U_1773,U_1769,U_1771) ),
inference(clausify,[status(thm)],[f_553_4]) ).
fof(f_554_1,plain,
! [V_n_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).
fof(f_554_2,plain,
! [U_1776,U_1775] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1775),U_1776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1776 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1775 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1775),U_1776) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
( ! [U_1780,U_1778] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1778),U_1780) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1778 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1779,U_1777] :
( U_1779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1777 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1777),U_1779) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_554_2]) ).
fof(f_554_4,plain,
( ! [U_1780,U_1778] :
( U_1780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP186(U_1780,U_1778) )
& ! [U_1780,U_1778] :
( U_1778 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP186(U_1780,U_1778) )
& ! [U_1780,U_1778] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1778),U_1780) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP186(U_1780,U_1778) )
& ! [U_1779,U_1777] :
( U_1779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1777 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1777),U_1779) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_554_3]) ).
cnf(f_554_5,plain,
( U_1779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1777 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1777),U_1779) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_554_4]) ).
cnf(f_554_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1778),U_1780) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP186(U_1780,U_1778) ),
inference(clausify,[status(thm)],[f_554_4]) ).
cnf(f_554_7,plain,
( U_1778 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP186(U_1780,U_1778) ),
inference(clausify,[status(thm)],[f_554_4]) ).
cnf(f_554_8,plain,
( U_1780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP186(U_1780,U_1778) ),
inference(clausify,[status(thm)],[f_554_4]) ).
fof(f_555_1,plain,
! [V_n] : ~ 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_555_2,plain,
! [U_1781] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1781,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
! [U_1781] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1781,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_555_2]) ).
cnf(f_555_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1781,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_555_3]) ).
fof(f_556_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_556_2,plain,
! [U_1782] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1782),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_556_1]) ).
fof(f_556_3,plain,
! [U_1782] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1782),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_556_2]) ).
cnf(f_556_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1782),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_556_3]) ).
fof(f_557_1,plain,
! [V_n_2,V_ma_2] :
( ( 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_ma_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) )
| ~ 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_ma_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).
fof(f_557_2,plain,
! [U_1784,U_1783] :
( ( 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_1783),U_1784))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1784)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1783) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1784)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1783) )
| ~ 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_1783),U_1784)) ) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
( ! [U_1788,U_1786] :
( 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_1786),U_1788))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1788)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1786) )
& ! [U_1787,U_1785] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1787)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1785) )
| ~ 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_1785),U_1787)) ) ),
inference(miniscope,[status(thm)],[f_557_2]) ).
fof(f_557_4,plain,
( ! [U_1785,U_1787] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1787)
| ~ sP187(U_1785,U_1787) )
& ! [U_1785,U_1787] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1785)
| ~ sP187(U_1785,U_1787) )
& ! [U_1788,U_1786] :
( 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_1786),U_1788))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1788)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1786) )
& ! [U_1785,U_1787] :
( sP187(U_1785,U_1787)
| ~ 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_1785),U_1787)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_557_3]) ).
cnf(f_557_5,plain,
( sP187(U_1785,U_1787)
| ~ 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_1785),U_1787)) ),
inference(clausify,[status(thm)],[f_557_4]) ).
cnf(f_557_6,plain,
( 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_1786),U_1788))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1788)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1786) ),
inference(clausify,[status(thm)],[f_557_4]) ).
cnf(f_557_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1785)
| ~ sP187(U_1785,U_1787) ),
inference(clausify,[status(thm)],[f_557_4]) ).
cnf(f_557_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1787)
| ~ sP187(U_1785,U_1787) ),
inference(clausify,[status(thm)],[f_557_4]) ).
fof(f_558_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_558_2,plain,
! [U_1789] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1789) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
! [U_1789] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1789) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_558_2]) ).
cnf(f_558_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1789) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_558_3]) ).
fof(f_559_1,plain,
! [V_n_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).
fof(f_559_2,plain,
! [U_1790] :
( ( U_1790 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1790) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1790)
| U_1790 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
( ! [U_1792] :
( U_1792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1792) )
& ! [U_1791] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1791)
| U_1791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_559_2]) ).
fof(f_559_4,plain,
( ! [U_1792] :
( U_1792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1792) )
& ! [U_1791] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1791)
| U_1791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_559_3]) ).
cnf(f_559_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1791)
| U_1791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_559_4]) ).
cnf(f_559_6,plain,
( U_1792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1792) ),
inference(clausify,[status(thm)],[f_559_4]) ).
fof(f_560_1,plain,
! [V_n] : ~ 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_560_2,plain,
! [U_1793] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1793,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
! [U_1793] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1793,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_560_2]) ).
cnf(f_560_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1793,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_560_3]) ).
fof(f_561_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_561_2,plain,
! [U_1795,U_1794] :
( U_1794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1795 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1794 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1794),U_1795) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
! [U_1794,U_1795] :
( U_1794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1795 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1794 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1794),U_1795) ),
inference(definitional_conversion,[status(esa)],[f_561_2]) ).
cnf(f_561_4,plain,
( U_1794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1795 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1794 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1794),U_1795) ),
inference(clausify,[status(thm)],[f_561_3]) ).
fof(f_562_1,plain,
! [V_n,V_m] :
( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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_562_2,plain,
! [U_1797,U_1796] :
( U_1797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1796,U_1797) != U_1796 ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
! [U_1797] :
( ! [U_1796] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1796,U_1797) != U_1796
| U_1797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_562_2]) ).
fof(f_562_4,plain,
! [U_1797,U_1796] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1796,U_1797) != U_1796
| U_1797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_562_3]) ).
cnf(f_562_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1796,U_1797) != U_1796
| U_1797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_562_4]) ).
fof(f_563_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).
fof(f_563_2,plain,
! [U_1799,U_1798] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1798,U_1799) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1799 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1798 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_1799 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1798 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1798,U_1799) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
( ! [U_1803,U_1801] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1801,U_1803) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1803 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1801 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1802,U_1800] :
( ( U_1802 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1800,U_1802) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_563_2]) ).
fof(f_563_4,plain,
( ! [U_1800,U_1802] :
( U_1802 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP188(U_1800,U_1802) )
& ! [U_1800,U_1802] :
( U_1800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP188(U_1800,U_1802) )
& ! [U_1803,U_1801] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1801,U_1803) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1803 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1801 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1800,U_1802] :
( sP188(U_1800,U_1802)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1800,U_1802) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_563_3]) ).
cnf(f_563_5,plain,
( sP188(U_1800,U_1802)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1800,U_1802) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_563_4]) ).
cnf(f_563_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1801,U_1803) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1803 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1801 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_563_4]) ).
cnf(f_563_7,plain,
( U_1800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP188(U_1800,U_1802) ),
inference(clausify,[status(thm)],[f_563_4]) ).
cnf(f_563_8,plain,
( U_1802 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP188(U_1800,U_1802) ),
inference(clausify,[status(thm)],[f_563_4]) ).
fof(f_564_1,plain,
! [V_m] : 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_564_2,plain,
! [U_1804] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1804,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1804,
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
! [U_1804] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1804,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1804,
inference(definitional_conversion,[status(esa)],[f_564_2]) ).
cnf(f_564_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1804,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1804,
inference(clausify,[status(thm)],[f_564_3]) ).
fof(f_565_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).
fof(f_565_2,plain,
! [U_1806,U_1805] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1805,U_1806))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1806)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1805) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1806)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1805)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1805,U_1806)) ) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
( ! [U_1810,U_1808] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1808,U_1810))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1810)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1808) ) )
& ! [U_1809,U_1807] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1809)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1807)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1807,U_1809)) ) ),
inference(miniscope,[status(thm)],[f_565_2]) ).
fof(f_565_4,plain,
( ! [U_1808,U_1810] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1810)
| ~ sP189(U_1808,U_1810) )
& ! [U_1808,U_1810] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1808)
| ~ sP189(U_1808,U_1810) )
& ! [U_1808,U_1810] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1808,U_1810))
| sP189(U_1808,U_1810) )
& ! [U_1807,U_1809] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1809)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1807)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1807,U_1809)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_565_3]) ).
cnf(f_565_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1809)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1807)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1807,U_1809)) ),
inference(clausify,[status(thm)],[f_565_4]) ).
cnf(f_565_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1808,U_1810))
| sP189(U_1808,U_1810) ),
inference(clausify,[status(thm)],[f_565_4]) ).
cnf(f_565_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1808)
| ~ sP189(U_1808,U_1810) ),
inference(clausify,[status(thm)],[f_565_4]) ).
cnf(f_565_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1810)
| ~ sP189(U_1808,U_1810) ),
inference(clausify,[status(thm)],[f_565_4]) ).
fof(f_566_1,plain,
! [V_n] : 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_566_2,plain,
! [U_1811] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1811) = U_1811,
inference(variable_rename,[status(thm)],[f_566_1]) ).
fof(f_566_3,plain,
! [U_1811] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1811) = U_1811,
inference(definitional_conversion,[status(esa)],[f_566_2]) ).
cnf(f_566_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1811) = U_1811,
inference(clausify,[status(thm)],[f_566_3]) ).
fof(f_567_1,plain,
! [V_x,T_a] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| 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)
| ~ 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_567_2,plain,
! [U_1813,U_1812] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Ouminus__class_Ouminus(U_1812,c_Groups_Oone__class_Oone(U_1812))
| c_Orderings_Oord__class_Oless(U_1812,c_Groups_Ozero__class_Ozero(U_1812),U_1813) )
& ( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Oone__class_Oone(U_1812)
| ~ c_Orderings_Oord__class_Oless(U_1812,c_Groups_Ozero__class_Ozero(U_1812),U_1813) ) )
| U_1813 = c_Groups_Ozero__class_Ozero(U_1812) )
& ( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Ozero__class_Ozero(U_1812)
| U_1813 != c_Groups_Ozero__class_Ozero(U_1812) ) )
| ~ class_Groups_Osgn__if(U_1812) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
( ! [U_1813,U_1812] :
( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Ouminus__class_Ouminus(U_1812,c_Groups_Oone__class_Oone(U_1812))
| c_Orderings_Oord__class_Oless(U_1812,c_Groups_Ozero__class_Ozero(U_1812),U_1813)
| ~ sP190(U_1813,U_1812) )
& ! [U_1813,U_1812] :
( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Oone__class_Oone(U_1812)
| ~ c_Orderings_Oord__class_Oless(U_1812,c_Groups_Ozero__class_Ozero(U_1812),U_1813)
| ~ sP190(U_1813,U_1812) )
& ! [U_1813,U_1812] :
( sP190(U_1813,U_1812)
| U_1813 = c_Groups_Ozero__class_Ozero(U_1812)
| ~ sP191(U_1813,U_1812) )
& ! [U_1813,U_1812] :
( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Ozero__class_Ozero(U_1812)
| U_1813 != c_Groups_Ozero__class_Ozero(U_1812)
| ~ sP191(U_1813,U_1812) )
& ! [U_1813,U_1812] :
( sP191(U_1813,U_1812)
| ~ class_Groups_Osgn__if(U_1812) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190,sP191])],[f_567_2]) ).
cnf(f_567_4,plain,
( sP191(U_1813,U_1812)
| ~ class_Groups_Osgn__if(U_1812) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_5,plain,
( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Ozero__class_Ozero(U_1812)
| U_1813 != c_Groups_Ozero__class_Ozero(U_1812)
| ~ sP191(U_1813,U_1812) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_6,plain,
( sP190(U_1813,U_1812)
| U_1813 = c_Groups_Ozero__class_Ozero(U_1812)
| ~ sP191(U_1813,U_1812) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_7,plain,
( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Oone__class_Oone(U_1812)
| ~ c_Orderings_Oord__class_Oless(U_1812,c_Groups_Ozero__class_Ozero(U_1812),U_1813)
| ~ sP190(U_1813,U_1812) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_8,plain,
( c_Groups_Osgn__class_Osgn(U_1812,U_1813) = c_Groups_Ouminus__class_Ouminus(U_1812,c_Groups_Oone__class_Oone(U_1812))
| c_Orderings_Oord__class_Oless(U_1812,c_Groups_Ozero__class_Ozero(U_1812),U_1813)
| ~ sP190(U_1813,U_1812) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Groups_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).
fof(f_568_2,plain,
! [U_1815,U_1814] :
( ( ( c_Groups_Osgn__class_Osgn(U_1814,U_1815) = c_Groups_Ouminus__class_Ouminus(U_1814,c_Groups_Oone__class_Oone(U_1814))
| ~ c_Orderings_Oord__class_Oless(U_1814,U_1815,c_Groups_Ozero__class_Ozero(U_1814)) )
& ( c_Orderings_Oord__class_Oless(U_1814,U_1815,c_Groups_Ozero__class_Ozero(U_1814))
| c_Groups_Osgn__class_Osgn(U_1814,U_1815) != c_Groups_Ouminus__class_Ouminus(U_1814,c_Groups_Oone__class_Oone(U_1814)) ) )
| ~ class_Rings_Olinordered__idom(U_1814) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
( ! [U_1815,U_1814] :
( c_Groups_Osgn__class_Osgn(U_1814,U_1815) = c_Groups_Ouminus__class_Ouminus(U_1814,c_Groups_Oone__class_Oone(U_1814))
| ~ c_Orderings_Oord__class_Oless(U_1814,U_1815,c_Groups_Ozero__class_Ozero(U_1814))
| ~ sP192(U_1815,U_1814) )
& ! [U_1815,U_1814] :
( c_Orderings_Oord__class_Oless(U_1814,U_1815,c_Groups_Ozero__class_Ozero(U_1814))
| c_Groups_Osgn__class_Osgn(U_1814,U_1815) != c_Groups_Ouminus__class_Ouminus(U_1814,c_Groups_Oone__class_Oone(U_1814))
| ~ sP192(U_1815,U_1814) )
& ! [U_1815,U_1814] :
( sP192(U_1815,U_1814)
| ~ class_Rings_Olinordered__idom(U_1814) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_568_2]) ).
cnf(f_568_4,plain,
( sP192(U_1815,U_1814)
| ~ class_Rings_Olinordered__idom(U_1814) ),
inference(clausify,[status(thm)],[f_568_3]) ).
cnf(f_568_5,plain,
( c_Orderings_Oord__class_Oless(U_1814,U_1815,c_Groups_Ozero__class_Ozero(U_1814))
| c_Groups_Osgn__class_Osgn(U_1814,U_1815) != c_Groups_Ouminus__class_Ouminus(U_1814,c_Groups_Oone__class_Oone(U_1814))
| ~ sP192(U_1815,U_1814) ),
inference(clausify,[status(thm)],[f_568_3]) ).
cnf(f_568_6,plain,
( c_Groups_Osgn__class_Osgn(U_1814,U_1815) = c_Groups_Ouminus__class_Ouminus(U_1814,c_Groups_Oone__class_Oone(U_1814))
| ~ c_Orderings_Oord__class_Oless(U_1814,U_1815,c_Groups_Ozero__class_Ozero(U_1814))
| ~ sP192(U_1815,U_1814) ),
inference(clausify,[status(thm)],[f_568_3]) ).
fof(f_569_1,plain,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff]) ).
fof(f_569_2,plain,
! [U_1819,U_1818,U_1817,U_1816] :
( ( ( c_Orderings_Oord__class_Oless(U_1816,c_Groups_Oabs__class_Oabs(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1817,U_1818)),U_1819)
| ~ c_Orderings_Oord__class_Oless(U_1816,U_1817,c_Groups_Oplus__class_Oplus(U_1816,U_1818,U_1819))
| ~ c_Orderings_Oord__class_Oless(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1818,U_1819),U_1817) )
& ( ( c_Orderings_Oord__class_Oless(U_1816,U_1817,c_Groups_Oplus__class_Oplus(U_1816,U_1818,U_1819))
& c_Orderings_Oord__class_Oless(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1818,U_1819),U_1817) )
| ~ c_Orderings_Oord__class_Oless(U_1816,c_Groups_Oabs__class_Oabs(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1817,U_1818)),U_1819) ) )
| ~ class_Rings_Olinordered__idom(U_1816) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
( ! [U_1816,U_1817,U_1819,U_1818] :
( c_Orderings_Oord__class_Oless(U_1816,U_1817,c_Groups_Oplus__class_Oplus(U_1816,U_1818,U_1819))
| ~ sP193(U_1816,U_1817,U_1819,U_1818) )
& ! [U_1816,U_1817,U_1819,U_1818] :
( c_Orderings_Oord__class_Oless(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1818,U_1819),U_1817)
| ~ sP193(U_1816,U_1817,U_1819,U_1818) )
& ! [U_1816,U_1817,U_1819,U_1818] :
( c_Orderings_Oord__class_Oless(U_1816,c_Groups_Oabs__class_Oabs(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1817,U_1818)),U_1819)
| ~ c_Orderings_Oord__class_Oless(U_1816,U_1817,c_Groups_Oplus__class_Oplus(U_1816,U_1818,U_1819))
| ~ c_Orderings_Oord__class_Oless(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1818,U_1819),U_1817)
| ~ sP194(U_1816,U_1817,U_1819,U_1818) )
& ! [U_1816,U_1817,U_1819,U_1818] :
( sP193(U_1816,U_1817,U_1819,U_1818)
| ~ c_Orderings_Oord__class_Oless(U_1816,c_Groups_Oabs__class_Oabs(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1817,U_1818)),U_1819)
| ~ sP194(U_1816,U_1817,U_1819,U_1818) )
& ! [U_1816,U_1817,U_1819,U_1818] :
( sP194(U_1816,U_1817,U_1819,U_1818)
| ~ class_Rings_Olinordered__idom(U_1816) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193,sP194])],[f_569_2]) ).
cnf(f_569_4,plain,
( sP194(U_1816,U_1817,U_1819,U_1818)
| ~ class_Rings_Olinordered__idom(U_1816) ),
inference(clausify,[status(thm)],[f_569_3]) ).
cnf(f_569_5,plain,
( sP193(U_1816,U_1817,U_1819,U_1818)
| ~ c_Orderings_Oord__class_Oless(U_1816,c_Groups_Oabs__class_Oabs(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1817,U_1818)),U_1819)
| ~ sP194(U_1816,U_1817,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_569_3]) ).
cnf(f_569_6,plain,
( c_Orderings_Oord__class_Oless(U_1816,c_Groups_Oabs__class_Oabs(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1817,U_1818)),U_1819)
| ~ c_Orderings_Oord__class_Oless(U_1816,U_1817,c_Groups_Oplus__class_Oplus(U_1816,U_1818,U_1819))
| ~ c_Orderings_Oord__class_Oless(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1818,U_1819),U_1817)
| ~ sP194(U_1816,U_1817,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_569_3]) ).
cnf(f_569_7,plain,
( c_Orderings_Oord__class_Oless(U_1816,c_Groups_Ominus__class_Ominus(U_1816,U_1818,U_1819),U_1817)
| ~ sP193(U_1816,U_1817,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_569_3]) ).
cnf(f_569_8,plain,
( c_Orderings_Oord__class_Oless(U_1816,U_1817,c_Groups_Oplus__class_Oplus(U_1816,U_1818,U_1819))
| ~ sP193(U_1816,U_1817,U_1819,U_1818) ),
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_1,plain,
! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)),
inference(fof_nnf,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).
fof(f_570_2,plain,
! [U_1821,U_1820] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_1820,U_1821)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1820)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1821)),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
! [U_1820,U_1821] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_1820,U_1821)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1820)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1821)),
inference(definitional_conversion,[status(esa)],[f_570_2]) ).
cnf(f_570_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_1820,U_1821)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1820)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1821)),
inference(clausify,[status(thm)],[f_570_3]) ).
fof(f_571_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) )
| ~ 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_571_2,plain,
! [U_1824,U_1823,U_1822] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1823,U_1824) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1823,U_1824)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1822) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
( ! [U_1824,U_1822,U_1823] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1823,U_1824)
| ~ sP195(U_1824,U_1822,U_1823) )
& ! [U_1824,U_1822,U_1823] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1823,U_1824)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824))
| ~ sP195(U_1824,U_1822,U_1823) )
& ! [U_1824,U_1822,U_1823] :
( sP195(U_1824,U_1822,U_1823)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1822) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_571_2]) ).
cnf(f_571_4,plain,
( sP195(U_1824,U_1822,U_1823)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1822) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1823,U_1824)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824))
| ~ sP195(U_1824,U_1822,U_1823) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1823,U_1824)
| ~ sP195(U_1824,U_1822,U_1823) ),
inference(clausify,[status(thm)],[f_571_3]) ).
fof(f_572_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
inference(fof_nnf,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(f_572_2,plain,
! [U_1825] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1825)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1825)),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
! [U_1825] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1825)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1825)),
inference(definitional_conversion,[status(esa)],[f_572_2]) ).
cnf(f_572_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1825)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1825)),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_1,plain,
! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
| ~ 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_573_2,plain,
! [U_1830,U_1829,U_1828,U_1827,U_1826] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1826),U_1828),U_1829),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1827),U_1828),U_1830))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1827,U_1826)),U_1828),U_1830)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1827,U_1826)),U_1828),U_1830))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1826),U_1828),U_1829),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1827),U_1828),U_1830)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1826,U_1827) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
( ! [U_1826,U_1827,U_1828,U_1829,U_1830] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1826),U_1828),U_1829),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1827),U_1828),U_1830))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1827,U_1826)),U_1828),U_1830))
| ~ sP196(U_1826,U_1827,U_1828,U_1829,U_1830) )
& ! [U_1826,U_1827,U_1828,U_1829,U_1830] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1827,U_1826)),U_1828),U_1830))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1826),U_1828),U_1829),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1827),U_1828),U_1830))
| ~ sP196(U_1826,U_1827,U_1828,U_1829,U_1830) )
& ! [U_1826,U_1827,U_1828,U_1829,U_1830] :
( sP196(U_1826,U_1827,U_1828,U_1829,U_1830)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1826,U_1827) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_573_2]) ).
cnf(f_573_4,plain,
( sP196(U_1826,U_1827,U_1828,U_1829,U_1830)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1826,U_1827) ),
inference(clausify,[status(thm)],[f_573_3]) ).
cnf(f_573_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1827,U_1826)),U_1828),U_1830))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1826),U_1828),U_1829),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1827),U_1828),U_1830))
| ~ sP196(U_1826,U_1827,U_1828,U_1829,U_1830) ),
inference(clausify,[status(thm)],[f_573_3]) ).
cnf(f_573_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1826),U_1828),U_1829),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1827),U_1828),U_1830))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1827,U_1826)),U_1828),U_1830))
| ~ sP196(U_1826,U_1827,U_1828,U_1829,U_1830) ),
inference(clausify,[status(thm)],[f_573_3]) ).
fof(f_574_1,plain,
! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
| ~ 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_574_2,plain,
! [U_1835,U_1834,U_1833,U_1832,U_1831] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1832),U_1833),U_1834),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833),U_1835))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1832,U_1831)),U_1833),U_1834),U_1835) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1832,U_1831)),U_1833),U_1834),U_1835)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1832),U_1833),U_1834),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833),U_1835)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1831,U_1832) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
( ! [U_1832,U_1834,U_1835,U_1833,U_1831] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1832),U_1833),U_1834),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833),U_1835))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1832,U_1831)),U_1833),U_1834),U_1835)
| ~ sP197(U_1832,U_1834,U_1835,U_1833,U_1831) )
& ! [U_1832,U_1834,U_1835,U_1833,U_1831] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1832,U_1831)),U_1833),U_1834),U_1835)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1832),U_1833),U_1834),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833),U_1835))
| ~ sP197(U_1832,U_1834,U_1835,U_1833,U_1831) )
& ! [U_1832,U_1834,U_1835,U_1833,U_1831] :
( sP197(U_1832,U_1834,U_1835,U_1833,U_1831)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1831,U_1832) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_574_2]) ).
cnf(f_574_4,plain,
( sP197(U_1832,U_1834,U_1835,U_1833,U_1831)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1831,U_1832) ),
inference(clausify,[status(thm)],[f_574_3]) ).
cnf(f_574_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1832,U_1831)),U_1833),U_1834),U_1835)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1832),U_1833),U_1834),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833),U_1835))
| ~ sP197(U_1832,U_1834,U_1835,U_1833,U_1831) ),
inference(clausify,[status(thm)],[f_574_3]) ).
cnf(f_574_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1832),U_1833),U_1834),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833),U_1835))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1832,U_1831)),U_1833),U_1834),U_1835)
| ~ sP197(U_1832,U_1834,U_1835,U_1833,U_1831) ),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).
fof(f_575_2,plain,
! [U_1837,U_1836] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1836,U_1837) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1837,U_1836),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
! [U_1836,U_1837] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1836,U_1837) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1837,U_1836),
inference(definitional_conversion,[status(esa)],[f_575_2]) ).
cnf(f_575_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1836,U_1837) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1837,U_1836),
inference(clausify,[status(thm)],[f_575_3]) ).
fof(f_576_1,plain,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).
fof(f_576_2,plain,
! [U_1840,U_1839,U_1838] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1838,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1839,U_1840)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1839,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1838,U_1840)),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
! [U_1838,U_1839,U_1840] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1838,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1839,U_1840)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1839,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1838,U_1840)),
inference(definitional_conversion,[status(esa)],[f_576_2]) ).
cnf(f_576_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1838,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1839,U_1840)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1839,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1838,U_1840)),
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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_577_2,plain,
! [U_1842,U_1841] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1841,U_1842),U_1842) = U_1841,
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
! [U_1841,U_1842] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1841,U_1842),U_1842) = U_1841,
inference(definitional_conversion,[status(esa)],[f_577_2]) ).
cnf(f_577_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1841,U_1842),U_1842) = U_1841,
inference(clausify,[status(thm)],[f_577_3]) ).
fof(f_578_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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_578_2,plain,
! [U_1844,U_1843] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1843,U_1844),U_1843) = U_1844,
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
! [U_1844,U_1843] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1843,U_1844),U_1843) = U_1844,
inference(definitional_conversion,[status(esa)],[f_578_2]) ).
cnf(f_578_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1843,U_1844),U_1843) = U_1844,
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_1,plain,
! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).
fof(f_579_2,plain,
! [U_1847,U_1846,U_1845] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1845,U_1846),U_1847) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1845,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1846,U_1847)),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
! [U_1846,U_1845,U_1847] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1845,U_1846),U_1847) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1845,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1846,U_1847)),
inference(definitional_conversion,[status(esa)],[f_579_2]) ).
cnf(f_579_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1845,U_1846),U_1847) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1845,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1846,U_1847)),
inference(clausify,[status(thm)],[f_579_3]) ).
fof(f_580_1,plain,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).
fof(f_580_2,plain,
! [U_1850,U_1849,U_1848] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1848,U_1849),U_1850) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1848,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1849,U_1850)),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
! [U_1849,U_1848,U_1850] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1848,U_1849),U_1850) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1848,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1849,U_1850)),
inference(definitional_conversion,[status(esa)],[f_580_2]) ).
cnf(f_580_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1848,U_1849),U_1850) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1848,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1849,U_1850)),
inference(clausify,[status(thm)],[f_580_3]) ).
fof(f_581_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).
fof(f_581_2,plain,
! [U_1853,U_1852,U_1851] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1851,U_1852) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1851,U_1853)
| U_1852 != U_1853 )
& ( U_1852 = U_1853
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1851,U_1852) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1851,U_1853) ) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
( ! [U_1859,U_1857] :
( ! [U_1855] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1855,U_1857) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1855,U_1859)
| U_1857 != U_1859 )
& ! [U_1858,U_1856] :
( ! [U_1854] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1854,U_1856) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1854,U_1858)
| U_1856 = U_1858 ) ),
inference(miniscope,[status(thm)],[f_581_2]) ).
fof(f_581_4,plain,
( ! [U_1855,U_1859,U_1857] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1855,U_1857) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1855,U_1859)
| U_1857 != U_1859 )
& ! [U_1854,U_1856,U_1858] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1854,U_1856) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1854,U_1858)
| U_1856 = U_1858 ) ),
inference(definitional_conversion,[status(esa)],[f_581_3]) ).
cnf(f_581_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1854,U_1856) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1854,U_1858)
| U_1856 = U_1858 ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1855,U_1857) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1855,U_1859)
| U_1857 != U_1859 ),
inference(clausify,[status(thm)],[f_581_4]) ).
fof(f_582_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).
fof(f_582_2,plain,
! [U_1862,U_1861,U_1860] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1860,U_1861) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1862,U_1861)
| U_1860 != U_1862 )
& ( U_1860 = U_1862
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1860,U_1861) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1862,U_1861) ) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
( ! [U_1868,U_1866,U_1864] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1864,U_1866) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1868,U_1866)
| U_1864 != U_1868 )
& ! [U_1867,U_1865,U_1863] :
( U_1863 = U_1867
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1863,U_1865) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1867,U_1865) ) ),
inference(miniscope,[status(thm)],[f_582_2]) ).
fof(f_582_4,plain,
( ! [U_1866,U_1868,U_1864] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1864,U_1866) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1868,U_1866)
| U_1864 != U_1868 )
& ! [U_1863,U_1865,U_1867] :
( U_1863 = U_1867
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1863,U_1865) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1867,U_1865) ) ),
inference(definitional_conversion,[status(esa)],[f_582_3]) ).
cnf(f_582_5,plain,
( U_1863 = U_1867
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1863,U_1865) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1867,U_1865) ),
inference(clausify,[status(thm)],[f_582_4]) ).
cnf(f_582_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1864,U_1866) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1868,U_1866)
| U_1864 != U_1868 ),
inference(clausify,[status(thm)],[f_582_4]) ).
fof(f_583_1,plain,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).
fof(f_583_2,plain,
! [U_1871,U_1870,U_1869] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1869,U_1870),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1869,U_1871)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1870,U_1871),
inference(variable_rename,[status(thm)],[f_583_1]) ).
fof(f_583_3,plain,
! [U_1869,U_1870,U_1871] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1869,U_1870),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1869,U_1871)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1870,U_1871),
inference(definitional_conversion,[status(esa)],[f_583_2]) ).
cnf(f_583_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1869,U_1870),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1869,U_1871)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1870,U_1871),
inference(clausify,[status(thm)],[f_583_3]) ).
fof(f_584_1,plain,
! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).
fof(f_584_2,plain,
! [U_1874,U_1873,U_1872] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1872,U_1873),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1874,U_1873)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1872,U_1874),
inference(variable_rename,[status(thm)],[f_584_1]) ).
fof(f_584_3,plain,
! [U_1873,U_1872,U_1874] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1872,U_1873),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1874,U_1873)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1872,U_1874),
inference(definitional_conversion,[status(esa)],[f_584_2]) ).
cnf(f_584_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1872,U_1873),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1874,U_1873)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1872,U_1874),
inference(clausify,[status(thm)],[f_584_3]) ).
fof(f_585_1,plain,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j),
inference(fof_nnf,[status(thm)],[fact_diff__commute]) ).
fof(f_585_2,plain,
! [U_1877,U_1876,U_1875] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1875,U_1876),U_1877) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1875,U_1877),U_1876),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
! [U_1876,U_1875,U_1877] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1875,U_1876),U_1877) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1875,U_1877),U_1876),
inference(definitional_conversion,[status(esa)],[f_585_2]) ).
cnf(f_585_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1875,U_1876),U_1877) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1875,U_1877),U_1876),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = 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_586_2,plain,
! [U_1880,U_1879,U_1878] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1878,U_1879)),U_1880) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1878),U_1880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1879),U_1880)),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
! [U_1878,U_1879,U_1880] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1878,U_1879)),U_1880) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1878),U_1880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1879),U_1880)),
inference(definitional_conversion,[status(esa)],[f_586_2]) ).
cnf(f_586_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1878,U_1879)),U_1880) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1878),U_1880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1879),U_1880)),
inference(clausify,[status(thm)],[f_586_3]) ).
fof(f_587_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_587_2,plain,
! [U_1883,U_1882,U_1881] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1881),U_1882)),U_1883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1882),U_1883)),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
! [U_1881,U_1882,U_1883] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1881),U_1882)),U_1883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1882),U_1883)),
inference(definitional_conversion,[status(esa)],[f_587_2]) ).
cnf(f_587_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1881),U_1882)),U_1883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1882),U_1883)),
inference(clausify,[status(thm)],[f_587_3]) ).
fof(f_588_1,plain,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = 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_588_2,plain,
! [U_1886,U_1885,U_1884] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1885,U_1886)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1886)),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
! [U_1884,U_1885,U_1886] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1885,U_1886)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1886)),
inference(definitional_conversion,[status(esa)],[f_588_2]) ).
cnf(f_588_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1885,U_1886)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1886)),
inference(clausify,[status(thm)],[f_588_3]) ).
fof(f_589_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_589_2,plain,
! [U_1888,U_1887] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),U_1888) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1888),U_1887),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
! [U_1887,U_1888] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),U_1888) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1888),U_1887),
inference(definitional_conversion,[status(esa)],[f_589_2]) ).
cnf(f_589_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),U_1888) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1888),U_1887),
inference(clausify,[status(thm)],[f_589_3]) ).
fof(f_590_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_590_2,plain,
! [U_1889] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1889) = U_1889,
inference(variable_rename,[status(thm)],[f_590_1]) ).
fof(f_590_3,plain,
! [U_1889] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1889) = U_1889,
inference(definitional_conversion,[status(esa)],[f_590_2]) ).
cnf(f_590_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1889) = U_1889,
inference(clausify,[status(thm)],[f_590_3]) ).
fof(f_591_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_ma_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_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_ma_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).
fof(f_591_2,plain,
! [U_1891,U_1890] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1890),U_1891)
| U_1891 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1890 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1891 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1890 = 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_1890),U_1891) ) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
( ! [U_1895,U_1893] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1895)
| U_1895 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1893 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1894,U_1892] :
( ( U_1894 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1892 = 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_1892),U_1894) ) ),
inference(miniscope,[status(thm)],[f_591_2]) ).
fof(f_591_4,plain,
( ! [U_1894,U_1892] :
( U_1894 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP198(U_1894,U_1892) )
& ! [U_1894,U_1892] :
( U_1892 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP198(U_1894,U_1892) )
& ! [U_1895,U_1893] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1895)
| U_1895 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1893 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1894,U_1892] :
( sP198(U_1894,U_1892)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1892),U_1894) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_591_3]) ).
cnf(f_591_5,plain,
( sP198(U_1894,U_1892)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1892),U_1894) ),
inference(clausify,[status(thm)],[f_591_4]) ).
cnf(f_591_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1895)
| U_1895 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1893 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_591_4]) ).
cnf(f_591_7,plain,
( U_1892 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP198(U_1894,U_1892) ),
inference(clausify,[status(thm)],[f_591_4]) ).
cnf(f_591_8,plain,
( U_1894 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP198(U_1894,U_1892) ),
inference(clausify,[status(thm)],[f_591_4]) ).
fof(f_592_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_592_2,plain,
! [U_1896] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1896),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1896,
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
! [U_1896] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1896),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1896,
inference(definitional_conversion,[status(esa)],[f_592_2]) ).
cnf(f_592_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1896),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1896,
inference(clausify,[status(thm)],[f_592_3]) ).
fof(f_593_1,plain,
! [V_n_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_ma_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).
fof(f_593_2,plain,
! [U_1898,U_1897] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1897),U_1898) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1898 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1897 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1898 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1897 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1897),U_1898) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
( ! [U_1902,U_1900] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1900),U_1902) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1902 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1900 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1901,U_1899] :
( ( U_1901 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1899 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1899),U_1901) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_593_2]) ).
fof(f_593_4,plain,
( ! [U_1901,U_1899] :
( U_1901 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP199(U_1901,U_1899) )
& ! [U_1901,U_1899] :
( U_1899 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP199(U_1901,U_1899) )
& ! [U_1902,U_1900] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1900),U_1902) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1902 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1900 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1901,U_1899] :
( sP199(U_1901,U_1899)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1899),U_1901) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_593_3]) ).
cnf(f_593_5,plain,
( sP199(U_1901,U_1899)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1899),U_1901) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_593_4]) ).
cnf(f_593_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1900),U_1902) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1902 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1900 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_593_4]) ).
cnf(f_593_7,plain,
( U_1899 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP199(U_1901,U_1899) ),
inference(clausify,[status(thm)],[f_593_4]) ).
cnf(f_593_8,plain,
( U_1901 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP199(U_1901,U_1899) ),
inference(clausify,[status(thm)],[f_593_4]) ).
fof(f_594_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = 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_594_2,plain,
! [U_1905,U_1904,U_1903] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1903,U_1904)),U_1905) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1903),U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1904),U_1905)),
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
! [U_1904,U_1905,U_1903] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1903,U_1904)),U_1905) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1903),U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1904),U_1905)),
inference(definitional_conversion,[status(esa)],[f_594_2]) ).
cnf(f_594_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1903,U_1904)),U_1905) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1903),U_1905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1904),U_1905)),
inference(clausify,[status(thm)],[f_594_3]) ).
fof(f_595_1,plain,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = 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_595_2,plain,
! [U_1908,U_1907,U_1906] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1907,U_1908)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),U_1907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),U_1908)),
inference(variable_rename,[status(thm)],[f_595_1]) ).
fof(f_595_3,plain,
! [U_1906,U_1907,U_1908] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1907,U_1908)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),U_1907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),U_1908)),
inference(definitional_conversion,[status(esa)],[f_595_2]) ).
cnf(f_595_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1907,U_1908)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),U_1907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1906),U_1908)),
inference(clausify,[status(thm)],[f_595_3]) ).
fof(f_596_1,plain,
! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_596_2,plain,
! [U_1912,U_1911,U_1910,U_1909] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1909),U_1910),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1911),U_1910),U_1912)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1909,U_1911)),U_1910),U_1912),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
! [U_1909,U_1910,U_1911,U_1912] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1909),U_1910),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1911),U_1910),U_1912)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1909,U_1911)),U_1910),U_1912),
inference(definitional_conversion,[status(esa)],[f_596_2]) ).
cnf(f_596_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1909),U_1910),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1911),U_1910),U_1912)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1909,U_1911)),U_1910),U_1912),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| ( V_ma_2 != V_n_2
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_ma_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).
fof(f_597_2,plain,
! [U_1915,U_1914,U_1913] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1913),U_1914) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1913),U_1915)
| ( U_1914 != U_1915
& U_1913 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1914 = U_1915
| U_1913 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1913),U_1914) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1913),U_1915) ) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
( ! [U_1921,U_1919,U_1917] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1917),U_1919) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1917),U_1921)
| ( U_1919 != U_1921
& U_1917 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1920,U_1918,U_1916] :
( U_1918 = U_1920
| U_1916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1916),U_1918) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1916),U_1920) ) ),
inference(miniscope,[status(thm)],[f_597_2]) ).
fof(f_597_4,plain,
( ! [U_1921,U_1919,U_1917] :
( U_1919 != U_1921
| ~ sP200(U_1921,U_1919,U_1917) )
& ! [U_1921,U_1919,U_1917] :
( U_1917 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP200(U_1921,U_1919,U_1917) )
& ! [U_1921,U_1919,U_1917] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1917),U_1919) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1917),U_1921)
| sP200(U_1921,U_1919,U_1917) )
& ! [U_1918,U_1916,U_1920] :
( U_1918 = U_1920
| U_1916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1916),U_1918) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1916),U_1920) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200])],[f_597_3]) ).
cnf(f_597_5,plain,
( U_1918 = U_1920
| U_1916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1916),U_1918) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1916),U_1920) ),
inference(clausify,[status(thm)],[f_597_4]) ).
cnf(f_597_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1917),U_1919) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1917),U_1921)
| sP200(U_1921,U_1919,U_1917) ),
inference(clausify,[status(thm)],[f_597_4]) ).
cnf(f_597_7,plain,
( U_1917 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP200(U_1921,U_1919,U_1917) ),
inference(clausify,[status(thm)],[f_597_4]) ).
cnf(f_597_8,plain,
( U_1919 != U_1921
| ~ sP200(U_1921,U_1919,U_1917) ),
inference(clausify,[status(thm)],[f_597_4]) ).
fof(f_598_1,plain,
! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
( ( ( 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_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
| V_ma_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) )
& ( V_ma_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)
| 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_ma_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2) ) )
| ~ 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_598_2,plain,
! [U_1926,U_1925,U_1924,U_1923,U_1922] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1922),U_1924),U_1925) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1923),U_1924),U_1926)
| U_1925 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1923,U_1922)),U_1924),U_1926) )
& ( U_1925 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1923,U_1922)),U_1924),U_1926)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1922),U_1924),U_1925) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1923),U_1924),U_1926) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1922,U_1923) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
fof(f_598_3,plain,
( ! [U_1922,U_1923,U_1924,U_1925,U_1926] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1922),U_1924),U_1925) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1923),U_1924),U_1926)
| U_1925 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1923,U_1922)),U_1924),U_1926)
| ~ sP201(U_1922,U_1923,U_1924,U_1925,U_1926) )
& ! [U_1922,U_1923,U_1924,U_1925,U_1926] :
( U_1925 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1923,U_1922)),U_1924),U_1926)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1922),U_1924),U_1925) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1923),U_1924),U_1926)
| ~ sP201(U_1922,U_1923,U_1924,U_1925,U_1926) )
& ! [U_1922,U_1923,U_1924,U_1925,U_1926] :
( sP201(U_1922,U_1923,U_1924,U_1925,U_1926)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1922,U_1923) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_598_2]) ).
cnf(f_598_4,plain,
( sP201(U_1922,U_1923,U_1924,U_1925,U_1926)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1922,U_1923) ),
inference(clausify,[status(thm)],[f_598_3]) ).
cnf(f_598_5,plain,
( U_1925 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1923,U_1922)),U_1924),U_1926)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1922),U_1924),U_1925) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1923),U_1924),U_1926)
| ~ sP201(U_1922,U_1923,U_1924,U_1925,U_1926) ),
inference(clausify,[status(thm)],[f_598_3]) ).
cnf(f_598_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1922),U_1924),U_1925) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1923),U_1924),U_1926)
| U_1925 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1923,U_1922)),U_1924),U_1926)
| ~ sP201(U_1922,U_1923,U_1924,U_1925,U_1926) ),
inference(clausify,[status(thm)],[f_598_3]) ).
fof(f_599_1,plain,
! [V_n,V_m,V_u,V_j,V_i] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n))
| ~ 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_599_2,plain,
! [U_1931,U_1930,U_1929,U_1928,U_1927] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1927),U_1929),U_1930),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1928),U_1929),U_1931)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1930,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1928,U_1927)),U_1929),U_1931))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1927,U_1928) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
fof(f_599_3,plain,
! [U_1929,U_1927,U_1930,U_1931,U_1928] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1927),U_1929),U_1930),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1928),U_1929),U_1931)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1930,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1928,U_1927)),U_1929),U_1931))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1927,U_1928) ),
inference(definitional_conversion,[status(esa)],[f_599_2]) ).
cnf(f_599_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1927),U_1929),U_1930),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1928),U_1929),U_1931)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1930,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1928,U_1927)),U_1929),U_1931))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1927,U_1928) ),
inference(clausify,[status(thm)],[f_599_3]) ).
fof(f_600_1,plain,
! [V_n_2,V_ma_2,V_u_2,V_j_2,V_i_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
| ~ 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_600_2,plain,
! [U_1936,U_1935,U_1934,U_1933,U_1932] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1932),U_1934),U_1935),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1933),U_1934),U_1936))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1935,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1933,U_1932)),U_1934),U_1936)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1935,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1933,U_1932)),U_1934),U_1936))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1932),U_1934),U_1935),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1933),U_1934),U_1936)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1932,U_1933) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
fof(f_600_3,plain,
( ! [U_1932,U_1933,U_1934,U_1935,U_1936] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1932),U_1934),U_1935),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1933),U_1934),U_1936))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1935,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1933,U_1932)),U_1934),U_1936))
| ~ sP202(U_1932,U_1933,U_1934,U_1935,U_1936) )
& ! [U_1932,U_1933,U_1934,U_1935,U_1936] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1935,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1933,U_1932)),U_1934),U_1936))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1932),U_1934),U_1935),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1933),U_1934),U_1936))
| ~ sP202(U_1932,U_1933,U_1934,U_1935,U_1936) )
& ! [U_1932,U_1933,U_1934,U_1935,U_1936] :
( sP202(U_1932,U_1933,U_1934,U_1935,U_1936)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1932,U_1933) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_600_2]) ).
cnf(f_600_4,plain,
( sP202(U_1932,U_1933,U_1934,U_1935,U_1936)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1932,U_1933) ),
inference(clausify,[status(thm)],[f_600_3]) ).
cnf(f_600_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1935,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1933,U_1932)),U_1934),U_1936))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1932),U_1934),U_1935),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1933),U_1934),U_1936))
| ~ sP202(U_1932,U_1933,U_1934,U_1935,U_1936) ),
inference(clausify,[status(thm)],[f_600_3]) ).
cnf(f_600_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1932),U_1934),U_1935),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1933),U_1934),U_1936))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1935,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1933,U_1932)),U_1934),U_1936))
| ~ sP202(U_1932,U_1933,U_1934,U_1935,U_1936) ),
inference(clausify,[status(thm)],[f_600_3]) ).
fof(f_601_1,plain,
! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
( ( ( 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_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2) != V_n_2 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2) = V_n_2
| 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_ma_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2) ) )
| ~ 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_601_2,plain,
! [U_1941,U_1940,U_1939,U_1938,U_1937] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1938),U_1939),U_1940) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1937),U_1939),U_1941)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1938,U_1937)),U_1939),U_1940) != U_1941 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1938,U_1937)),U_1939),U_1940) = U_1941
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1938),U_1939),U_1940) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1937),U_1939),U_1941) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1937,U_1938) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
( ! [U_1938,U_1937,U_1939,U_1940,U_1941] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1938),U_1939),U_1940) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1937),U_1939),U_1941)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1938,U_1937)),U_1939),U_1940) != U_1941
| ~ sP203(U_1938,U_1937,U_1939,U_1940,U_1941) )
& ! [U_1938,U_1937,U_1939,U_1940,U_1941] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1938,U_1937)),U_1939),U_1940) = U_1941
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1938),U_1939),U_1940) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1937),U_1939),U_1941)
| ~ sP203(U_1938,U_1937,U_1939,U_1940,U_1941) )
& ! [U_1938,U_1937,U_1939,U_1940,U_1941] :
( sP203(U_1938,U_1937,U_1939,U_1940,U_1941)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1937,U_1938) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_601_2]) ).
cnf(f_601_4,plain,
( sP203(U_1938,U_1937,U_1939,U_1940,U_1941)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1937,U_1938) ),
inference(clausify,[status(thm)],[f_601_3]) ).
cnf(f_601_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1938,U_1937)),U_1939),U_1940) = U_1941
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1938),U_1939),U_1940) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1937),U_1939),U_1941)
| ~ sP203(U_1938,U_1937,U_1939,U_1940,U_1941) ),
inference(clausify,[status(thm)],[f_601_3]) ).
cnf(f_601_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1938),U_1939),U_1940) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1937),U_1939),U_1941)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1938,U_1937)),U_1939),U_1940) != U_1941
| ~ sP203(U_1938,U_1937,U_1939,U_1940,U_1941) ),
inference(clausify,[status(thm)],[f_601_3]) ).
fof(f_602_1,plain,
! [V_n,V_m,V_u,V_i,V_j] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n)
| ~ 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_602_2,plain,
! [U_1946,U_1945,U_1944,U_1943,U_1942] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1943),U_1944),U_1945),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1942),U_1944),U_1946)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1943,U_1942)),U_1944),U_1945),U_1946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1942,U_1943) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
! [U_1942,U_1944,U_1945,U_1943,U_1946] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1943),U_1944),U_1945),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1942),U_1944),U_1946)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1943,U_1942)),U_1944),U_1945),U_1946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1942,U_1943) ),
inference(definitional_conversion,[status(esa)],[f_602_2]) ).
cnf(f_602_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1943),U_1944),U_1945),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1942),U_1944),U_1946)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1943,U_1942)),U_1944),U_1945),U_1946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1942,U_1943) ),
inference(clausify,[status(thm)],[f_602_3]) ).
fof(f_603_1,plain,
! [V_n_2,V_ma_2,V_u_2,V_i_2,V_j_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_ma_2),V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
| ~ 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_603_2,plain,
! [U_1951,U_1950,U_1949,U_1948,U_1947] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1948),U_1949),U_1950),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1947),U_1949),U_1951))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1948,U_1947)),U_1949),U_1950),U_1951) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1948,U_1947)),U_1949),U_1950),U_1951)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1948),U_1949),U_1950),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1947),U_1949),U_1951)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1947,U_1948) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
( ! [U_1947,U_1949,U_1948,U_1950,U_1951] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1948),U_1949),U_1950),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1947),U_1949),U_1951))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1948,U_1947)),U_1949),U_1950),U_1951)
| ~ sP204(U_1947,U_1949,U_1948,U_1950,U_1951) )
& ! [U_1947,U_1949,U_1948,U_1950,U_1951] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1948,U_1947)),U_1949),U_1950),U_1951)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1948),U_1949),U_1950),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1947),U_1949),U_1951))
| ~ sP204(U_1947,U_1949,U_1948,U_1950,U_1951) )
& ! [U_1947,U_1949,U_1948,U_1950,U_1951] :
( sP204(U_1947,U_1949,U_1948,U_1950,U_1951)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1947,U_1948) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_603_2]) ).
cnf(f_603_4,plain,
( sP204(U_1947,U_1949,U_1948,U_1950,U_1951)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1947,U_1948) ),
inference(clausify,[status(thm)],[f_603_3]) ).
cnf(f_603_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1948,U_1947)),U_1949),U_1950),U_1951)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1948),U_1949),U_1950),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1947),U_1949),U_1951))
| ~ sP204(U_1947,U_1949,U_1948,U_1950,U_1951) ),
inference(clausify,[status(thm)],[f_603_3]) ).
cnf(f_603_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1948),U_1949),U_1950),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1947),U_1949),U_1951))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1948,U_1947)),U_1949),U_1950),U_1951)
| ~ sP204(U_1947,U_1949,U_1948,U_1950,U_1951) ),
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_1,plain,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
inference(fof_nnf,[status(thm)],[fact_complex__diff__def]) ).
fof(f_604_2,plain,
! [U_1953,U_1952] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_1952,U_1953) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_1952,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_1953)),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
! [U_1953,U_1952] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_1952,U_1953) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_1952,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_1953)),
inference(definitional_conversion,[status(esa)],[f_604_2]) ).
cnf(f_604_4,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_1952,U_1953) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_1952,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_1953)),
inference(clausify,[status(thm)],[f_604_3]) ).
fof(f_605_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) )
| ~ 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_605_2,plain,
! [U_1956,U_1955,U_1954] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1956)
| U_1955 != U_1956 )
& ( U_1955 = U_1956
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1955) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1956) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1954) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
fof(f_605_3,plain,
( ! [U_1955,U_1956,U_1954] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1956)
| U_1955 != U_1956
| ~ sP205(U_1955,U_1956,U_1954) )
& ! [U_1955,U_1956,U_1954] :
( U_1955 = U_1956
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1955) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1956)
| ~ sP205(U_1955,U_1956,U_1954) )
& ! [U_1955,U_1956,U_1954] :
( sP205(U_1955,U_1956,U_1954)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1954) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_605_2]) ).
cnf(f_605_4,plain,
( sP205(U_1955,U_1956,U_1954)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1954) ),
inference(clausify,[status(thm)],[f_605_3]) ).
cnf(f_605_5,plain,
( U_1955 = U_1956
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1955) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1956)
| ~ sP205(U_1955,U_1956,U_1954) ),
inference(clausify,[status(thm)],[f_605_3]) ).
cnf(f_605_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1954),U_1956)
| U_1955 != U_1956
| ~ sP205(U_1955,U_1956,U_1954) ),
inference(clausify,[status(thm)],[f_605_3]) ).
fof(f_606_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) )
| ~ 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_606_2,plain,
! [U_1959,U_1958,U_1957] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1959))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1958,U_1959) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1958,U_1959)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1959)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1957) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
( ! [U_1957,U_1958,U_1959] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1959))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1958,U_1959)
| ~ sP206(U_1957,U_1958,U_1959) )
& ! [U_1957,U_1958,U_1959] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1958,U_1959)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1959))
| ~ sP206(U_1957,U_1958,U_1959) )
& ! [U_1957,U_1958,U_1959] :
( sP206(U_1957,U_1958,U_1959)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1957) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_606_2]) ).
cnf(f_606_4,plain,
( sP206(U_1957,U_1958,U_1959)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1957) ),
inference(clausify,[status(thm)],[f_606_3]) ).
cnf(f_606_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1958,U_1959)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1959))
| ~ sP206(U_1957,U_1958,U_1959) ),
inference(clausify,[status(thm)],[f_606_3]) ).
cnf(f_606_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1957),U_1959))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1958,U_1959)
| ~ sP206(U_1957,U_1958,U_1959) ),
inference(clausify,[status(thm)],[f_606_3]) ).
fof(f_607_1,plain,
! [V_x] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__add__one]) ).
fof(f_607_2,plain,
! [U_1960] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1960,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1960),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1960) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
fof(f_607_3,plain,
! [U_1960] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1960,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1960),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1960) ),
inference(definitional_conversion,[status(esa)],[f_607_2]) ).
cnf(f_607_4,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1960,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1960),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1960) ),
inference(clausify,[status(thm)],[f_607_3]) ).
fof(f_608_1,plain,
! [V_x] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__add__one]) ).
fof(f_608_2,plain,
! [U_1961] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1961,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1961),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1961) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
! [U_1961] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1961,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1961),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1961) ),
inference(definitional_conversion,[status(esa)],[f_608_2]) ).
cnf(f_608_4,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1961,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_1961),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1961) ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ 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_609_2,plain,
! [U_1964,U_1963,U_1962] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1963,U_1964))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,U_1963) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
fof(f_609_3,plain,
! [U_1964,U_1963,U_1962] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1963,U_1964))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,U_1963) ),
inference(definitional_conversion,[status(esa)],[f_609_2]) ).
cnf(f_609_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1963,U_1964))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,U_1963) ),
inference(clausify,[status(thm)],[f_609_3]) ).
fof(f_610_1,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natfloor__zero]) ).
fof(f_610_2,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_610_1]) ).
cnf(f_610_3,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_610_2]) ).
fof(f_611_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),
inference(fof_nnf,[status(thm)],[fact_zero__le__natfloor]) ).
fof(f_611_2,plain,
! [U_1965] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_1965)),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
! [U_1965] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_1965)),
inference(definitional_conversion,[status(esa)],[f_611_2]) ).
cnf(f_611_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_1965)),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__mono]) ).
fof(f_612_2,plain,
! [U_1967,U_1966] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1966),c_RComplete_Onatfloor(U_1967))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1966,U_1967) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
! [U_1966,U_1967] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1966),c_RComplete_Onatfloor(U_1967))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1966,U_1967) ),
inference(definitional_conversion,[status(esa)],[f_612_2]) ).
cnf(f_612_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1966),c_RComplete_Onatfloor(U_1967))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1966,U_1967) ),
inference(clausify,[status(thm)],[f_612_3]) ).
fof(f_613_1,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natfloor__one]) ).
fof(f_613_2,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_613_1]) ).
cnf(f_613_3,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_1,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natceiling__zero]) ).
fof(f_614_2,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_614_1]) ).
cnf(f_614_3,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),
inference(fof_nnf,[status(thm)],[fact_zero__le__natceiling]) ).
fof(f_615_2,plain,
! [U_1968] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1968)),
inference(variable_rename,[status(thm)],[f_615_1]) ).
fof(f_615_3,plain,
! [U_1968] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1968)),
inference(definitional_conversion,[status(esa)],[f_615_2]) ).
cnf(f_615_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1968)),
inference(clausify,[status(thm)],[f_615_3]) ).
fof(f_616_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__mono]) ).
fof(f_616_2,plain,
! [U_1970,U_1969] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1969),c_RComplete_Onatceiling(U_1970))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1969,U_1970) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
! [U_1969,U_1970] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1969),c_RComplete_Onatceiling(U_1970))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1969,U_1970) ),
inference(definitional_conversion,[status(esa)],[f_616_2]) ).
cnf(f_616_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1969),c_RComplete_Onatceiling(U_1970))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1969,U_1970) ),
inference(clausify,[status(thm)],[f_616_3]) ).
fof(f_617_1,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natceiling__one]) ).
fof(f_617_2,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_617_1]) ).
cnf(f_617_3,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_617_2]) ).
fof(f_618_1,plain,
! [V_x] :
( c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__neg]) ).
fof(f_618_2,plain,
! [U_1971] :
( c_RComplete_Onatfloor(U_1971) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1971,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
! [U_1971] :
( c_RComplete_Onatfloor(U_1971) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1971,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_618_2]) ).
cnf(f_618_4,plain,
( c_RComplete_Onatfloor(U_1971) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1971,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_618_3]) ).
fof(f_619_1,plain,
! [V_x] :
( c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__neg]) ).
fof(f_619_2,plain,
! [U_1972] :
( c_RComplete_Onatceiling(U_1972) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1972,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
! [U_1972] :
( c_RComplete_Onatceiling(U_1972) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1972,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_619_2]) ).
cnf(f_619_4,plain,
( c_RComplete_Onatceiling(U_1972) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1972,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one]) ).
fof(f_620_2,plain,
! [U_1973] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1973))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1973) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1973)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1973)) ) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
( ! [U_1975] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1975))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1975) )
& ! [U_1974] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1974)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1974)) ) ),
inference(miniscope,[status(thm)],[f_620_2]) ).
fof(f_620_4,plain,
( ! [U_1975] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1975))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1975) )
& ! [U_1974] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1974)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1974)) ) ),
inference(definitional_conversion,[status(esa)],[f_620_3]) ).
cnf(f_620_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1974)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1974)) ),
inference(clausify,[status(thm)],[f_620_4]) ).
cnf(f_620_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_1975))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1975) ),
inference(clausify,[status(thm)],[f_620_4]) ).
fof(f_621_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one]) ).
fof(f_621_2,plain,
! [U_1976] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1976),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1976,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1976,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1976),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
( ! [U_1978] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1978),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1978,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_1977] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1977,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1977),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_621_2]) ).
fof(f_621_4,plain,
( ! [U_1978] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1978),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1978,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_1977] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1977,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1977),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa)],[f_621_3]) ).
cnf(f_621_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1977,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1977),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_621_4]) ).
cnf(f_621_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1978),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1978,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_621_4]) ).
fof(f_622_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) ),
inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor]) ).
fof(f_622_2,plain,
! [U_1980,U_1979] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1979)),c_RComplete_Onatfloor(U_1980)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1979),U_1980)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1980)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1979) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
! [U_1980,U_1979] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1979)),c_RComplete_Onatfloor(U_1980)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1979),U_1980)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1980)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1979) ),
inference(definitional_conversion,[status(esa)],[f_622_2]) ).
cnf(f_622_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1979)),c_RComplete_Onatfloor(U_1980)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1979),U_1980)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1980)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1979) ),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ 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_623_2,plain,
! [U_1983,U_1982,U_1981] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1981,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1983,U_1982))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1981,U_1982) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
! [U_1983,U_1982,U_1981] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1981,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1983,U_1982))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1981,U_1982) ),
inference(definitional_conversion,[status(esa)],[f_623_2]) ).
cnf(f_623_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1981,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1983,U_1982))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1981,U_1982) ),
inference(clausify,[status(thm)],[f_623_3]) ).
fof(f_624_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ 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_624_2,plain,
! [U_1986,U_1985,U_1984] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1985,U_1986))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,U_1985) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
! [U_1986,U_1985,U_1984] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1985,U_1986))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,U_1985) ),
inference(definitional_conversion,[status(esa)],[f_624_2]) ).
cnf(f_624_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1985,U_1986))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,U_1985) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
| ~ 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_625_2,plain,
! [U_1988,U_1987] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1987,U_1988)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1987,U_1988) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
! [U_1987,U_1988] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1987,U_1988)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1987,U_1988) ),
inference(definitional_conversion,[status(esa)],[f_625_2]) ).
cnf(f_625_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1987,U_1988)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1987,U_1988) ),
inference(clausify,[status(thm)],[f_625_3]) ).
fof(f_626_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ 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_626_2,plain,
! [U_1991,U_1990,U_1989] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1989,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1991,U_1990))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1989,U_1990) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
fof(f_626_3,plain,
! [U_1991,U_1990,U_1989] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1989,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1991,U_1990))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1989,U_1990) ),
inference(definitional_conversion,[status(esa)],[f_626_2]) ).
cnf(f_626_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1989,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1991,U_1990))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1989,U_1990) ),
inference(clausify,[status(thm)],[f_626_3]) ).
fof(f_627_1,plain,
! [V_x,V_n] :
( c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__eq]) ).
fof(f_627_2,plain,
! [U_1993,U_1992] :
( c_RComplete_Onatceiling(U_1993) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1992,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1993,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1992),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1992),U_1993) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
! [U_1992,U_1993] :
( c_RComplete_Onatceiling(U_1993) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1992,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1993,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1992),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1992),U_1993) ),
inference(definitional_conversion,[status(esa)],[f_627_2]) ).
cnf(f_627_4,plain,
( c_RComplete_Onatceiling(U_1993) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1992,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1993,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1992),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1992),U_1993) ),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus]) ).
fof(f_628_2,plain,
! [U_1996,U_1995,U_1994] :
( c_Groups_Ominus__class_Ominus(U_1994,c_Groups_Ouminus__class_Ouminus(U_1994,U_1995),c_Groups_Ouminus__class_Ouminus(U_1994,U_1996)) = c_Groups_Ouminus__class_Ouminus(U_1994,c_Groups_Ominus__class_Ominus(U_1994,U_1995,U_1996))
| ~ class_Groups_Oab__group__add(U_1994) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
! [U_1994,U_1995,U_1996] :
( c_Groups_Ominus__class_Ominus(U_1994,c_Groups_Ouminus__class_Ouminus(U_1994,U_1995),c_Groups_Ouminus__class_Ouminus(U_1994,U_1996)) = c_Groups_Ouminus__class_Ouminus(U_1994,c_Groups_Ominus__class_Ominus(U_1994,U_1995,U_1996))
| ~ class_Groups_Oab__group__add(U_1994) ),
inference(definitional_conversion,[status(esa)],[f_628_2]) ).
cnf(f_628_4,plain,
( c_Groups_Ominus__class_Ominus(U_1994,c_Groups_Ouminus__class_Ouminus(U_1994,U_1995),c_Groups_Ouminus__class_Ouminus(U_1994,U_1996)) = c_Groups_Ouminus__class_Ouminus(U_1994,c_Groups_Ominus__class_Ominus(U_1994,U_1995,U_1996))
| ~ class_Groups_Oab__group__add(U_1994) ),
inference(clausify,[status(thm)],[f_628_3]) ).
fof(f_629_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add]) ).
fof(f_629_2,plain,
! [U_2001,U_2000,U_1999,U_1998,U_1997] :
( c_Groups_Ominus__class_Ominus(U_1997,c_Groups_Oplus__class_Oplus(U_1997,U_1998,U_1999),c_Groups_Oplus__class_Oplus(U_1997,U_2000,U_2001)) = c_Groups_Oplus__class_Oplus(U_1997,c_Groups_Ominus__class_Ominus(U_1997,U_1998,U_2000),c_Groups_Ominus__class_Ominus(U_1997,U_1999,U_2001))
| ~ class_Groups_Oab__group__add(U_1997) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
fof(f_629_3,plain,
! [U_1997,U_1998,U_1999,U_2000,U_2001] :
( c_Groups_Ominus__class_Ominus(U_1997,c_Groups_Oplus__class_Oplus(U_1997,U_1998,U_1999),c_Groups_Oplus__class_Oplus(U_1997,U_2000,U_2001)) = c_Groups_Oplus__class_Oplus(U_1997,c_Groups_Ominus__class_Ominus(U_1997,U_1998,U_2000),c_Groups_Ominus__class_Ominus(U_1997,U_1999,U_2001))
| ~ class_Groups_Oab__group__add(U_1997) ),
inference(definitional_conversion,[status(esa)],[f_629_2]) ).
cnf(f_629_4,plain,
( c_Groups_Ominus__class_Ominus(U_1997,c_Groups_Oplus__class_Oplus(U_1997,U_1998,U_1999),c_Groups_Oplus__class_Oplus(U_1997,U_2000,U_2001)) = c_Groups_Oplus__class_Oplus(U_1997,c_Groups_Ominus__class_Ominus(U_1997,U_1998,U_2000),c_Groups_Ominus__class_Ominus(U_1997,U_1999,U_2001))
| ~ class_Groups_Oab__group__add(U_1997) ),
inference(clausify,[status(thm)],[f_629_3]) ).
fof(f_630_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(f_630_2,plain,
! [U_2002] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2002)),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
! [U_2002] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2002)),
inference(definitional_conversion,[status(esa)],[f_630_2]) ).
cnf(f_630_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2002)),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_1,plain,
! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
inference(fof_nnf,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(f_631_2,plain,
! [U_2003] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2003)) = U_2003,
inference(variable_rename,[status(thm)],[f_631_1]) ).
fof(f_631_3,plain,
! [U_2003] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2003)) = U_2003,
inference(definitional_conversion,[status(esa)],[f_631_2]) ).
cnf(f_631_4,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2003)) = U_2003,
inference(clausify,[status(thm)],[f_631_3]) ).
fof(f_632_1,plain,
! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
inference(fof_nnf,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(f_632_2,plain,
! [U_2004] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2004)) = U_2004,
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
! [U_2004] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2004)) = U_2004,
inference(definitional_conversion,[status(esa)],[f_632_2]) ).
cnf(f_632_4,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2004)) = U_2004,
inference(clausify,[status(thm)],[f_632_3]) ).
fof(f_633_1,plain,
! [V_ma_2,V_n_2] :
( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
| V_n_2 != V_ma_2 )
& ( V_n_2 = V_ma_2
| c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_RealDef_Oreal(tc_Nat_Onat,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject]) ).
fof(f_633_2,plain,
! [U_2006,U_2005] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_2005) = c_RealDef_Oreal(tc_Nat_Onat,U_2006)
| U_2005 != U_2006 )
& ( U_2005 = U_2006
| c_RealDef_Oreal(tc_Nat_Onat,U_2005) != c_RealDef_Oreal(tc_Nat_Onat,U_2006) ) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
( ! [U_2010,U_2008] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2008) = c_RealDef_Oreal(tc_Nat_Onat,U_2010)
| U_2008 != U_2010 )
& ! [U_2009,U_2007] :
( U_2007 = U_2009
| c_RealDef_Oreal(tc_Nat_Onat,U_2007) != c_RealDef_Oreal(tc_Nat_Onat,U_2009) ) ),
inference(miniscope,[status(thm)],[f_633_2]) ).
fof(f_633_4,plain,
( ! [U_2010,U_2008] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2008) = c_RealDef_Oreal(tc_Nat_Onat,U_2010)
| U_2008 != U_2010 )
& ! [U_2007,U_2009] :
( U_2007 = U_2009
| c_RealDef_Oreal(tc_Nat_Onat,U_2007) != c_RealDef_Oreal(tc_Nat_Onat,U_2009) ) ),
inference(definitional_conversion,[status(esa)],[f_633_3]) ).
cnf(f_633_5,plain,
( U_2007 = U_2009
| c_RealDef_Oreal(tc_Nat_Onat,U_2007) != c_RealDef_Oreal(tc_Nat_Onat,U_2009) ),
inference(clausify,[status(thm)],[f_633_4]) ).
cnf(f_633_6,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_2008) = c_RealDef_Oreal(tc_Nat_Onat,U_2010)
| U_2008 != U_2010 ),
inference(clausify,[status(thm)],[f_633_4]) ).
fof(f_634_1,plain,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
inference(fof_nnf,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
fof(f_634_2,plain,
! [U_2011] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2011)) = c_RealDef_Oreal(tc_Nat_Onat,U_2011),
inference(variable_rename,[status(thm)],[f_634_1]) ).
fof(f_634_3,plain,
! [U_2011] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2011)) = c_RealDef_Oreal(tc_Nat_Onat,U_2011),
inference(definitional_conversion,[status(esa)],[f_634_2]) ).
cnf(f_634_4,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2011)) = c_RealDef_Oreal(tc_Nat_Onat,U_2011),
inference(clausify,[status(thm)],[f_634_3]) ).
fof(f_635_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero]) ).
fof(f_635_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_635_1]) ).
cnf(f_635_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_635_2]) ).
fof(f_636_1,plain,
! [V_n_2] :
( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero__iff]) ).
fof(f_636_2,plain,
! [U_2012] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_2012) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2012 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2012) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
( ! [U_2014] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2014) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2014 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2013] :
( U_2013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2013) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_636_2]) ).
fof(f_636_4,plain,
( ! [U_2014] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2014) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2014 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2013] :
( U_2013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2013) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_636_3]) ).
cnf(f_636_5,plain,
( U_2013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2013) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_636_4]) ).
cnf(f_636_6,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_2014) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2014 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_636_4]) ).
fof(f_637_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(f_637_2,plain,
! [U_2015] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2015),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
! [U_2015] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2015),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_637_2]) ).
cnf(f_637_4,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2015),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff]) ).
fof(f_638_2,plain,
! [U_2017,U_2016] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2016),c_RealDef_Oreal(tc_Nat_Onat,U_2017))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2016,U_2017) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2016,U_2017)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2016),c_RealDef_Oreal(tc_Nat_Onat,U_2017)) ) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
( ! [U_2021,U_2019] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2019),c_RealDef_Oreal(tc_Nat_Onat,U_2021))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2019,U_2021) )
& ! [U_2020,U_2018] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2018,U_2020)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2018),c_RealDef_Oreal(tc_Nat_Onat,U_2020)) ) ),
inference(miniscope,[status(thm)],[f_638_2]) ).
fof(f_638_4,plain,
( ! [U_2019,U_2021] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2019),c_RealDef_Oreal(tc_Nat_Onat,U_2021))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2019,U_2021) )
& ! [U_2020,U_2018] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2018,U_2020)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2018),c_RealDef_Oreal(tc_Nat_Onat,U_2020)) ) ),
inference(definitional_conversion,[status(esa)],[f_638_3]) ).
cnf(f_638_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2018,U_2020)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2018),c_RealDef_Oreal(tc_Nat_Onat,U_2020)) ),
inference(clausify,[status(thm)],[f_638_4]) ).
cnf(f_638_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2019),c_RealDef_Oreal(tc_Nat_Onat,U_2021))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2019,U_2021) ),
inference(clausify,[status(thm)],[f_638_4]) ).
fof(f_639_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff]) ).
fof(f_639_2,plain,
! [U_2023,U_2022] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2022),c_RealDef_Oreal(tc_Nat_Onat,U_2023))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2022,U_2023) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2022,U_2023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2022),c_RealDef_Oreal(tc_Nat_Onat,U_2023)) ) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
fof(f_639_3,plain,
( ! [U_2027,U_2025] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2025),c_RealDef_Oreal(tc_Nat_Onat,U_2027))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2025,U_2027) )
& ! [U_2026,U_2024] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2024,U_2026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2024),c_RealDef_Oreal(tc_Nat_Onat,U_2026)) ) ),
inference(miniscope,[status(thm)],[f_639_2]) ).
fof(f_639_4,plain,
( ! [U_2027,U_2025] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2025),c_RealDef_Oreal(tc_Nat_Onat,U_2027))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2025,U_2027) )
& ! [U_2026,U_2024] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2024,U_2026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2024),c_RealDef_Oreal(tc_Nat_Onat,U_2026)) ) ),
inference(definitional_conversion,[status(esa)],[f_639_3]) ).
cnf(f_639_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2024,U_2026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2024),c_RealDef_Oreal(tc_Nat_Onat,U_2026)) ),
inference(clausify,[status(thm)],[f_639_4]) ).
cnf(f_639_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2025),c_RealDef_Oreal(tc_Nat_Onat,U_2027))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2025,U_2027) ),
inference(clausify,[status(thm)],[f_639_4]) ).
fof(f_640_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__mult]) ).
fof(f_640_2,plain,
! [U_2029,U_2028] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2028),U_2029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2028)),c_RealDef_Oreal(tc_Nat_Onat,U_2029)),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
! [U_2028,U_2029] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2028),U_2029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2028)),c_RealDef_Oreal(tc_Nat_Onat,U_2029)),
inference(definitional_conversion,[status(esa)],[f_640_2]) ).
cnf(f_640_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2028),U_2029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2028)),c_RealDef_Oreal(tc_Nat_Onat,U_2029)),
inference(clausify,[status(thm)],[f_640_3]) ).
fof(f_641_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__add]) ).
fof(f_641_2,plain,
! [U_2031,U_2030] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2030,U_2031)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2030),c_RealDef_Oreal(tc_Nat_Onat,U_2031)),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
! [U_2030,U_2031] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2030,U_2031)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2030),c_RealDef_Oreal(tc_Nat_Onat,U_2031)),
inference(definitional_conversion,[status(esa)],[f_641_2]) ).
cnf(f_641_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2030,U_2031)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2030),c_RealDef_Oreal(tc_Nat_Onat,U_2031)),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__1]) ).
fof(f_642_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_642_1]) ).
cnf(f_642_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_642_2]) ).
fof(f_643_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))),
inference(fof_nnf,[status(thm)],[fact_real__natceiling__ge]) ).
fof(f_643_2,plain,
! [U_2032] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2032,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_2032))),
inference(variable_rename,[status(thm)],[f_643_1]) ).
fof(f_643_3,plain,
! [U_2032] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2032,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_2032))),
inference(definitional_conversion,[status(esa)],[f_643_2]) ).
cnf(f_643_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2032,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_2032))),
inference(clausify,[status(thm)],[f_643_3]) ).
fof(f_644_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__zero__cancel__iff]) ).
fof(f_644_2,plain,
! [U_2033] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2033),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2033),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
( ! [U_2035] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2035),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2034] :
( U_2034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2034),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_644_2]) ).
fof(f_644_4,plain,
( ! [U_2035] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2035),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2034] :
( U_2034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2034),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_644_3]) ).
cnf(f_644_5,plain,
( U_2034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2034),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2035),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_644_4]) ).
fof(f_645_1,plain,
! [V_m,V_n] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff]) ).
fof(f_645_2,plain,
! [U_2037,U_2036] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2037,U_2036)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2037),c_RealDef_Oreal(tc_Nat_Onat,U_2036))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2036,U_2037) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
! [U_2037,U_2036] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2037,U_2036)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2037),c_RealDef_Oreal(tc_Nat_Onat,U_2036))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2036,U_2037) ),
inference(definitional_conversion,[status(esa)],[f_645_2]) ).
cnf(f_645_4,plain,
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2037,U_2036)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2037),c_RealDef_Oreal(tc_Nat_Onat,U_2036))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2036,U_2037) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__natfloor__le]) ).
fof(f_646_2,plain,
! [U_2038] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2038)),U_2038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2038) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
! [U_2038] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2038)),U_2038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2038) ),
inference(definitional_conversion,[status(esa)],[f_646_2]) ).
cnf(f_646_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2038)),U_2038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2038) ),
inference(clausify,[status(thm)],[f_646_3]) ).
fof(f_647_1,plain,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a) ),
inference(fof_nnf,[status(thm)],[fact_le__natfloor]) ).
fof(f_647_2,plain,
! [U_2040,U_2039] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2039,c_RComplete_Onatfloor(U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2039),U_2040) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
! [U_2039,U_2040] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2039,c_RComplete_Onatfloor(U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2039),U_2040) ),
inference(definitional_conversion,[status(esa)],[f_647_2]) ).
cnf(f_647_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2039,c_RComplete_Onatfloor(U_2040))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2039),U_2040) ),
inference(clausify,[status(thm)],[f_647_3]) ).
fof(f_648_1,plain,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__le]) ).
fof(f_648_2,plain,
! [U_2042,U_2041] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2041),U_2042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2041,c_RealDef_Oreal(tc_Nat_Onat,U_2042)) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
fof(f_648_3,plain,
! [U_2041,U_2042] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2041),U_2042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2041,c_RealDef_Oreal(tc_Nat_Onat,U_2042)) ),
inference(definitional_conversion,[status(esa)],[f_648_2]) ).
cnf(f_648_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2041),U_2042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2041,c_RealDef_Oreal(tc_Nat_Onat,U_2042)) ),
inference(clausify,[status(thm)],[f_648_3]) ).
fof(f_649_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff]) ).
fof(f_649_2,plain,
! [U_2043] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2043))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2043) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2043)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2043)) ) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
fof(f_649_3,plain,
( ! [U_2045] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2045))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2045) )
& ! [U_2044] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2044)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2044)) ) ),
inference(miniscope,[status(thm)],[f_649_2]) ).
fof(f_649_4,plain,
( ! [U_2045] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2045))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2045) )
& ! [U_2044] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2044)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2044)) ) ),
inference(definitional_conversion,[status(esa)],[f_649_3]) ).
cnf(f_649_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2044)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2044)) ),
inference(clausify,[status(thm)],[f_649_4]) ).
cnf(f_649_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2045))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2045) ),
inference(clausify,[status(thm)],[f_649_4]) ).
fof(f_650_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__real__le]) ).
fof(f_650_2,plain,
! [U_2047,U_2046] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2047)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2046),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2047)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2046),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2047))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2047) ) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
fof(f_650_3,plain,
( ! [U_2051,U_2049] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2049,U_2051)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2049),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2051)) )
& ! [U_2050,U_2048] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2048),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2050))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2048,U_2050) ) ),
inference(miniscope,[status(thm)],[f_650_2]) ).
fof(f_650_4,plain,
( ! [U_2051,U_2049] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2049,U_2051)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2049),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2051)) )
& ! [U_2048,U_2050] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2048),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2050))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2048,U_2050) ) ),
inference(definitional_conversion,[status(esa)],[f_650_3]) ).
cnf(f_650_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2048),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2050))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2048,U_2050) ),
inference(clausify,[status(thm)],[f_650_4]) ).
cnf(f_650_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2049,U_2051)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2049),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2051)) ),
inference(clausify,[status(thm)],[f_650_4]) ).
fof(f_651_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__real__less]) ).
fof(f_651_2,plain,
! [U_2053,U_2052] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2052,U_2053)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2052),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2053),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2052),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2053),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2052,U_2053) ) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
fof(f_651_3,plain,
( ! [U_2057,U_2055] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2055,U_2057)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2055),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2057),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ! [U_2056,U_2054] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2054),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2056),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2054,U_2056) ) ),
inference(miniscope,[status(thm)],[f_651_2]) ).
fof(f_651_4,plain,
( ! [U_2055,U_2057] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2055,U_2057)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2055),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2057),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ! [U_2054,U_2056] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2054),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2056),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2054,U_2056) ) ),
inference(definitional_conversion,[status(esa)],[f_651_3]) ).
cnf(f_651_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2054),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2056),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2054,U_2056) ),
inference(clausify,[status(thm)],[f_651_4]) ).
cnf(f_651_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2055,U_2057)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2055),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2057),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_651_4]) ).
fof(f_652_1,plain,
! [V_a_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq]) ).
fof(f_652_2,plain,
! [U_2059,U_2058] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_RComplete_Onatfloor(U_2058))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2059),U_2058) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2059),U_2058)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_RComplete_Onatfloor(U_2058)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2058) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
( ! [U_2058,U_2059] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_RComplete_Onatfloor(U_2058))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2059),U_2058)
| ~ sP207(U_2058,U_2059) )
& ! [U_2058,U_2059] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2059),U_2058)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_RComplete_Onatfloor(U_2058))
| ~ sP207(U_2058,U_2059) )
& ! [U_2058,U_2059] :
( sP207(U_2058,U_2059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2058) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_652_2]) ).
cnf(f_652_4,plain,
( sP207(U_2058,U_2059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2058) ),
inference(clausify,[status(thm)],[f_652_3]) ).
cnf(f_652_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2059),U_2058)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_RComplete_Onatfloor(U_2058))
| ~ sP207(U_2058,U_2059) ),
inference(clausify,[status(thm)],[f_652_3]) ).
cnf(f_652_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_RComplete_Onatfloor(U_2058))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2059),U_2058)
| ~ sP207(U_2058,U_2059) ),
inference(clausify,[status(thm)],[f_652_3]) ).
fof(f_653_1,plain,
! [V_a_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq]) ).
fof(f_653_2,plain,
! [U_2061,U_2060] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2060),U_2061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2060,c_RealDef_Oreal(tc_Nat_Onat,U_2061)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2060,c_RealDef_Oreal(tc_Nat_Onat,U_2061))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2060),U_2061) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2060) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
( ! [U_2060,U_2061] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2060),U_2061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2060,c_RealDef_Oreal(tc_Nat_Onat,U_2061))
| ~ sP208(U_2060,U_2061) )
& ! [U_2060,U_2061] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2060,c_RealDef_Oreal(tc_Nat_Onat,U_2061))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2060),U_2061)
| ~ sP208(U_2060,U_2061) )
& ! [U_2060,U_2061] :
( sP208(U_2060,U_2061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2060) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_653_2]) ).
cnf(f_653_4,plain,
( sP208(U_2060,U_2061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2060) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2060,c_RealDef_Oreal(tc_Nat_Onat,U_2061))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2060),U_2061)
| ~ sP208(U_2060,U_2061) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2060),U_2061)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2060,c_RealDef_Oreal(tc_Nat_Onat,U_2061))
| ~ sP208(U_2060,U_2061) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_nnf,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(f_654_2,plain,
! [U_2062] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2062,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2062)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
! [U_2062] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2062,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2062)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(definitional_conversion,[status(esa)],[f_654_2]) ).
cnf(f_654_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2062,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2062)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_1,plain,
! [V_x,V_a] :
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__subtract]) ).
fof(f_655_2,plain,
! [U_2064,U_2063] :
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2064,c_RealDef_Oreal(tc_Nat_Onat,U_2063))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2064),U_2063)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2063),U_2064) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
! [U_2063,U_2064] :
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2064,c_RealDef_Oreal(tc_Nat_Onat,U_2063))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2064),U_2063)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2063),U_2064) ),
inference(definitional_conversion,[status(esa)],[f_655_2]) ).
cnf(f_655_4,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2064,c_RealDef_Oreal(tc_Nat_Onat,U_2063))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2064),U_2063)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2063),U_2064) ),
inference(clausify,[status(thm)],[f_655_3]) ).
fof(f_656_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),
inference(fof_nnf,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).
fof(f_656_2,plain,
! [U_2065] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2065,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2065))),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
! [U_2065] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2065,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2065))),
inference(definitional_conversion,[status(esa)],[f_656_2]) ).
cnf(f_656_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2065,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2065))),
inference(clausify,[status(thm)],[f_656_3]) ).
fof(f_657_1,plain,
! [V_x,V_a] :
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__subtract]) ).
fof(f_657_2,plain,
! [U_2067,U_2066] :
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2067,c_RealDef_Oreal(tc_Nat_Onat,U_2066))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2067),U_2066)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2066),U_2067) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
! [U_2066,U_2067] :
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2067,c_RealDef_Oreal(tc_Nat_Onat,U_2066))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2067),U_2066)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2066),U_2067) ),
inference(definitional_conversion,[status(esa)],[f_657_2]) ).
cnf(f_657_4,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2067,c_RealDef_Oreal(tc_Nat_Onat,U_2066))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2067),U_2066)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2066),U_2067) ),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_less__natfloor]) ).
fof(f_658_2,plain,
! [U_2069,U_2068] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_2068),U_2069)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2068,c_RealDef_Oreal(tc_Nat_Onat,U_2069))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2068) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
! [U_2068,U_2069] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_2068),U_2069)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2068,c_RealDef_Oreal(tc_Nat_Onat,U_2069))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2068) ),
inference(definitional_conversion,[status(esa)],[f_658_2]) ).
cnf(f_658_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_2068),U_2069)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2068,c_RealDef_Oreal(tc_Nat_Onat,U_2069))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2068) ),
inference(clausify,[status(thm)],[f_658_3]) ).
fof(f_659_1,plain,
! [V_a,V_x] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__add]) ).
fof(f_659_2,plain,
! [U_2071,U_2070] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2070,c_RealDef_Oreal(tc_Nat_Onat,U_2071))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2070),U_2071)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2070) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
! [U_2071,U_2070] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2070,c_RealDef_Oreal(tc_Nat_Onat,U_2071))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2070),U_2071)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2070) ),
inference(definitional_conversion,[status(esa)],[f_659_2]) ).
cnf(f_659_4,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2070,c_RealDef_Oreal(tc_Nat_Onat,U_2071))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2070),U_2071)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2070) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_1,plain,
! [V_n,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt]) ).
fof(f_660_2,plain,
! [U_2073,U_2072] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2072,c_RealDef_Oreal(tc_Nat_Onat,U_2073))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2072),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2073) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
! [U_2073,U_2072] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2072,c_RealDef_Oreal(tc_Nat_Onat,U_2073))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2072),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2073) ),
inference(definitional_conversion,[status(esa)],[f_660_2]) ).
cnf(f_660_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2072,c_RealDef_Oreal(tc_Nat_Onat,U_2073))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2072),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2073) ),
inference(clausify,[status(thm)],[f_660_3]) ).
fof(f_661_1,plain,
! [V_x,V_n] :
( c_RComplete_Onatfloor(V_x) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__eq]) ).
fof(f_661_2,plain,
! [U_2075,U_2074] :
( c_RComplete_Onatfloor(U_2075) = U_2074
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2075,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2074),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2074),U_2075) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
! [U_2074,U_2075] :
( c_RComplete_Onatfloor(U_2075) = U_2074
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2075,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2074),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2074),U_2075) ),
inference(definitional_conversion,[status(esa)],[f_661_2]) ).
cnf(f_661_4,plain,
( c_RComplete_Onatfloor(U_2075) = U_2074
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2075,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2074),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2074),U_2075) ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [V_a,V_x] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__add]) ).
fof(f_662_2,plain,
! [U_2077,U_2076] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2076,c_RealDef_Oreal(tc_Nat_Onat,U_2077))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2076),U_2077)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2076) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_2076,U_2077] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2076,c_RealDef_Oreal(tc_Nat_Onat,U_2077))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2076),U_2077)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2076) ),
inference(definitional_conversion,[status(esa)],[f_662_2]) ).
cnf(f_662_4,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2076,c_RealDef_Oreal(tc_Nat_Onat,U_2077))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2076),U_2077)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2076) ),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_1,plain,
! [V_r] :
( ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) ),
inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6]) ).
fof(f_663_2,plain,
! [U_2079] :
( ? [U_2078] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2079,c_RealDef_Oreal(tc_Nat_Onat,U_2078))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2078,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2079) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2079) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
! [U_2079] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2079,c_RealDef_Oreal(tc_Nat_Onat,sK21(U_2079)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK21(U_2079),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2079) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2079) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_2078,sK21(U_2079))],[f_663_2]) ).
fof(f_663_4,plain,
( ! [U_2079] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2079,c_RealDef_Oreal(tc_Nat_Onat,sK21(U_2079)))
| ~ sP209(U_2079) )
& ! [U_2079] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK21(U_2079),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2079)
| ~ sP209(U_2079) )
& ! [U_2079] :
( sP209(U_2079)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2079) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_663_3]) ).
cnf(f_663_5,plain,
( sP209(U_2079)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2079) ),
inference(clausify,[status(thm)],[f_663_4]) ).
cnf(f_663_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK21(U_2079),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2079)
| ~ sP209(U_2079) ),
inference(clausify,[status(thm)],[f_663_4]) ).
cnf(f_663_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2079,c_RealDef_Oreal(tc_Nat_Onat,sK21(U_2079)))
| ~ sP209(U_2079) ),
inference(clausify,[status(thm)],[f_663_4]) ).
fof(f_664_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).
fof(f_664_2,plain,
! [U_2082,U_2081,U_2080] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2080,c_Groups_Ouminus__class_Ouminus(U_2080,U_2081),c_Groups_Ouminus__class_Ouminus(U_2080,U_2082))
| ~ c_Orderings_Oord__class_Oless__eq(U_2080,U_2082,U_2081) )
& ( c_Orderings_Oord__class_Oless__eq(U_2080,U_2082,U_2081)
| ~ c_Orderings_Oord__class_Oless__eq(U_2080,c_Groups_Ouminus__class_Ouminus(U_2080,U_2081),c_Groups_Ouminus__class_Ouminus(U_2080,U_2082)) ) )
| ~ class_Lattices_Oboolean__algebra(U_2080) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
( ! [U_2080,U_2081,U_2082] :
( c_Orderings_Oord__class_Oless__eq(U_2080,c_Groups_Ouminus__class_Ouminus(U_2080,U_2081),c_Groups_Ouminus__class_Ouminus(U_2080,U_2082))
| ~ c_Orderings_Oord__class_Oless__eq(U_2080,U_2082,U_2081)
| ~ sP210(U_2080,U_2081,U_2082) )
& ! [U_2080,U_2081,U_2082] :
( c_Orderings_Oord__class_Oless__eq(U_2080,U_2082,U_2081)
| ~ c_Orderings_Oord__class_Oless__eq(U_2080,c_Groups_Ouminus__class_Ouminus(U_2080,U_2081),c_Groups_Ouminus__class_Ouminus(U_2080,U_2082))
| ~ sP210(U_2080,U_2081,U_2082) )
& ! [U_2080,U_2081,U_2082] :
( sP210(U_2080,U_2081,U_2082)
| ~ class_Lattices_Oboolean__algebra(U_2080) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_664_2]) ).
cnf(f_664_4,plain,
( sP210(U_2080,U_2081,U_2082)
| ~ class_Lattices_Oboolean__algebra(U_2080) ),
inference(clausify,[status(thm)],[f_664_3]) ).
cnf(f_664_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2080,U_2082,U_2081)
| ~ c_Orderings_Oord__class_Oless__eq(U_2080,c_Groups_Ouminus__class_Ouminus(U_2080,U_2081),c_Groups_Ouminus__class_Ouminus(U_2080,U_2082))
| ~ sP210(U_2080,U_2081,U_2082) ),
inference(clausify,[status(thm)],[f_664_3]) ).
cnf(f_664_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2080,c_Groups_Ouminus__class_Ouminus(U_2080,U_2081),c_Groups_Ouminus__class_Ouminus(U_2080,U_2082))
| ~ c_Orderings_Oord__class_Oless__eq(U_2080,U_2082,U_2081)
| ~ sP210(U_2080,U_2081,U_2082) ),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x))
| ~ 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_665_2,plain,
! [U_2085,U_2084,U_2083] :
( c_Orderings_Oord__class_Oless__eq(U_2083,c_Groups_Ouminus__class_Ouminus(U_2083,U_2085),c_Groups_Ouminus__class_Ouminus(U_2083,U_2084))
| ~ c_Orderings_Oord__class_Oless__eq(U_2083,U_2084,U_2085)
| ~ class_Lattices_Oboolean__algebra(U_2083) ),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
! [U_2084,U_2085,U_2083] :
( c_Orderings_Oord__class_Oless__eq(U_2083,c_Groups_Ouminus__class_Ouminus(U_2083,U_2085),c_Groups_Ouminus__class_Ouminus(U_2083,U_2084))
| ~ c_Orderings_Oord__class_Oless__eq(U_2083,U_2084,U_2085)
| ~ class_Lattices_Oboolean__algebra(U_2083) ),
inference(definitional_conversion,[status(esa)],[f_665_2]) ).
cnf(f_665_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2083,c_Groups_Ouminus__class_Ouminus(U_2083,U_2085),c_Groups_Ouminus__class_Ouminus(U_2083,U_2084))
| ~ c_Orderings_Oord__class_Oless__eq(U_2083,U_2084,U_2085)
| ~ class_Lattices_Oboolean__algebra(U_2083) ),
inference(clausify,[status(thm)],[f_665_3]) ).
fof(f_666_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_666_2,plain,
! [U_2087,U_2086] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2086),U_2087),U_2087) = U_2087
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2086) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
! [U_2086,U_2087] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2086),U_2087),U_2087) = U_2087
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2086) ),
inference(definitional_conversion,[status(esa)],[f_666_2]) ).
cnf(f_666_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2086),U_2087),U_2087) = U_2087
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2086) ),
inference(clausify,[status(thm)],[f_666_3]) ).
fof(f_667_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_667_2,plain,
! [U_2089,U_2088] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2088),U_2089),U_2089) = U_2089
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2088) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
! [U_2088,U_2089] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2088),U_2089),U_2089) = U_2089
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2088) ),
inference(definitional_conversion,[status(esa)],[f_667_2]) ).
cnf(f_667_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2088),U_2089),U_2089) = U_2089
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2088) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_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_668_2,plain,
! [U_2092,U_2091,U_2090] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2090) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
! [U_2090,U_2091,U_2092] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2090) ),
inference(definitional_conversion,[status(esa)],[f_668_2]) ).
cnf(f_668_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2090),U_2091),U_2092)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2090) ),
inference(clausify,[status(thm)],[f_668_3]) ).
fof(f_669_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).
fof(f_669_2,plain,
! [U_2097,U_2096,U_2095,U_2094,U_2093] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2094,U_2093),U_2095,U_2096),U_2097) = c_Groups_Ominus__class_Ominus(U_2093,hAPP(U_2095,U_2097),hAPP(U_2096,U_2097))
| ~ class_Groups_Ominus(U_2093) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
! [U_2093,U_2094,U_2095,U_2096,U_2097] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2094,U_2093),U_2095,U_2096),U_2097) = c_Groups_Ominus__class_Ominus(U_2093,hAPP(U_2095,U_2097),hAPP(U_2096,U_2097))
| ~ class_Groups_Ominus(U_2093) ),
inference(definitional_conversion,[status(esa)],[f_669_2]) ).
cnf(f_669_4,plain,
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2094,U_2093),U_2095,U_2096),U_2097) = c_Groups_Ominus__class_Ominus(U_2093,hAPP(U_2095,U_2097),hAPP(U_2096,U_2097))
| ~ class_Groups_Ominus(U_2093) ),
inference(clausify,[status(thm)],[f_669_3]) ).
fof(f_670_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).
fof(f_670_2,plain,
! [U_2100,U_2099,U_2098] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_2098,U_2099) = c_Groups_Ouminus__class_Ouminus(U_2098,U_2100)
| U_2099 != U_2100 )
& ( U_2099 = U_2100
| c_Groups_Ouminus__class_Ouminus(U_2098,U_2099) != c_Groups_Ouminus__class_Ouminus(U_2098,U_2100) ) )
| ~ class_Lattices_Oboolean__algebra(U_2098) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
fof(f_670_3,plain,
( ! [U_2099,U_2098,U_2100] :
( c_Groups_Ouminus__class_Ouminus(U_2098,U_2099) = c_Groups_Ouminus__class_Ouminus(U_2098,U_2100)
| U_2099 != U_2100
| ~ sP211(U_2099,U_2098,U_2100) )
& ! [U_2099,U_2098,U_2100] :
( U_2099 = U_2100
| c_Groups_Ouminus__class_Ouminus(U_2098,U_2099) != c_Groups_Ouminus__class_Ouminus(U_2098,U_2100)
| ~ sP211(U_2099,U_2098,U_2100) )
& ! [U_2099,U_2098,U_2100] :
( sP211(U_2099,U_2098,U_2100)
| ~ class_Lattices_Oboolean__algebra(U_2098) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_670_2]) ).
cnf(f_670_4,plain,
( sP211(U_2099,U_2098,U_2100)
| ~ class_Lattices_Oboolean__algebra(U_2098) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_5,plain,
( U_2099 = U_2100
| c_Groups_Ouminus__class_Ouminus(U_2098,U_2099) != c_Groups_Ouminus__class_Ouminus(U_2098,U_2100)
| ~ sP211(U_2099,U_2098,U_2100) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_2098,U_2099) = c_Groups_Ouminus__class_Ouminus(U_2098,U_2100)
| U_2099 != U_2100
| ~ sP211(U_2099,U_2098,U_2100) ),
inference(clausify,[status(thm)],[f_670_3]) ).
fof(f_671_1,plain,
! [V_x_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).
fof(f_671_2,plain,
! [U_2104,U_2103,U_2102,U_2101] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2102,U_2101),U_2103),U_2104) = c_Groups_Ouminus__class_Ouminus(U_2101,hAPP(U_2103,U_2104))
| ~ class_Groups_Ouminus(U_2101) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
fof(f_671_3,plain,
! [U_2102,U_2103,U_2104,U_2101] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2102,U_2101),U_2103),U_2104) = c_Groups_Ouminus__class_Ouminus(U_2101,hAPP(U_2103,U_2104))
| ~ class_Groups_Ouminus(U_2101) ),
inference(definitional_conversion,[status(esa)],[f_671_2]) ).
cnf(f_671_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2102,U_2101),U_2103),U_2104) = c_Groups_Ouminus__class_Ouminus(U_2101,hAPP(U_2103,U_2104))
| ~ class_Groups_Ouminus(U_2101) ),
inference(clausify,[status(thm)],[f_671_3]) ).
fof(f_672_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,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_672_2,plain,
! [U_2106,U_2105] :
( c_Groups_Ouminus__class_Ouminus(U_2105,c_Groups_Ouminus__class_Ouminus(U_2105,U_2106)) = U_2106
| ~ class_Lattices_Oboolean__algebra(U_2105) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
! [U_2105,U_2106] :
( c_Groups_Ouminus__class_Ouminus(U_2105,c_Groups_Ouminus__class_Ouminus(U_2105,U_2106)) = U_2106
| ~ class_Lattices_Oboolean__algebra(U_2105) ),
inference(definitional_conversion,[status(esa)],[f_672_2]) ).
cnf(f_672_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_2105,c_Groups_Ouminus__class_Ouminus(U_2105,U_2106)) = U_2106
| ~ class_Lattices_Oboolean__algebra(U_2105) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_1,plain,
! [V_b,V_x,V_a] :
( ? [B_d] :
( ! [B_y] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y,V_b)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a,B_y) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x) ),
inference(fof_nnf,[status(thm)],[fact_lemma__interval]) ).
fof(f_673_2,plain,
! [U_2111,U_2110,U_2109] :
( ? [U_2108] :
( ! [U_2107] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2107,U_2111)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2109,U_2107) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2110,U_2107)),U_2108) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2108) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2109,U_2110) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
! [U_2111,U_2110,U_2109] :
( ( ! [U_2107] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2107,U_2111)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2109,U_2107) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2110,U_2107)),sK22(U_2111,U_2110,U_2109)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_2111,U_2110,U_2109)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2109,U_2110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_2108,sK22(U_2111,U_2110,U_2109))],[f_673_2]) ).
fof(f_673_4,plain,
( ! [U_2107,U_2109,U_2111] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2107,U_2111)
| ~ sP212(U_2107,U_2109,U_2111) )
& ! [U_2107,U_2109,U_2111] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2109,U_2107)
| ~ sP212(U_2107,U_2109,U_2111) )
& ! [U_2107,U_2109,U_2110,U_2111] :
( sP212(U_2107,U_2109,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2110,U_2107)),sK22(U_2111,U_2110,U_2109))
| ~ sP213(U_2107,U_2109,U_2110,U_2111) )
& ! [U_2107,U_2109,U_2110,U_2111] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_2111,U_2110,U_2109))
| ~ sP213(U_2107,U_2109,U_2110,U_2111) )
& ! [U_2107,U_2109,U_2110,U_2111] :
( sP213(U_2107,U_2109,U_2110,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2109,U_2110) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212,sP213])],[f_673_3]) ).
cnf(f_673_5,plain,
( sP213(U_2107,U_2109,U_2110,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2109,U_2110) ),
inference(clausify,[status(thm)],[f_673_4]) ).
cnf(f_673_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_2111,U_2110,U_2109))
| ~ sP213(U_2107,U_2109,U_2110,U_2111) ),
inference(clausify,[status(thm)],[f_673_4]) ).
cnf(f_673_7,plain,
( sP212(U_2107,U_2109,U_2111)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2110,U_2107)),sK22(U_2111,U_2110,U_2109))
| ~ sP213(U_2107,U_2109,U_2110,U_2111) ),
inference(clausify,[status(thm)],[f_673_4]) ).
cnf(f_673_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2109,U_2107)
| ~ sP212(U_2107,U_2109,U_2111) ),
inference(clausify,[status(thm)],[f_673_4]) ).
cnf(f_673_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2107,U_2111)
| ~ sP212(U_2107,U_2109,U_2111) ),
inference(clausify,[status(thm)],[f_673_4]) ).
fof(f_674_1,plain,
! [V_n_2,V_P_2] :
( ? [B_k] :
( hBOOL(hAPP(V_P_2,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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) )
| ~ hBOOL(hAPP(V_P_2,V_n_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_674_2,plain,
! [U_2115,U_2114] :
( ? [U_2113] :
( hBOOL(hAPP(U_2114,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2113,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_2112] :
( ~ hBOOL(hAPP(U_2114,U_2112))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2112,U_2113) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2113,U_2115) )
| ~ hBOOL(hAPP(U_2114,U_2115))
| hBOOL(hAPP(U_2114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
fof(f_674_3,plain,
! [U_2115,U_2114] :
( ( hBOOL(hAPP(U_2114,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK23(U_2115,U_2114),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_2112] :
( ~ hBOOL(hAPP(U_2114,U_2112))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2112,sK23(U_2115,U_2114)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23(U_2115,U_2114),U_2115) )
| ~ hBOOL(hAPP(U_2114,U_2115))
| hBOOL(hAPP(U_2114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_2113,sK23(U_2115,U_2114))],[f_674_2]) ).
fof(f_674_4,plain,
( ! [U_2112,U_2115,U_2114] :
( hBOOL(hAPP(U_2114,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK23(U_2115,U_2114),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP214(U_2112,U_2115,U_2114) )
& ! [U_2112,U_2115,U_2114] :
( ~ hBOOL(hAPP(U_2114,U_2112))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2112,sK23(U_2115,U_2114))
| ~ sP214(U_2112,U_2115,U_2114) )
& ! [U_2112,U_2115,U_2114] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23(U_2115,U_2114),U_2115)
| ~ sP214(U_2112,U_2115,U_2114) )
& ! [U_2112,U_2115,U_2114] :
( sP214(U_2112,U_2115,U_2114)
| ~ hBOOL(hAPP(U_2114,U_2115))
| hBOOL(hAPP(U_2114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_674_3]) ).
cnf(f_674_5,plain,
( sP214(U_2112,U_2115,U_2114)
| ~ hBOOL(hAPP(U_2114,U_2115))
| hBOOL(hAPP(U_2114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_674_4]) ).
cnf(f_674_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23(U_2115,U_2114),U_2115)
| ~ sP214(U_2112,U_2115,U_2114) ),
inference(clausify,[status(thm)],[f_674_4]) ).
cnf(f_674_7,plain,
( ~ hBOOL(hAPP(U_2114,U_2112))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2112,sK23(U_2115,U_2114))
| ~ sP214(U_2112,U_2115,U_2114) ),
inference(clausify,[status(thm)],[f_674_4]) ).
cnf(f_674_8,plain,
( hBOOL(hAPP(U_2114,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK23(U_2115,U_2114),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP214(U_2112,U_2115,U_2114) ),
inference(clausify,[status(thm)],[f_674_4]) ).
fof(f_675_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
| ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) )
& ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__poly__def]) ).
fof(f_675_2,plain,
! [U_2118,U_2117,U_2116] :
( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2116),U_2117,U_2118)
| ~ c_Polynomial_Opos__poly(U_2116,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2116),U_2118,U_2117)) )
& ( c_Polynomial_Opos__poly(U_2116,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2116),U_2118,U_2117))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2116),U_2117,U_2118) ) )
| ~ class_Rings_Olinordered__idom(U_2116) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
fof(f_675_3,plain,
( ! [U_2117,U_2116,U_2118] :
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2116),U_2117,U_2118)
| ~ c_Polynomial_Opos__poly(U_2116,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2116),U_2118,U_2117))
| ~ sP215(U_2117,U_2116,U_2118) )
& ! [U_2117,U_2116,U_2118] :
( c_Polynomial_Opos__poly(U_2116,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2116),U_2118,U_2117))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2116),U_2117,U_2118)
| ~ sP215(U_2117,U_2116,U_2118) )
& ! [U_2117,U_2116,U_2118] :
( sP215(U_2117,U_2116,U_2118)
| ~ class_Rings_Olinordered__idom(U_2116) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_675_2]) ).
cnf(f_675_4,plain,
( sP215(U_2117,U_2116,U_2118)
| ~ class_Rings_Olinordered__idom(U_2116) ),
inference(clausify,[status(thm)],[f_675_3]) ).
cnf(f_675_5,plain,
( c_Polynomial_Opos__poly(U_2116,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2116),U_2118,U_2117))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2116),U_2117,U_2118)
| ~ sP215(U_2117,U_2116,U_2118) ),
inference(clausify,[status(thm)],[f_675_3]) ).
cnf(f_675_6,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2116),U_2117,U_2118)
| ~ c_Polynomial_Opos__poly(U_2116,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2116),U_2118,U_2117))
| ~ sP215(U_2117,U_2116,U_2118) ),
inference(clausify,[status(thm)],[f_675_3]) ).
fof(f_676_1,plain,
! [T_a] :
( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__pos__poly__0]) ).
fof(f_676_2,plain,
! [U_2119] :
( ~ c_Polynomial_Opos__poly(U_2119,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2119)))
| ~ class_Rings_Olinordered__idom(U_2119) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
fof(f_676_3,plain,
! [U_2119] :
( ~ c_Polynomial_Opos__poly(U_2119,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2119)))
| ~ class_Rings_Olinordered__idom(U_2119) ),
inference(definitional_conversion,[status(esa)],[f_676_2]) ).
cnf(f_676_4,plain,
( ~ c_Polynomial_Opos__poly(U_2119,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2119)))
| ~ class_Rings_Olinordered__idom(U_2119) ),
inference(clausify,[status(thm)],[f_676_3]) ).
fof(f_677_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))
| ~ c_Polynomial_Opos__poly(T_a,V_q)
| ~ c_Polynomial_Opos__poly(T_a,V_p)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__add]) ).
fof(f_677_2,plain,
! [U_2122,U_2121,U_2120] :
( c_Polynomial_Opos__poly(U_2120,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2120),U_2121,U_2122))
| ~ c_Polynomial_Opos__poly(U_2120,U_2122)
| ~ c_Polynomial_Opos__poly(U_2120,U_2121)
| ~ class_Rings_Olinordered__idom(U_2120) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
fof(f_677_3,plain,
! [U_2122,U_2120,U_2121] :
( c_Polynomial_Opos__poly(U_2120,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2120),U_2121,U_2122))
| ~ c_Polynomial_Opos__poly(U_2120,U_2122)
| ~ c_Polynomial_Opos__poly(U_2120,U_2121)
| ~ class_Rings_Olinordered__idom(U_2120) ),
inference(definitional_conversion,[status(esa)],[f_677_2]) ).
cnf(f_677_4,plain,
( c_Polynomial_Opos__poly(U_2120,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2120),U_2121,U_2122))
| ~ c_Polynomial_Opos__poly(U_2120,U_2122)
| ~ c_Polynomial_Opos__poly(U_2120,U_2121)
| ~ class_Rings_Olinordered__idom(U_2120) ),
inference(clausify,[status(thm)],[f_677_3]) ).
fof(f_678_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))
| ~ c_Polynomial_Opos__poly(T_a,V_q)
| ~ c_Polynomial_Opos__poly(T_a,V_p)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__mult]) ).
fof(f_678_2,plain,
! [U_2125,U_2124,U_2123] :
( c_Polynomial_Opos__poly(U_2123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2123)),U_2124),U_2125))
| ~ c_Polynomial_Opos__poly(U_2123,U_2125)
| ~ c_Polynomial_Opos__poly(U_2123,U_2124)
| ~ class_Rings_Olinordered__idom(U_2123) ),
inference(variable_rename,[status(thm)],[f_678_1]) ).
fof(f_678_3,plain,
! [U_2123,U_2125,U_2124] :
( c_Polynomial_Opos__poly(U_2123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2123)),U_2124),U_2125))
| ~ c_Polynomial_Opos__poly(U_2123,U_2125)
| ~ c_Polynomial_Opos__poly(U_2123,U_2124)
| ~ class_Rings_Olinordered__idom(U_2123) ),
inference(definitional_conversion,[status(esa)],[f_678_2]) ).
cnf(f_678_4,plain,
( c_Polynomial_Opos__poly(U_2123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2123)),U_2124),U_2125))
| ~ c_Polynomial_Opos__poly(U_2123,U_2125)
| ~ c_Polynomial_Opos__poly(U_2123,U_2124)
| ~ class_Rings_Olinordered__idom(U_2123) ),
inference(clausify,[status(thm)],[f_678_3]) ).
fof(f_679_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
| ( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
& V_x_2 != V_y_2 ) )
& ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def]) ).
fof(f_679_2,plain,
! [U_2128,U_2127,U_2126] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2126),U_2127,U_2128)
| ( ~ c_Polynomial_Opos__poly(U_2126,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2126),U_2128,U_2127))
& U_2127 != U_2128 ) )
& ( c_Polynomial_Opos__poly(U_2126,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2126),U_2128,U_2127))
| U_2127 = U_2128
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2126),U_2127,U_2128) ) )
| ~ class_Rings_Olinordered__idom(U_2126) ),
inference(variable_rename,[status(thm)],[f_679_1]) ).
fof(f_679_3,plain,
( ! [U_2127,U_2126,U_2128] :
( ~ c_Polynomial_Opos__poly(U_2126,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2126),U_2128,U_2127))
| ~ sP216(U_2127,U_2126,U_2128) )
& ! [U_2127,U_2126,U_2128] :
( U_2127 != U_2128
| ~ sP216(U_2127,U_2126,U_2128) )
& ! [U_2127,U_2126,U_2128] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2126),U_2127,U_2128)
| sP216(U_2127,U_2126,U_2128)
| ~ sP217(U_2127,U_2126,U_2128) )
& ! [U_2127,U_2126,U_2128] :
( c_Polynomial_Opos__poly(U_2126,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2126),U_2128,U_2127))
| U_2127 = U_2128
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2126),U_2127,U_2128)
| ~ sP217(U_2127,U_2126,U_2128) )
& ! [U_2127,U_2126,U_2128] :
( sP217(U_2127,U_2126,U_2128)
| ~ class_Rings_Olinordered__idom(U_2126) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216,sP217])],[f_679_2]) ).
cnf(f_679_4,plain,
( sP217(U_2127,U_2126,U_2128)
| ~ class_Rings_Olinordered__idom(U_2126) ),
inference(clausify,[status(thm)],[f_679_3]) ).
cnf(f_679_5,plain,
( c_Polynomial_Opos__poly(U_2126,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2126),U_2128,U_2127))
| U_2127 = U_2128
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2126),U_2127,U_2128)
| ~ sP217(U_2127,U_2126,U_2128) ),
inference(clausify,[status(thm)],[f_679_3]) ).
cnf(f_679_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2126),U_2127,U_2128)
| sP216(U_2127,U_2126,U_2128)
| ~ sP217(U_2127,U_2126,U_2128) ),
inference(clausify,[status(thm)],[f_679_3]) ).
cnf(f_679_7,plain,
( U_2127 != U_2128
| ~ sP216(U_2127,U_2126,U_2128) ),
inference(clausify,[status(thm)],[f_679_3]) ).
cnf(f_679_8,plain,
( ~ c_Polynomial_Opos__poly(U_2126,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2126),U_2128,U_2127))
| ~ sP216(U_2127,U_2126,U_2128) ),
inference(clausify,[status(thm)],[f_679_3]) ).
fof(f_680_1,plain,
! [V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| c_Polynomial_Opos__poly(T_a,V_p)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__total]) ).
fof(f_680_2,plain,
! [U_2130,U_2129] :
( c_Polynomial_Opos__poly(U_2129,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2129),U_2130))
| c_Polynomial_Opos__poly(U_2129,U_2130)
| U_2130 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2129))
| ~ class_Rings_Olinordered__idom(U_2129) ),
inference(variable_rename,[status(thm)],[f_680_1]) ).
fof(f_680_3,plain,
! [U_2129,U_2130] :
( c_Polynomial_Opos__poly(U_2129,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2129),U_2130))
| c_Polynomial_Opos__poly(U_2129,U_2130)
| U_2130 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2129))
| ~ class_Rings_Olinordered__idom(U_2129) ),
inference(definitional_conversion,[status(esa)],[f_680_2]) ).
cnf(f_680_4,plain,
( c_Polynomial_Opos__poly(U_2129,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2129),U_2130))
| c_Polynomial_Opos__poly(U_2129,U_2130)
| U_2130 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2129))
| ~ class_Rings_Olinordered__idom(U_2129) ),
inference(clausify,[status(thm)],[f_680_3]) ).
fof(f_681_1,plain,
! [V_b,V_x,V_a] :
( ? [B_d] :
( ! [B_y] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,V_b)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,B_y) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,B_y)),B_d) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,V_x) ),
inference(fof_nnf,[status(thm)],[fact_lemma__interval__lt]) ).
fof(f_681_2,plain,
! [U_2135,U_2134,U_2133] :
( ? [U_2132] :
( ! [U_2131] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2131,U_2135)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2131) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2134,U_2131)),U_2132) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2132) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2134,U_2135)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2134) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
! [U_2135,U_2134,U_2133] :
( ( ! [U_2131] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2131,U_2135)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2131) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2134,U_2131)),sK24(U_2135,U_2134,U_2133)) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_2135,U_2134,U_2133)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2134,U_2135)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2134) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_2132,sK24(U_2135,U_2134,U_2133))],[f_681_2]) ).
fof(f_681_4,plain,
( ! [U_2135,U_2131,U_2133] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2131,U_2135)
| ~ sP218(U_2135,U_2131,U_2133) )
& ! [U_2135,U_2131,U_2133] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2131)
| ~ sP218(U_2135,U_2131,U_2133) )
& ! [U_2135,U_2131,U_2133,U_2134] :
( sP218(U_2135,U_2131,U_2133)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2134,U_2131)),sK24(U_2135,U_2134,U_2133))
| ~ sP219(U_2135,U_2131,U_2133,U_2134) )
& ! [U_2135,U_2131,U_2133,U_2134] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_2135,U_2134,U_2133))
| ~ sP219(U_2135,U_2131,U_2133,U_2134) )
& ! [U_2135,U_2131,U_2133,U_2134] :
( sP219(U_2135,U_2131,U_2133,U_2134)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2134,U_2135)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2134) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218,sP219])],[f_681_3]) ).
cnf(f_681_5,plain,
( sP219(U_2135,U_2131,U_2133,U_2134)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2134,U_2135)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2134) ),
inference(clausify,[status(thm)],[f_681_4]) ).
cnf(f_681_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_2135,U_2134,U_2133))
| ~ sP219(U_2135,U_2131,U_2133,U_2134) ),
inference(clausify,[status(thm)],[f_681_4]) ).
cnf(f_681_7,plain,
( sP218(U_2135,U_2131,U_2133)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2134,U_2131)),sK24(U_2135,U_2134,U_2133))
| ~ sP219(U_2135,U_2131,U_2133,U_2134) ),
inference(clausify,[status(thm)],[f_681_4]) ).
cnf(f_681_8,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2133,U_2131)
| ~ sP218(U_2135,U_2131,U_2133) ),
inference(clausify,[status(thm)],[f_681_4]) ).
cnf(f_681_9,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2131,U_2135)
| ~ sP218(U_2135,U_2131,U_2133) ),
inference(clausify,[status(thm)],[f_681_4]) ).
fof(f_682_1,plain,
! [V_X_2,V_M_2,T_a,T_b] :
( ! [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) )
| ? [B_n] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) )
| ~ class_Orderings_Oord(T_a)
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemmaCauchy]) ).
fof(f_682_2,plain,
! [U_2141,U_2140,U_2139,U_2138] :
( ! [U_2137] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2137)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2140))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,U_2137) )
| ? [U_2136] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,c_Groups_Ominus__class_Ominus(U_2138,hAPP(U_2141,U_2140),hAPP(U_2141,U_2136))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,U_2136) )
| ~ class_Orderings_Oord(U_2139)
| ~ class_RealVector_Oreal__normed__vector(U_2138) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
fof(f_682_3,plain,
! [U_2141,U_2140,U_2139,U_2138] :
( ! [U_2137] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2137)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2140))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,U_2137) )
| ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,c_Groups_Ominus__class_Ominus(U_2138,hAPP(U_2141,U_2140),hAPP(U_2141,sK25(U_2141,U_2140,U_2139,U_2138)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,sK25(U_2141,U_2140,U_2139,U_2138)) )
| ~ class_Orderings_Oord(U_2139)
| ~ class_RealVector_Oreal__normed__vector(U_2138) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_2136,sK25(U_2141,U_2140,U_2139,U_2138))],[f_682_2]) ).
fof(f_682_4,plain,
( ! [U_2138,U_2139,U_2140,U_2141] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,c_Groups_Ominus__class_Ominus(U_2138,hAPP(U_2141,U_2140),hAPP(U_2141,sK25(U_2141,U_2140,U_2139,U_2138)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ sP220(U_2138,U_2139,U_2140,U_2141) )
& ! [U_2138,U_2139,U_2140,U_2141] :
( c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,sK25(U_2141,U_2140,U_2139,U_2138))
| ~ sP220(U_2138,U_2139,U_2140,U_2141) )
& ! [U_2138,U_2137,U_2139,U_2140,U_2141] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2137)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2140))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,U_2137)
| sP220(U_2138,U_2139,U_2140,U_2141)
| ~ class_Orderings_Oord(U_2139)
| ~ class_RealVector_Oreal__normed__vector(U_2138) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_682_3]) ).
cnf(f_682_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2137)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2138,hAPP(U_2141,U_2140))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,U_2137)
| sP220(U_2138,U_2139,U_2140,U_2141)
| ~ class_Orderings_Oord(U_2139)
| ~ class_RealVector_Oreal__normed__vector(U_2138) ),
inference(clausify,[status(thm)],[f_682_4]) ).
cnf(f_682_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2139,U_2140,sK25(U_2141,U_2140,U_2139,U_2138))
| ~ sP220(U_2138,U_2139,U_2140,U_2141) ),
inference(clausify,[status(thm)],[f_682_4]) ).
cnf(f_682_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2138,c_Groups_Ominus__class_Ominus(U_2138,hAPP(U_2141,U_2140),hAPP(U_2141,sK25(U_2141,U_2140,U_2139,U_2138)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ sP220(U_2138,U_2139,U_2140,U_2141) ),
inference(clausify,[status(thm)],[f_682_4]) ).
fof(f_683_1,plain,
! [V_x] :
( ! [B_y] :
? [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_reals__Archimedean3]) ).
fof(f_683_2,plain,
! [U_2144] :
( ! [U_2143] :
? [U_2142] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2143,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2142)),U_2144))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2144) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
fof(f_683_3,plain,
! [U_2144] :
( ! [U_2143] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2143,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK26(U_2144,U_2143))),U_2144))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2144) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_2142,sK26(U_2144,U_2143))],[f_683_2]) ).
fof(f_683_4,plain,
! [U_2144,U_2143] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2143,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK26(U_2144,U_2143))),U_2144))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2144) ),
inference(definitional_conversion,[status(esa)],[f_683_3]) ).
cnf(f_683_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2143,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK26(U_2144,U_2143))),U_2144))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2144) ),
inference(clausify,[status(thm)],[f_683_4]) ).
fof(f_684_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Odecseq(T_a,V_X_2)
| ? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) )
& ( ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
| ~ c_SEQ_Odecseq(T_a,V_X_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_decseq__def]) ).
fof(f_684_2,plain,
! [U_2150,U_2149] :
( ( ( c_SEQ_Odecseq(U_2149,U_2150)
| ? [U_2148,U_2147] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,U_2147),hAPP(U_2150,U_2148))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2148,U_2147) ) )
& ( ! [U_2146,U_2145] :
( c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,U_2145),hAPP(U_2150,U_2146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2146,U_2145) )
| ~ c_SEQ_Odecseq(U_2149,U_2150) ) )
| ~ class_Orderings_Oorder(U_2149) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
fof(f_684_3,plain,
! [U_2150,U_2149] :
( ( ( c_SEQ_Odecseq(U_2149,U_2150)
| ? [U_2147] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,U_2147),hAPP(U_2150,sK27(U_2150,U_2149)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(U_2150,U_2149),U_2147) ) )
& ( ! [U_2146,U_2145] :
( c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,U_2145),hAPP(U_2150,U_2146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2146,U_2145) )
| ~ c_SEQ_Odecseq(U_2149,U_2150) ) )
| ~ class_Orderings_Oorder(U_2149) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_2148,sK27(U_2150,U_2149))],[f_684_2]) ).
fof(f_684_4,plain,
! [U_2150,U_2149] :
( ( ( c_SEQ_Odecseq(U_2149,U_2150)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,sK28(U_2150,U_2149)),hAPP(U_2150,sK27(U_2150,U_2149)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(U_2150,U_2149),sK28(U_2150,U_2149)) ) )
& ( ! [U_2146,U_2145] :
( c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,U_2145),hAPP(U_2150,U_2146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2146,U_2145) )
| ~ c_SEQ_Odecseq(U_2149,U_2150) ) )
| ~ class_Orderings_Oorder(U_2149) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_2147,sK28(U_2150,U_2149))],[f_684_3]) ).
fof(f_684_5,plain,
( ! [U_2149,U_2150] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,sK28(U_2150,U_2149)),hAPP(U_2150,sK27(U_2150,U_2149)))
| ~ sP221(U_2149,U_2150) )
& ! [U_2149,U_2150] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(U_2150,U_2149),sK28(U_2150,U_2149))
| ~ sP221(U_2149,U_2150) )
& ! [U_2146,U_2145,U_2149,U_2150] :
( c_SEQ_Odecseq(U_2149,U_2150)
| sP221(U_2149,U_2150)
| ~ sP222(U_2146,U_2145,U_2149,U_2150) )
& ! [U_2146,U_2145,U_2149,U_2150] :
( c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,U_2145),hAPP(U_2150,U_2146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2146,U_2145)
| ~ c_SEQ_Odecseq(U_2149,U_2150)
| ~ sP222(U_2146,U_2145,U_2149,U_2150) )
& ! [U_2146,U_2145,U_2149,U_2150] :
( sP222(U_2146,U_2145,U_2149,U_2150)
| ~ class_Orderings_Oorder(U_2149) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221,sP222])],[f_684_4]) ).
cnf(f_684_6,plain,
( sP222(U_2146,U_2145,U_2149,U_2150)
| ~ class_Orderings_Oorder(U_2149) ),
inference(clausify,[status(thm)],[f_684_5]) ).
cnf(f_684_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,U_2145),hAPP(U_2150,U_2146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2146,U_2145)
| ~ c_SEQ_Odecseq(U_2149,U_2150)
| ~ sP222(U_2146,U_2145,U_2149,U_2150) ),
inference(clausify,[status(thm)],[f_684_5]) ).
cnf(f_684_8,plain,
( c_SEQ_Odecseq(U_2149,U_2150)
| sP221(U_2149,U_2150)
| ~ sP222(U_2146,U_2145,U_2149,U_2150) ),
inference(clausify,[status(thm)],[f_684_5]) ).
cnf(f_684_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK27(U_2150,U_2149),sK28(U_2150,U_2149))
| ~ sP221(U_2149,U_2150) ),
inference(clausify,[status(thm)],[f_684_5]) ).
cnf(f_684_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2149,hAPP(U_2150,sK28(U_2150,U_2149)),hAPP(U_2150,sK27(U_2150,U_2149)))
| ~ sP221(U_2149,U_2150) ),
inference(clausify,[status(thm)],[f_684_5]) ).
fof(f_685_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma]) ).
fof(f_685_2,plain,
! [U_2152,U_2151] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2152)),U_2151),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2151,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2151) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
fof(f_685_3,plain,
! [U_2152,U_2151] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2152)),U_2151),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2151,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2151) ),
inference(definitional_conversion,[status(esa)],[f_685_2]) ).
cnf(f_685_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2152)),U_2151),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2151,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2151) ),
inference(clausify,[status(thm)],[f_685_3]) ).
fof(f_686_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) )
& ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__def]) ).
fof(f_686_2,plain,
! [U_2158,U_2157] :
( ( ( c_SEQ_OBseq(U_2157,U_2158)
| ! [U_2156] :
( ? [U_2155] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,U_2155)),U_2156)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2156) ) )
& ( ? [U_2154] :
( ! [U_2153] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,U_2153)),U_2154)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2154) )
| ~ c_SEQ_OBseq(U_2157,U_2158) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2157) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
fof(f_686_3,plain,
! [U_2158,U_2157] :
( ( ( c_SEQ_OBseq(U_2157,U_2158)
| ! [U_2156] :
( ? [U_2155] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,U_2155)),U_2156)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2156) ) )
& ( ( ! [U_2153] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,U_2153)),sK29(U_2158,U_2157))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK29(U_2158,U_2157)) )
| ~ c_SEQ_OBseq(U_2157,U_2158) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2157) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_2154,sK29(U_2158,U_2157))],[f_686_2]) ).
fof(f_686_4,plain,
! [U_2158,U_2157] :
( ( ( c_SEQ_OBseq(U_2157,U_2158)
| ! [U_2156] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,sK30(U_2158,U_2157,U_2156))),U_2156)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2156) ) )
& ( ( ! [U_2153] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,U_2153)),sK29(U_2158,U_2157))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK29(U_2158,U_2157)) )
| ~ c_SEQ_OBseq(U_2157,U_2158) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2157) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_2155,sK30(U_2158,U_2157,U_2156))],[f_686_3]) ).
fof(f_686_5,plain,
( ! [U_2153,U_2157,U_2158] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,U_2153)),sK29(U_2158,U_2157))
| ~ sP223(U_2153,U_2157,U_2158) )
& ! [U_2153,U_2157,U_2158] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK29(U_2158,U_2157))
| ~ sP223(U_2153,U_2157,U_2158) )
& ! [U_2153,U_2156,U_2157,U_2158] :
( c_SEQ_OBseq(U_2157,U_2158)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,sK30(U_2158,U_2157,U_2156))),U_2156)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2156)
| ~ sP224(U_2153,U_2156,U_2157,U_2158) )
& ! [U_2153,U_2156,U_2157,U_2158] :
( sP223(U_2153,U_2157,U_2158)
| ~ c_SEQ_OBseq(U_2157,U_2158)
| ~ sP224(U_2153,U_2156,U_2157,U_2158) )
& ! [U_2153,U_2156,U_2157,U_2158] :
( sP224(U_2153,U_2156,U_2157,U_2158)
| ~ class_RealVector_Oreal__normed__vector(U_2157) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223,sP224])],[f_686_4]) ).
cnf(f_686_6,plain,
( sP224(U_2153,U_2156,U_2157,U_2158)
| ~ class_RealVector_Oreal__normed__vector(U_2157) ),
inference(clausify,[status(thm)],[f_686_5]) ).
cnf(f_686_7,plain,
( sP223(U_2153,U_2157,U_2158)
| ~ c_SEQ_OBseq(U_2157,U_2158)
| ~ sP224(U_2153,U_2156,U_2157,U_2158) ),
inference(clausify,[status(thm)],[f_686_5]) ).
cnf(f_686_8,plain,
( c_SEQ_OBseq(U_2157,U_2158)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,sK30(U_2158,U_2157,U_2156))),U_2156)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2156)
| ~ sP224(U_2153,U_2156,U_2157,U_2158) ),
inference(clausify,[status(thm)],[f_686_5]) ).
cnf(f_686_9,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK29(U_2158,U_2157))
| ~ sP223(U_2153,U_2157,U_2158) ),
inference(clausify,[status(thm)],[f_686_5]) ).
cnf(f_686_10,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2157,hAPP(U_2158,U_2153)),sK29(U_2158,U_2157))
| ~ sP223(U_2153,U_2157,U_2158) ),
inference(clausify,[status(thm)],[f_686_5]) ).
fof(f_687_1,plain,
! [V_n,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))
| ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__power__ineq]) ).
fof(f_687_2,plain,
! [U_2161,U_2160,U_2159] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2159,hAPP(hAPP(c_Power_Opower__class_Opower(U_2159),U_2160),U_2161)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2159,U_2160)),U_2161))
| ~ class_RealVector_Oreal__normed__algebra__1(U_2159) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
fof(f_687_3,plain,
! [U_2161,U_2160,U_2159] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2159,hAPP(hAPP(c_Power_Opower__class_Opower(U_2159),U_2160),U_2161)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2159,U_2160)),U_2161))
| ~ class_RealVector_Oreal__normed__algebra__1(U_2159) ),
inference(definitional_conversion,[status(esa)],[f_687_2]) ).
cnf(f_687_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2159,hAPP(hAPP(c_Power_Opower__class_Opower(U_2159),U_2160),U_2161)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2159,U_2160)),U_2161))
| ~ class_RealVector_Oreal__normed__algebra__1(U_2159) ),
inference(clausify,[status(thm)],[f_687_3]) ).
fof(f_688_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_688_2,plain,
! [U_2163,U_2162] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2162),U_2163),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2162)
| ~ class_Rings_Ocomm__semiring__1(U_2162) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
fof(f_688_3,plain,
! [U_2162,U_2163] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2162),U_2163),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2162)
| ~ class_Rings_Ocomm__semiring__1(U_2162) ),
inference(definitional_conversion,[status(esa)],[f_688_2]) ).
cnf(f_688_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2162),U_2163),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2162)
| ~ class_Rings_Ocomm__semiring__1(U_2162) ),
inference(clausify,[status(thm)],[f_688_3]) ).
fof(f_689_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),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_689_2,plain,
! [U_2167,U_2166,U_2165,U_2164] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2164),hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),U_2166)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),U_2167)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2166,U_2167))
| ~ class_Rings_Ocomm__semiring__1(U_2164) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
fof(f_689_3,plain,
! [U_2164,U_2165,U_2166,U_2167] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2164),hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),U_2166)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),U_2167)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2166,U_2167))
| ~ class_Rings_Ocomm__semiring__1(U_2164) ),
inference(definitional_conversion,[status(esa)],[f_689_2]) ).
cnf(f_689_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2164),hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),U_2166)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),U_2167)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2164),U_2165),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2166,U_2167))
| ~ class_Rings_Ocomm__semiring__1(U_2164) ),
inference(clausify,[status(thm)],[f_689_3]) ).
fof(f_690_1,plain,
! [V_n,V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)
| ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__power]) ).
fof(f_690_2,plain,
! [U_2170,U_2169,U_2168] :
( c_RealVector_Onorm__class_Onorm(U_2168,hAPP(hAPP(c_Power_Opower__class_Opower(U_2168),U_2169),U_2170)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2168,U_2169)),U_2170)
| ~ class_RealVector_Oreal__normed__div__algebra(U_2168) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
fof(f_690_3,plain,
! [U_2168,U_2169,U_2170] :
( c_RealVector_Onorm__class_Onorm(U_2168,hAPP(hAPP(c_Power_Opower__class_Opower(U_2168),U_2169),U_2170)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2168,U_2169)),U_2170)
| ~ class_RealVector_Oreal__normed__div__algebra(U_2168) ),
inference(definitional_conversion,[status(esa)],[f_690_2]) ).
cnf(f_690_4,plain,
( c_RealVector_Onorm__class_Onorm(U_2168,hAPP(hAPP(c_Power_Opower__class_Opower(U_2168),U_2169),U_2170)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2168,U_2169)),U_2170)
| ~ class_RealVector_Oreal__normed__div__algebra(U_2168) ),
inference(clausify,[status(thm)],[f_690_3]) ).
fof(f_691_1,plain,
! [V_x,V_n,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__power]) ).
fof(f_691_2,plain,
! [U_2174,U_2173,U_2172,U_2171] :
( hAPP(c_Polynomial_Opoly(U_2171,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2171)),U_2172),U_2173)),U_2174) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2171),hAPP(c_Polynomial_Opoly(U_2171,U_2172),U_2174)),U_2173)
| ~ class_Rings_Ocomm__semiring__1(U_2171) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
fof(f_691_3,plain,
! [U_2171,U_2172,U_2173,U_2174] :
( hAPP(c_Polynomial_Opoly(U_2171,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2171)),U_2172),U_2173)),U_2174) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2171),hAPP(c_Polynomial_Opoly(U_2171,U_2172),U_2174)),U_2173)
| ~ class_Rings_Ocomm__semiring__1(U_2171) ),
inference(definitional_conversion,[status(esa)],[f_691_2]) ).
cnf(f_691_4,plain,
( hAPP(c_Polynomial_Opoly(U_2171,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2171)),U_2172),U_2173)),U_2174) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2171),hAPP(c_Polynomial_Opoly(U_2171,U_2172),U_2174)),U_2173)
| ~ class_Rings_Ocomm__semiring__1(U_2171) ),
inference(clausify,[status(thm)],[f_691_3]) ).
fof(f_692_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_692_2,plain,
! [U_2178,U_2177,U_2176,U_2175] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),U_2176),U_2177)),U_2178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),U_2176),U_2178)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),U_2177),U_2178))
| ~ class_Rings_Ocomm__semiring__1(U_2175) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
! [U_2175,U_2176,U_2177,U_2178] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),U_2176),U_2177)),U_2178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),U_2176),U_2178)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),U_2177),U_2178))
| ~ class_Rings_Ocomm__semiring__1(U_2175) ),
inference(definitional_conversion,[status(esa)],[f_692_2]) ).
cnf(f_692_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),U_2176),U_2177)),U_2178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2175),hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),U_2176),U_2178)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2175),U_2177),U_2178))
| ~ class_Rings_Ocomm__semiring__1(U_2175) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_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_693_2,plain,
! [U_2180,U_2179] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2179),U_2180),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2180
| ~ class_Rings_Ocomm__semiring__1(U_2179) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
fof(f_693_3,plain,
! [U_2180,U_2179] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2179),U_2180),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2180
| ~ class_Rings_Ocomm__semiring__1(U_2179) ),
inference(definitional_conversion,[status(esa)],[f_693_2]) ).
cnf(f_693_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2179),U_2180),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2180
| ~ class_Rings_Ocomm__semiring__1(U_2179) ),
inference(clausify,[status(thm)],[f_693_3]) ).
fof(f_694_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_694_2,plain,
! [U_2184,U_2183,U_2182,U_2181] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),U_2182),U_2183)),U_2184) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),U_2182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2183),U_2184))
| ~ class_Rings_Ocomm__semiring__1(U_2181) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
! [U_2181,U_2182,U_2183,U_2184] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),U_2182),U_2183)),U_2184) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),U_2182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2183),U_2184))
| ~ class_Rings_Ocomm__semiring__1(U_2181) ),
inference(definitional_conversion,[status(esa)],[f_694_2]) ).
cnf(f_694_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),U_2182),U_2183)),U_2184) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2181),U_2182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2183),U_2184))
| ~ class_Rings_Ocomm__semiring__1(U_2181) ),
inference(clausify,[status(thm)],[f_694_3]) ).
fof(f_695_1,plain,
! [V_x,V_n,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult]) ).
fof(f_695_2,plain,
! [U_2187,U_2186,U_2185] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2185),hAPP(hAPP(c_Power_Opower__class_Opower(U_2185),U_2187),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2187) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2185),U_2187),U_2186)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2186)
| ~ class_Groups_Omonoid__mult(U_2185) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
fof(f_695_3,plain,
! [U_2185,U_2186,U_2187] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2185),hAPP(hAPP(c_Power_Opower__class_Opower(U_2185),U_2187),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2187) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2185),U_2187),U_2186)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2186)
| ~ class_Groups_Omonoid__mult(U_2185) ),
inference(definitional_conversion,[status(esa)],[f_695_2]) ).
cnf(f_695_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2185),hAPP(hAPP(c_Power_Opower__class_Opower(U_2185),U_2187),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2187) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2185),U_2187),U_2186)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2186)
| ~ class_Groups_Omonoid__mult(U_2185) ),
inference(clausify,[status(thm)],[f_695_3]) ).
fof(f_696_1,plain,
! [V_m,V_n,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),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_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a)
| V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if]) ).
fof(f_696_2,plain,
! [U_2190,U_2189,U_2188] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),U_2189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2190),hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2189,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),U_2189) = c_Groups_Oone__class_Oone(U_2188)
| U_2189 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Power_Opower(U_2188) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
( ! [U_2188,U_2189,U_2190] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),U_2189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2190),hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2189,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP225(U_2188,U_2189,U_2190) )
& ! [U_2188,U_2189,U_2190] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),U_2189) = c_Groups_Oone__class_Oone(U_2188)
| U_2189 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP225(U_2188,U_2189,U_2190) )
& ! [U_2188,U_2189,U_2190] :
( sP225(U_2188,U_2189,U_2190)
| ~ class_Power_Opower(U_2188) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_696_2]) ).
cnf(f_696_4,plain,
( sP225(U_2188,U_2189,U_2190)
| ~ class_Power_Opower(U_2188) ),
inference(clausify,[status(thm)],[f_696_3]) ).
cnf(f_696_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),U_2189) = c_Groups_Oone__class_Oone(U_2188)
| U_2189 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP225(U_2188,U_2189,U_2190) ),
inference(clausify,[status(thm)],[f_696_3]) ).
cnf(f_696_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),U_2189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2190),hAPP(hAPP(c_Power_Opower__class_Opower(U_2188),U_2190),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2189,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP225(U_2188,U_2189,U_2190) ),
inference(clausify,[status(thm)],[f_696_3]) ).
fof(f_697_1,plain,
! [V_n,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ 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_697_2,plain,
! [U_2194,U_2193,U_2192,U_2191] :
( c_Orderings_Oord__class_Oless(U_2191,hAPP(hAPP(c_Power_Opower__class_Opower(U_2191),U_2192),U_2194),hAPP(hAPP(c_Power_Opower__class_Opower(U_2191),U_2193),U_2194))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2194)
| ~ c_Orderings_Oord__class_Oless__eq(U_2191,c_Groups_Ozero__class_Ozero(U_2191),U_2192)
| ~ c_Orderings_Oord__class_Oless(U_2191,U_2192,U_2193)
| ~ class_Rings_Olinordered__semidom(U_2191) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
fof(f_697_3,plain,
! [U_2192,U_2194,U_2191,U_2193] :
( c_Orderings_Oord__class_Oless(U_2191,hAPP(hAPP(c_Power_Opower__class_Opower(U_2191),U_2192),U_2194),hAPP(hAPP(c_Power_Opower__class_Opower(U_2191),U_2193),U_2194))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2194)
| ~ c_Orderings_Oord__class_Oless__eq(U_2191,c_Groups_Ozero__class_Ozero(U_2191),U_2192)
| ~ c_Orderings_Oord__class_Oless(U_2191,U_2192,U_2193)
| ~ class_Rings_Olinordered__semidom(U_2191) ),
inference(definitional_conversion,[status(esa)],[f_697_2]) ).
cnf(f_697_4,plain,
( c_Orderings_Oord__class_Oless(U_2191,hAPP(hAPP(c_Power_Opower__class_Opower(U_2191),U_2192),U_2194),hAPP(hAPP(c_Power_Opower__class_Opower(U_2191),U_2193),U_2194))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2194)
| ~ c_Orderings_Oord__class_Oless__eq(U_2191,c_Groups_Ozero__class_Ozero(U_2191),U_2192)
| ~ c_Orderings_Oord__class_Oless(U_2191,U_2192,U_2193)
| ~ class_Rings_Olinordered__semidom(U_2191) ),
inference(clausify,[status(thm)],[f_697_3]) ).
fof(f_698_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ 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_698_2,plain,
! [U_2197,U_2196,U_2195] :
( c_Orderings_Oord__class_Oless(U_2195,c_Groups_Oone__class_Oone(U_2195),hAPP(hAPP(c_Power_Opower__class_Opower(U_2195),U_2196),U_2197))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2197)
| ~ c_Orderings_Oord__class_Oless(U_2195,c_Groups_Oone__class_Oone(U_2195),U_2196)
| ~ class_Rings_Olinordered__semidom(U_2195) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
fof(f_698_3,plain,
! [U_2196,U_2195,U_2197] :
( c_Orderings_Oord__class_Oless(U_2195,c_Groups_Oone__class_Oone(U_2195),hAPP(hAPP(c_Power_Opower__class_Opower(U_2195),U_2196),U_2197))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2197)
| ~ c_Orderings_Oord__class_Oless(U_2195,c_Groups_Oone__class_Oone(U_2195),U_2196)
| ~ class_Rings_Olinordered__semidom(U_2195) ),
inference(definitional_conversion,[status(esa)],[f_698_2]) ).
cnf(f_698_4,plain,
( c_Orderings_Oord__class_Oless(U_2195,c_Groups_Oone__class_Oone(U_2195),hAPP(hAPP(c_Power_Opower__class_Opower(U_2195),U_2196),U_2197))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2197)
| ~ c_Orderings_Oord__class_Oless(U_2195,c_Groups_Oone__class_Oone(U_2195),U_2196)
| ~ class_Rings_Olinordered__semidom(U_2195) ),
inference(clausify,[status(thm)],[f_698_3]) ).
fof(f_699_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_699_2,plain,
! [U_2199,U_2198] :
( ( 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_2198),U_2199))
| ( U_2199 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2198) ) )
& ( U_2199 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2198)
| ~ 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_2198),U_2199)) ) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
fof(f_699_3,plain,
( ! [U_2203,U_2201] :
( 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_2201),U_2203))
| ( U_2203 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2201) ) )
& ! [U_2202,U_2200] :
( U_2202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2200)
| ~ 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_2200),U_2202)) ) ),
inference(miniscope,[status(thm)],[f_699_2]) ).
fof(f_699_4,plain,
( ! [U_2203,U_2201] :
( U_2203 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP226(U_2203,U_2201) )
& ! [U_2203,U_2201] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2201)
| ~ sP226(U_2203,U_2201) )
& ! [U_2203,U_2201] :
( 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_2201),U_2203))
| sP226(U_2203,U_2201) )
& ! [U_2202,U_2200] :
( U_2202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2200)
| ~ 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_2200),U_2202)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_699_3]) ).
cnf(f_699_5,plain,
( U_2202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2200)
| ~ 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_2200),U_2202)) ),
inference(clausify,[status(thm)],[f_699_4]) ).
cnf(f_699_6,plain,
( 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_2201),U_2203))
| sP226(U_2203,U_2201) ),
inference(clausify,[status(thm)],[f_699_4]) ).
cnf(f_699_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2201)
| ~ sP226(U_2203,U_2201) ),
inference(clausify,[status(thm)],[f_699_4]) ).
cnf(f_699_8,plain,
( U_2203 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP226(U_2203,U_2201) ),
inference(clausify,[status(thm)],[f_699_4]) ).
fof(f_700_1,plain,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ 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))
| ~ 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_700_2,plain,
! [U_2206,U_2205,U_2204] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2205,U_2206)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2204),U_2205),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2204),U_2206))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2204) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
fof(f_700_3,plain,
! [U_2205,U_2206,U_2204] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2205,U_2206)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2204),U_2205),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2204),U_2206))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2204) ),
inference(definitional_conversion,[status(esa)],[f_700_2]) ).
cnf(f_700_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2205,U_2206)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2204),U_2205),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2204),U_2206))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2204) ),
inference(clausify,[status(thm)],[f_700_3]) ).
fof(f_701_1,plain,
! [V_n_2,V_x_2] :
( ( 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).
fof(f_701_2,plain,
! [U_2208,U_2207] :
( ( 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2207)),U_2208))
| ( U_2208 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2207 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_2208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2207 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2207)),U_2208)) ) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
fof(f_701_3,plain,
( ! [U_2212,U_2210] :
( 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2210)),U_2212))
| ( U_2212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2210 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2211,U_2209] :
( U_2211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2209 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2209)),U_2211)) ) ),
inference(miniscope,[status(thm)],[f_701_2]) ).
fof(f_701_4,plain,
( ! [U_2212,U_2210] :
( U_2212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP227(U_2212,U_2210) )
& ! [U_2212,U_2210] :
( U_2210 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP227(U_2212,U_2210) )
& ! [U_2212,U_2210] :
( 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2210)),U_2212))
| sP227(U_2212,U_2210) )
& ! [U_2211,U_2209] :
( U_2211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2209 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2209)),U_2211)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_701_3]) ).
cnf(f_701_5,plain,
( U_2211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2209 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2209)),U_2211)) ),
inference(clausify,[status(thm)],[f_701_4]) ).
cnf(f_701_6,plain,
( 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2210)),U_2212))
| sP227(U_2212,U_2210) ),
inference(clausify,[status(thm)],[f_701_4]) ).
cnf(f_701_7,plain,
( U_2210 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP227(U_2212,U_2210) ),
inference(clausify,[status(thm)],[f_701_4]) ).
cnf(f_701_8,plain,
( U_2212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP227(U_2212,U_2210) ),
inference(clausify,[status(thm)],[f_701_4]) ).
fof(f_702_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_702_2,plain,
! [U_2215,U_2214,U_2213] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2213),U_2214)),U_2215) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2214),U_2215)),
inference(variable_rename,[status(thm)],[f_702_1]) ).
fof(f_702_3,plain,
! [U_2213,U_2214,U_2215] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2213),U_2214)),U_2215) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2214),U_2215)),
inference(definitional_conversion,[status(esa)],[f_702_2]) ).
cnf(f_702_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2213),U_2214)),U_2215) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2214),U_2215)),
inference(clausify,[status(thm)],[f_702_3]) ).
fof(f_703_1,plain,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),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_703_2,plain,
! [U_2218,U_2217,U_2216] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2218)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),U_2217)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),U_2218)),
inference(variable_rename,[status(thm)],[f_703_1]) ).
fof(f_703_3,plain,
! [U_2216,U_2217,U_2218] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2218)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),U_2217)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),U_2218)),
inference(definitional_conversion,[status(esa)],[f_703_2]) ).
cnf(f_703_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2218)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),U_2217)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2216),U_2218)),
inference(clausify,[status(thm)],[f_703_3]) ).
fof(f_704_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_power__real__of__nat]) ).
fof(f_704_2,plain,
! [U_2220,U_2219] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2219)),U_2220) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2219),U_2220)),
inference(variable_rename,[status(thm)],[f_704_1]) ).
fof(f_704_3,plain,
! [U_2219,U_2220] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2219)),U_2220) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2219),U_2220)),
inference(definitional_conversion,[status(esa)],[f_704_2]) ).
cnf(f_704_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2219)),U_2220) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2219),U_2220)),
inference(clausify,[status(thm)],[f_704_3]) ).
fof(f_705_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__power]) ).
fof(f_705_2,plain,
! [U_2222,U_2221] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2221),U_2222)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2221)),U_2222),
inference(variable_rename,[status(thm)],[f_705_1]) ).
fof(f_705_3,plain,
! [U_2221,U_2222] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2221),U_2222)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2221)),U_2222),
inference(definitional_conversion,[status(esa)],[f_705_2]) ).
cnf(f_705_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2221),U_2222)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2221)),U_2222),
inference(clausify,[status(thm)],[f_705_3]) ).
fof(f_706_1,plain,
! [V_n,V_x] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n)
| V_x != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__power]) ).
fof(f_706_2,plain,
! [U_2224,U_2223] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2223),U_2224)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2223)),U_2224)
| U_2223 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2223)) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
fof(f_706_3,plain,
! [U_2223,U_2224] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2223),U_2224)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2223)),U_2224)
| U_2223 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2223)) ),
inference(definitional_conversion,[status(esa)],[f_706_2]) ).
cnf(f_706_4,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2223),U_2224)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2223)),U_2224)
| U_2223 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2223)) ),
inference(clausify,[status(thm)],[f_706_3]) ).
fof(f_707_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),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_707_2,plain,
! [U_2226,U_2225] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2226),U_2225) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2226),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2226),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2225,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2225 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2226),U_2225) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2225 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
fof(f_707_3,plain,
( ! [U_2230,U_2228] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2230),U_2228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2230),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2230),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2228,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2229,U_2227] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2229),U_2227) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2227 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_707_2]) ).
fof(f_707_4,plain,
( ! [U_2228,U_2230] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2230),U_2228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2230),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2230),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2228,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2229,U_2227] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2229),U_2227) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2227 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_707_3]) ).
cnf(f_707_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2229),U_2227) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2227 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_707_4]) ).
cnf(f_707_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2230),U_2228) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2230),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2230),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2228,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2228 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_707_4]) ).
fof(f_708_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_708_2,plain,
! [U_2233,U_2232,U_2231] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2231),U_2232),U_2233) != c_Groups_Ozero__class_Ozero(U_2231)
| U_2232 = c_Groups_Ozero__class_Ozero(U_2231)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2231) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
fof(f_708_3,plain,
! [U_2231,U_2232,U_2233] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2231),U_2232),U_2233) != c_Groups_Ozero__class_Ozero(U_2231)
| U_2232 = c_Groups_Ozero__class_Ozero(U_2231)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2231) ),
inference(definitional_conversion,[status(esa)],[f_708_2]) ).
cnf(f_708_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2231),U_2232),U_2233) != c_Groups_Ozero__class_Ozero(U_2231)
| U_2232 = c_Groups_Ozero__class_Ozero(U_2231)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2231) ),
inference(clausify,[status(thm)],[f_708_3]) ).
fof(f_709_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_709_2,plain,
! [U_2237,U_2236,U_2235,U_2234] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2234),U_2235),U_2236)),U_2237) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2234),hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),U_2235),U_2237)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),U_2236),U_2237))
| ~ class_Groups_Ocomm__monoid__mult(U_2234) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
fof(f_709_3,plain,
! [U_2234,U_2235,U_2236,U_2237] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2234),U_2235),U_2236)),U_2237) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2234),hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),U_2235),U_2237)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),U_2236),U_2237))
| ~ class_Groups_Ocomm__monoid__mult(U_2234) ),
inference(definitional_conversion,[status(esa)],[f_709_2]) ).
cnf(f_709_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2234),U_2235),U_2236)),U_2237) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2234),hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),U_2235),U_2237)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2234),U_2236),U_2237))
| ~ class_Groups_Ocomm__monoid__mult(U_2234) ),
inference(clausify,[status(thm)],[f_709_3]) ).
fof(f_710_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_710_2,plain,
! [U_2240,U_2239,U_2238] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2238),hAPP(hAPP(c_Power_Opower__class_Opower(U_2238),U_2239),U_2240)),U_2239) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2238),U_2239),hAPP(hAPP(c_Power_Opower__class_Opower(U_2238),U_2239),U_2240))
| ~ class_Groups_Omonoid__mult(U_2238) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
fof(f_710_3,plain,
! [U_2238,U_2239,U_2240] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2238),hAPP(hAPP(c_Power_Opower__class_Opower(U_2238),U_2239),U_2240)),U_2239) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2238),U_2239),hAPP(hAPP(c_Power_Opower__class_Opower(U_2238),U_2239),U_2240))
| ~ class_Groups_Omonoid__mult(U_2238) ),
inference(definitional_conversion,[status(esa)],[f_710_2]) ).
cnf(f_710_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2238),hAPP(hAPP(c_Power_Opower__class_Opower(U_2238),U_2239),U_2240)),U_2239) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2238),U_2239),hAPP(hAPP(c_Power_Opower__class_Opower(U_2238),U_2239),U_2240))
| ~ class_Groups_Omonoid__mult(U_2238) ),
inference(clausify,[status(thm)],[f_710_3]) ).
fof(f_711_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_711_2,plain,
! [U_2242,U_2241] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2241),c_Groups_Oone__class_Oone(U_2241)),U_2242) = c_Groups_Oone__class_Oone(U_2241)
| ~ class_Groups_Omonoid__mult(U_2241) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
fof(f_711_3,plain,
! [U_2241,U_2242] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2241),c_Groups_Oone__class_Oone(U_2241)),U_2242) = c_Groups_Oone__class_Oone(U_2241)
| ~ class_Groups_Omonoid__mult(U_2241) ),
inference(definitional_conversion,[status(esa)],[f_711_2]) ).
cnf(f_711_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2241),c_Groups_Oone__class_Oone(U_2241)),U_2242) = c_Groups_Oone__class_Oone(U_2241)
| ~ class_Groups_Omonoid__mult(U_2241) ),
inference(clausify,[status(thm)],[f_711_3]) ).
fof(f_712_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_712_2,plain,
! [U_2246,U_2245,U_2244,U_2243] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),U_2244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2245),U_2246)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),U_2244),U_2245)),U_2246)
| ~ class_Groups_Omonoid__mult(U_2243) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
! [U_2243,U_2244,U_2245,U_2246] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),U_2244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2245),U_2246)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),U_2244),U_2245)),U_2246)
| ~ class_Groups_Omonoid__mult(U_2243) ),
inference(definitional_conversion,[status(esa)],[f_712_2]) ).
cnf(f_712_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),U_2244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2245),U_2246)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),hAPP(hAPP(c_Power_Opower__class_Opower(U_2243),U_2244),U_2245)),U_2246)
| ~ class_Groups_Omonoid__mult(U_2243) ),
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [V_n,V_a,T_a] :
( 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),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_713_2,plain,
! [U_2249,U_2248,U_2247] :
( c_Groups_Oabs__class_Oabs(U_2247,hAPP(hAPP(c_Power_Opower__class_Opower(U_2247),U_2248),U_2249)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2247),c_Groups_Oabs__class_Oabs(U_2247,U_2248)),U_2249)
| ~ class_Rings_Olinordered__idom(U_2247) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
! [U_2247,U_2248,U_2249] :
( c_Groups_Oabs__class_Oabs(U_2247,hAPP(hAPP(c_Power_Opower__class_Opower(U_2247),U_2248),U_2249)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2247),c_Groups_Oabs__class_Oabs(U_2247,U_2248)),U_2249)
| ~ class_Rings_Olinordered__idom(U_2247) ),
inference(definitional_conversion,[status(esa)],[f_713_2]) ).
cnf(f_713_4,plain,
( c_Groups_Oabs__class_Oabs(U_2247,hAPP(hAPP(c_Power_Opower__class_Opower(U_2247),U_2248),U_2249)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2247),c_Groups_Oabs__class_Oabs(U_2247,U_2248)),U_2249)
| ~ class_Rings_Olinordered__idom(U_2247) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_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_714_2,plain,
! [U_2251,U_2250] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2250),U_2251),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2251
| ~ class_Groups_Omonoid__mult(U_2250) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
fof(f_714_3,plain,
! [U_2250,U_2251] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2250),U_2251),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2251
| ~ class_Groups_Omonoid__mult(U_2250) ),
inference(definitional_conversion,[status(esa)],[f_714_2]) ).
cnf(f_714_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2250),U_2251),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2251
| ~ class_Groups_Omonoid__mult(U_2250) ),
inference(clausify,[status(thm)],[f_714_3]) ).
fof(f_715_1,plain,
! [V_n,V_b,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ 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_715_2,plain,
! [U_2255,U_2254,U_2253,U_2252] :
( c_Orderings_Oord__class_Oless__eq(U_2252,hAPP(hAPP(c_Power_Opower__class_Opower(U_2252),U_2253),U_2255),hAPP(hAPP(c_Power_Opower__class_Opower(U_2252),U_2254),U_2255))
| ~ c_Orderings_Oord__class_Oless__eq(U_2252,c_Groups_Ozero__class_Ozero(U_2252),U_2253)
| ~ c_Orderings_Oord__class_Oless__eq(U_2252,U_2253,U_2254)
| ~ class_Rings_Olinordered__semidom(U_2252) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
fof(f_715_3,plain,
! [U_2252,U_2253,U_2254,U_2255] :
( c_Orderings_Oord__class_Oless__eq(U_2252,hAPP(hAPP(c_Power_Opower__class_Opower(U_2252),U_2253),U_2255),hAPP(hAPP(c_Power_Opower__class_Opower(U_2252),U_2254),U_2255))
| ~ c_Orderings_Oord__class_Oless__eq(U_2252,c_Groups_Ozero__class_Ozero(U_2252),U_2253)
| ~ c_Orderings_Oord__class_Oless__eq(U_2252,U_2253,U_2254)
| ~ class_Rings_Olinordered__semidom(U_2252) ),
inference(definitional_conversion,[status(esa)],[f_715_2]) ).
cnf(f_715_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2252,hAPP(hAPP(c_Power_Opower__class_Opower(U_2252),U_2253),U_2255),hAPP(hAPP(c_Power_Opower__class_Opower(U_2252),U_2254),U_2255))
| ~ c_Orderings_Oord__class_Oless__eq(U_2252,c_Groups_Ozero__class_Ozero(U_2252),U_2253)
| ~ c_Orderings_Oord__class_Oless__eq(U_2252,U_2253,U_2254)
| ~ class_Rings_Olinordered__semidom(U_2252) ),
inference(clausify,[status(thm)],[f_715_3]) ).
fof(f_716_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ 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_716_2,plain,
! [U_2258,U_2257,U_2256] :
( c_Orderings_Oord__class_Oless__eq(U_2256,c_Groups_Ozero__class_Ozero(U_2256),hAPP(hAPP(c_Power_Opower__class_Opower(U_2256),U_2257),U_2258))
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,c_Groups_Ozero__class_Ozero(U_2256),U_2257)
| ~ class_Rings_Olinordered__semidom(U_2256) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
fof(f_716_3,plain,
! [U_2256,U_2257,U_2258] :
( c_Orderings_Oord__class_Oless__eq(U_2256,c_Groups_Ozero__class_Ozero(U_2256),hAPP(hAPP(c_Power_Opower__class_Opower(U_2256),U_2257),U_2258))
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,c_Groups_Ozero__class_Ozero(U_2256),U_2257)
| ~ class_Rings_Olinordered__semidom(U_2256) ),
inference(definitional_conversion,[status(esa)],[f_716_2]) ).
cnf(f_716_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2256,c_Groups_Ozero__class_Ozero(U_2256),hAPP(hAPP(c_Power_Opower__class_Opower(U_2256),U_2257),U_2258))
| ~ c_Orderings_Oord__class_Oless__eq(U_2256,c_Groups_Ozero__class_Ozero(U_2256),U_2257)
| ~ class_Rings_Olinordered__semidom(U_2256) ),
inference(clausify,[status(thm)],[f_716_3]) ).
fof(f_717_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ 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_717_2,plain,
! [U_2261,U_2260,U_2259] :
( c_Orderings_Oord__class_Oless(U_2259,c_Groups_Ozero__class_Ozero(U_2259),hAPP(hAPP(c_Power_Opower__class_Opower(U_2259),U_2260),U_2261))
| ~ c_Orderings_Oord__class_Oless(U_2259,c_Groups_Ozero__class_Ozero(U_2259),U_2260)
| ~ class_Rings_Olinordered__semidom(U_2259) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
fof(f_717_3,plain,
! [U_2259,U_2260,U_2261] :
( c_Orderings_Oord__class_Oless(U_2259,c_Groups_Ozero__class_Ozero(U_2259),hAPP(hAPP(c_Power_Opower__class_Opower(U_2259),U_2260),U_2261))
| ~ c_Orderings_Oord__class_Oless(U_2259,c_Groups_Ozero__class_Ozero(U_2259),U_2260)
| ~ class_Rings_Olinordered__semidom(U_2259) ),
inference(definitional_conversion,[status(esa)],[f_717_2]) ).
cnf(f_717_4,plain,
( c_Orderings_Oord__class_Oless(U_2259,c_Groups_Ozero__class_Ozero(U_2259),hAPP(hAPP(c_Power_Opower__class_Opower(U_2259),U_2260),U_2261))
| ~ c_Orderings_Oord__class_Oless(U_2259,c_Groups_Ozero__class_Ozero(U_2259),U_2260)
| ~ class_Rings_Olinordered__semidom(U_2259) ),
inference(clausify,[status(thm)],[f_717_3]) ).
fof(f_718_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ 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_718_2,plain,
! [U_2264,U_2263,U_2262] :
( c_Orderings_Oord__class_Oless__eq(U_2262,c_Groups_Oone__class_Oone(U_2262),hAPP(hAPP(c_Power_Opower__class_Opower(U_2262),U_2263),U_2264))
| ~ c_Orderings_Oord__class_Oless__eq(U_2262,c_Groups_Oone__class_Oone(U_2262),U_2263)
| ~ class_Rings_Olinordered__semidom(U_2262) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
fof(f_718_3,plain,
! [U_2264,U_2262,U_2263] :
( c_Orderings_Oord__class_Oless__eq(U_2262,c_Groups_Oone__class_Oone(U_2262),hAPP(hAPP(c_Power_Opower__class_Opower(U_2262),U_2263),U_2264))
| ~ c_Orderings_Oord__class_Oless__eq(U_2262,c_Groups_Oone__class_Oone(U_2262),U_2263)
| ~ class_Rings_Olinordered__semidom(U_2262) ),
inference(definitional_conversion,[status(esa)],[f_718_2]) ).
cnf(f_718_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2262,c_Groups_Oone__class_Oone(U_2262),hAPP(hAPP(c_Power_Opower__class_Opower(U_2262),U_2263),U_2264))
| ~ c_Orderings_Oord__class_Oless__eq(U_2262,c_Groups_Oone__class_Oone(U_2262),U_2263)
| ~ class_Rings_Olinordered__semidom(U_2262) ),
inference(clausify,[status(thm)],[f_718_3]) ).
fof(f_719_1,plain,
! [V_n_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).
fof(f_719_2,plain,
! [U_2267,U_2266,U_2265] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2265),U_2266),U_2267) = c_Groups_Ozero__class_Ozero(U_2265)
| U_2267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2266 != c_Groups_Ozero__class_Ozero(U_2265) )
& ( ( U_2267 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2266 = c_Groups_Ozero__class_Ozero(U_2265) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2265),U_2266),U_2267) != c_Groups_Ozero__class_Ozero(U_2265) ) )
| ~ class_Rings_Ozero__neq__one(U_2265)
| ~ class_Rings_Ono__zero__divisors(U_2265)
| ~ class_Rings_Omult__zero(U_2265)
| ~ class_Power_Opower(U_2265) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
fof(f_719_3,plain,
( ! [U_2265,U_2266,U_2267] :
( U_2267 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP228(U_2265,U_2266,U_2267) )
& ! [U_2265,U_2266,U_2267] :
( U_2266 = c_Groups_Ozero__class_Ozero(U_2265)
| ~ sP228(U_2265,U_2266,U_2267) )
& ! [U_2265,U_2266,U_2267] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2265),U_2266),U_2267) = c_Groups_Ozero__class_Ozero(U_2265)
| U_2267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2266 != c_Groups_Ozero__class_Ozero(U_2265)
| ~ sP229(U_2265,U_2266,U_2267) )
& ! [U_2265,U_2266,U_2267] :
( sP228(U_2265,U_2266,U_2267)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2265),U_2266),U_2267) != c_Groups_Ozero__class_Ozero(U_2265)
| ~ sP229(U_2265,U_2266,U_2267) )
& ! [U_2265,U_2266,U_2267] :
( sP229(U_2265,U_2266,U_2267)
| ~ class_Rings_Ozero__neq__one(U_2265)
| ~ class_Rings_Ono__zero__divisors(U_2265)
| ~ class_Rings_Omult__zero(U_2265)
| ~ class_Power_Opower(U_2265) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228,sP229])],[f_719_2]) ).
cnf(f_719_4,plain,
( sP229(U_2265,U_2266,U_2267)
| ~ class_Rings_Ozero__neq__one(U_2265)
| ~ class_Rings_Ono__zero__divisors(U_2265)
| ~ class_Rings_Omult__zero(U_2265)
| ~ class_Power_Opower(U_2265) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_5,plain,
( sP228(U_2265,U_2266,U_2267)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2265),U_2266),U_2267) != c_Groups_Ozero__class_Ozero(U_2265)
| ~ sP229(U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2265),U_2266),U_2267) = c_Groups_Ozero__class_Ozero(U_2265)
| U_2267 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2266 != c_Groups_Ozero__class_Ozero(U_2265)
| ~ sP229(U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_7,plain,
( U_2266 = c_Groups_Ozero__class_Ozero(U_2265)
| ~ sP228(U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_8,plain,
( U_2267 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP228(U_2265,U_2266,U_2267) ),
inference(clausify,[status(thm)],[f_719_3]) ).
fof(f_720_1,plain,
! [V_n_2,V_ma_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).
fof(f_720_2,plain,
! [U_2271,U_2270,U_2269,U_2268] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2270) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2271)
| U_2270 != U_2271 )
& ( U_2270 = U_2271
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2270) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2271) ) )
| ~ c_Orderings_Oord__class_Oless(U_2268,c_Groups_Oone__class_Oone(U_2268),U_2269)
| ~ class_Rings_Olinordered__semidom(U_2268) ),
inference(variable_rename,[status(thm)],[f_720_1]) ).
fof(f_720_3,plain,
( ! [U_2271,U_2269,U_2270,U_2268] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2270) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2271)
| U_2270 != U_2271
| ~ sP230(U_2271,U_2269,U_2270,U_2268) )
& ! [U_2271,U_2269,U_2270,U_2268] :
( U_2270 = U_2271
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2270) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2271)
| ~ sP230(U_2271,U_2269,U_2270,U_2268) )
& ! [U_2271,U_2269,U_2270,U_2268] :
( sP230(U_2271,U_2269,U_2270,U_2268)
| ~ c_Orderings_Oord__class_Oless(U_2268,c_Groups_Oone__class_Oone(U_2268),U_2269)
| ~ class_Rings_Olinordered__semidom(U_2268) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_720_2]) ).
cnf(f_720_4,plain,
( sP230(U_2271,U_2269,U_2270,U_2268)
| ~ c_Orderings_Oord__class_Oless(U_2268,c_Groups_Oone__class_Oone(U_2268),U_2269)
| ~ class_Rings_Olinordered__semidom(U_2268) ),
inference(clausify,[status(thm)],[f_720_3]) ).
cnf(f_720_5,plain,
( U_2270 = U_2271
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2270) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2271)
| ~ sP230(U_2271,U_2269,U_2270,U_2268) ),
inference(clausify,[status(thm)],[f_720_3]) ).
cnf(f_720_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2270) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2268),U_2269),U_2271)
| U_2270 != U_2271
| ~ sP230(U_2271,U_2269,U_2270,U_2268) ),
inference(clausify,[status(thm)],[f_720_3]) ).
fof(f_721_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_721_2,plain,
! [U_2273,U_2272] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2272),U_2273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2272)
| ~ class_Power_Opower(U_2272) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
fof(f_721_3,plain,
! [U_2272,U_2273] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2272),U_2273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2272)
| ~ class_Power_Opower(U_2272) ),
inference(definitional_conversion,[status(esa)],[f_721_2]) ).
cnf(f_721_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2272),U_2273),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2272)
| ~ class_Power_Opower(U_2272) ),
inference(clausify,[status(thm)],[f_721_3]) ).
fof(f_722_1,plain,
! [V_n,V_m,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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_722_2,plain,
! [U_2277,U_2276,U_2275,U_2274] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2276,U_2277)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2274),hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),U_2276)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),U_2277))
| ~ class_Groups_Omonoid__mult(U_2274) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
! [U_2275,U_2276,U_2277,U_2274] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2276,U_2277)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2274),hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),U_2276)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),U_2277))
| ~ class_Groups_Omonoid__mult(U_2274) ),
inference(definitional_conversion,[status(esa)],[f_722_2]) ).
cnf(f_722_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2276,U_2277)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2274),hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),U_2276)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2274),U_2275),U_2277))
| ~ class_Groups_Omonoid__mult(U_2274) ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)) = 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_723_2,plain,
! [U_2280,U_2279,U_2278] :
( c_Groups_Oabs__class_Oabs(U_2278,hAPP(hAPP(c_Power_Opower__class_Opower(U_2278),c_Groups_Ouminus__class_Ouminus(U_2278,U_2279)),U_2280)) = c_Groups_Oabs__class_Oabs(U_2278,hAPP(hAPP(c_Power_Opower__class_Opower(U_2278),U_2279),U_2280))
| ~ class_Rings_Olinordered__idom(U_2278) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
! [U_2278,U_2279,U_2280] :
( c_Groups_Oabs__class_Oabs(U_2278,hAPP(hAPP(c_Power_Opower__class_Opower(U_2278),c_Groups_Ouminus__class_Ouminus(U_2278,U_2279)),U_2280)) = c_Groups_Oabs__class_Oabs(U_2278,hAPP(hAPP(c_Power_Opower__class_Opower(U_2278),U_2279),U_2280))
| ~ class_Rings_Olinordered__idom(U_2278) ),
inference(definitional_conversion,[status(esa)],[f_723_2]) ).
cnf(f_723_4,plain,
( c_Groups_Oabs__class_Oabs(U_2278,hAPP(hAPP(c_Power_Opower__class_Opower(U_2278),c_Groups_Ouminus__class_Ouminus(U_2278,U_2279)),U_2280)) = c_Groups_Oabs__class_Oabs(U_2278,hAPP(hAPP(c_Power_Opower__class_Opower(U_2278),U_2279),U_2280))
| ~ class_Rings_Olinordered__idom(U_2278) ),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_724_2,plain,
! [U_2284,U_2283,U_2282,U_2281] :
( c_Orderings_Oord__class_Oless(U_2281,U_2282,U_2284)
| ~ c_Orderings_Oord__class_Oless__eq(U_2281,c_Groups_Ozero__class_Ozero(U_2281),U_2284)
| ~ c_Orderings_Oord__class_Oless(U_2281,hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2282),U_2283),hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2284),U_2283))
| ~ class_Rings_Olinordered__semidom(U_2281) ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
fof(f_724_3,plain,
! [U_2281,U_2282,U_2283,U_2284] :
( c_Orderings_Oord__class_Oless(U_2281,U_2282,U_2284)
| ~ c_Orderings_Oord__class_Oless__eq(U_2281,c_Groups_Ozero__class_Ozero(U_2281),U_2284)
| ~ c_Orderings_Oord__class_Oless(U_2281,hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2282),U_2283),hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2284),U_2283))
| ~ class_Rings_Olinordered__semidom(U_2281) ),
inference(definitional_conversion,[status(esa)],[f_724_2]) ).
cnf(f_724_4,plain,
( c_Orderings_Oord__class_Oless(U_2281,U_2282,U_2284)
| ~ c_Orderings_Oord__class_Oless__eq(U_2281,c_Groups_Ozero__class_Ozero(U_2281),U_2284)
| ~ c_Orderings_Oord__class_Oless(U_2281,hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2282),U_2283),hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2284),U_2283))
| ~ class_Rings_Olinordered__semidom(U_2281) ),
inference(clausify,[status(thm)],[f_724_3]) ).
fof(f_725_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ 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_725_2,plain,
! [U_2287,U_2286,U_2285] :
( c_Orderings_Oord__class_Oless(U_2285,hAPP(hAPP(c_Power_Opower__class_Opower(U_2285),U_2286),U_2287),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2285),U_2286),hAPP(hAPP(c_Power_Opower__class_Opower(U_2285),U_2286),U_2287)))
| ~ c_Orderings_Oord__class_Oless(U_2285,c_Groups_Oone__class_Oone(U_2285),U_2286)
| ~ class_Rings_Olinordered__semidom(U_2285) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
! [U_2285,U_2286,U_2287] :
( c_Orderings_Oord__class_Oless(U_2285,hAPP(hAPP(c_Power_Opower__class_Opower(U_2285),U_2286),U_2287),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2285),U_2286),hAPP(hAPP(c_Power_Opower__class_Opower(U_2285),U_2286),U_2287)))
| ~ c_Orderings_Oord__class_Oless(U_2285,c_Groups_Oone__class_Oone(U_2285),U_2286)
| ~ class_Rings_Olinordered__semidom(U_2285) ),
inference(definitional_conversion,[status(esa)],[f_725_2]) ).
cnf(f_725_4,plain,
( c_Orderings_Oord__class_Oless(U_2285,hAPP(hAPP(c_Power_Opower__class_Opower(U_2285),U_2286),U_2287),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2285),U_2286),hAPP(hAPP(c_Power_Opower__class_Opower(U_2285),U_2286),U_2287)))
| ~ c_Orderings_Oord__class_Oless(U_2285,c_Groups_Oone__class_Oone(U_2285),U_2286)
| ~ class_Rings_Olinordered__semidom(U_2285) ),
inference(clausify,[status(thm)],[f_725_3]) ).
fof(f_726_1,plain,
! [V_n,V_a,T_a] :
( 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)))
| ~ 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_726_2,plain,
! [U_2290,U_2289,U_2288] :
( c_Orderings_Oord__class_Oless(U_2288,c_Groups_Oone__class_Oone(U_2288),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2288),U_2289),hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2289),U_2290)))
| ~ c_Orderings_Oord__class_Oless(U_2288,c_Groups_Oone__class_Oone(U_2288),U_2289)
| ~ class_Rings_Olinordered__semidom(U_2288) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
fof(f_726_3,plain,
! [U_2288,U_2289,U_2290] :
( c_Orderings_Oord__class_Oless(U_2288,c_Groups_Oone__class_Oone(U_2288),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2288),U_2289),hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2289),U_2290)))
| ~ c_Orderings_Oord__class_Oless(U_2288,c_Groups_Oone__class_Oone(U_2288),U_2289)
| ~ class_Rings_Olinordered__semidom(U_2288) ),
inference(definitional_conversion,[status(esa)],[f_726_2]) ).
cnf(f_726_4,plain,
( c_Orderings_Oord__class_Oless(U_2288,c_Groups_Oone__class_Oone(U_2288),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2288),U_2289),hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2289),U_2290)))
| ~ c_Orderings_Oord__class_Oless(U_2288,c_Groups_Oone__class_Oone(U_2288),U_2289)
| ~ class_Rings_Olinordered__semidom(U_2288) ),
inference(clausify,[status(thm)],[f_726_3]) ).
fof(f_727_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_727_2,plain,
! [U_2292,U_2291] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2291),c_Groups_Ozero__class_Ozero(U_2291)),U_2292) = c_Groups_Ozero__class_Ozero(U_2291)
| U_2292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2291),c_Groups_Ozero__class_Ozero(U_2291)),U_2292) = c_Groups_Oone__class_Oone(U_2291)
| U_2292 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_2291)
| ~ class_Power_Opower(U_2291) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
fof(f_727_3,plain,
( ! [U_2291,U_2292] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2291),c_Groups_Ozero__class_Ozero(U_2291)),U_2292) = c_Groups_Ozero__class_Ozero(U_2291)
| U_2292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP231(U_2291,U_2292) )
& ! [U_2291,U_2292] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2291),c_Groups_Ozero__class_Ozero(U_2291)),U_2292) = c_Groups_Oone__class_Oone(U_2291)
| U_2292 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP231(U_2291,U_2292) )
& ! [U_2291,U_2292] :
( sP231(U_2291,U_2292)
| ~ class_Rings_Osemiring__0(U_2291)
| ~ class_Power_Opower(U_2291) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_727_2]) ).
cnf(f_727_4,plain,
( sP231(U_2291,U_2292)
| ~ class_Rings_Osemiring__0(U_2291)
| ~ class_Power_Opower(U_2291) ),
inference(clausify,[status(thm)],[f_727_3]) ).
cnf(f_727_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2291),c_Groups_Ozero__class_Ozero(U_2291)),U_2292) = c_Groups_Oone__class_Oone(U_2291)
| U_2292 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP231(U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_727_3]) ).
cnf(f_727_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2291),c_Groups_Ozero__class_Ozero(U_2291)),U_2292) = c_Groups_Ozero__class_Ozero(U_2291)
| U_2292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP231(U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_727_3]) ).
fof(f_728_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_728_2,plain,
! [U_2295,U_2294,U_2293] :
( c_Orderings_Oord__class_Oless__eq(U_2293,c_Groups_Ozero__class_Ozero(U_2293),hAPP(hAPP(c_Power_Opower__class_Opower(U_2293),c_Groups_Oabs__class_Oabs(U_2293,U_2294)),U_2295))
| ~ class_Rings_Olinordered__idom(U_2293) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
! [U_2295,U_2293,U_2294] :
( c_Orderings_Oord__class_Oless__eq(U_2293,c_Groups_Ozero__class_Ozero(U_2293),hAPP(hAPP(c_Power_Opower__class_Opower(U_2293),c_Groups_Oabs__class_Oabs(U_2293,U_2294)),U_2295))
| ~ class_Rings_Olinordered__idom(U_2293) ),
inference(definitional_conversion,[status(esa)],[f_728_2]) ).
cnf(f_728_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2293,c_Groups_Ozero__class_Ozero(U_2293),hAPP(hAPP(c_Power_Opower__class_Opower(U_2293),c_Groups_Oabs__class_Oabs(U_2293,U_2294)),U_2295))
| ~ class_Rings_Olinordered__idom(U_2293) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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),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_729_2,plain,
! [U_2298,U_2297,U_2296] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),c_Groups_Ouminus__class_Ouminus(U_2296,U_2297)),U_2298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2296),hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),c_Groups_Ouminus__class_Ouminus(U_2296,c_Groups_Oone__class_Oone(U_2296))),U_2298)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),U_2297),U_2298))
| ~ class_Rings_Oring__1(U_2296) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
fof(f_729_3,plain,
! [U_2296,U_2297,U_2298] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),c_Groups_Ouminus__class_Ouminus(U_2296,U_2297)),U_2298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2296),hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),c_Groups_Ouminus__class_Ouminus(U_2296,c_Groups_Oone__class_Oone(U_2296))),U_2298)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),U_2297),U_2298))
| ~ class_Rings_Oring__1(U_2296) ),
inference(definitional_conversion,[status(esa)],[f_729_2]) ).
cnf(f_729_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),c_Groups_Ouminus__class_Ouminus(U_2296,U_2297)),U_2298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2296),hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),c_Groups_Ouminus__class_Ouminus(U_2296,c_Groups_Oone__class_Oone(U_2296))),U_2298)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2296),U_2297),U_2298))
| ~ class_Rings_Oring__1(U_2296) ),
inference(clausify,[status(thm)],[f_729_3]) ).
fof(f_730_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ 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_730_2,plain,
! [U_2302,U_2301,U_2300,U_2299] :
( c_Orderings_Oord__class_Oless(U_2299,hAPP(hAPP(c_Power_Opower__class_Opower(U_2299),U_2302),U_2300),hAPP(hAPP(c_Power_Opower__class_Opower(U_2299),U_2302),U_2301))
| ~ c_Orderings_Oord__class_Oless(U_2299,c_Groups_Oone__class_Oone(U_2299),U_2302)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2300,U_2301)
| ~ class_Rings_Olinordered__semidom(U_2299) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
! [U_2299,U_2300,U_2301,U_2302] :
( c_Orderings_Oord__class_Oless(U_2299,hAPP(hAPP(c_Power_Opower__class_Opower(U_2299),U_2302),U_2300),hAPP(hAPP(c_Power_Opower__class_Opower(U_2299),U_2302),U_2301))
| ~ c_Orderings_Oord__class_Oless(U_2299,c_Groups_Oone__class_Oone(U_2299),U_2302)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2300,U_2301)
| ~ class_Rings_Olinordered__semidom(U_2299) ),
inference(definitional_conversion,[status(esa)],[f_730_2]) ).
cnf(f_730_4,plain,
( c_Orderings_Oord__class_Oless(U_2299,hAPP(hAPP(c_Power_Opower__class_Opower(U_2299),U_2302),U_2300),hAPP(hAPP(c_Power_Opower__class_Opower(U_2299),U_2302),U_2301))
| ~ c_Orderings_Oord__class_Oless(U_2299,c_Groups_Oone__class_Oone(U_2299),U_2302)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2300,U_2301)
| ~ class_Rings_Olinordered__semidom(U_2299) ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ 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))
| ~ 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_731_2,plain,
! [U_2306,U_2305,U_2304,U_2303] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2305,U_2306)
| ~ c_Orderings_Oord__class_Oless(U_2303,hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2305),hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2306))
| ~ c_Orderings_Oord__class_Oless(U_2303,c_Groups_Oone__class_Oone(U_2303),U_2304)
| ~ class_Rings_Olinordered__semidom(U_2303) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
fof(f_731_3,plain,
! [U_2303,U_2304,U_2305,U_2306] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2305,U_2306)
| ~ c_Orderings_Oord__class_Oless(U_2303,hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2305),hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2306))
| ~ c_Orderings_Oord__class_Oless(U_2303,c_Groups_Oone__class_Oone(U_2303),U_2304)
| ~ class_Rings_Olinordered__semidom(U_2303) ),
inference(definitional_conversion,[status(esa)],[f_731_2]) ).
cnf(f_731_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2305,U_2306)
| ~ c_Orderings_Oord__class_Oless(U_2303,hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2305),hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2306))
| ~ c_Orderings_Oord__class_Oless(U_2303,c_Groups_Oone__class_Oone(U_2303),U_2304)
| ~ class_Rings_Olinordered__semidom(U_2303) ),
inference(clausify,[status(thm)],[f_731_3]) ).
fof(f_732_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_732_2,plain,
! [U_2310,U_2309,U_2308,U_2307] :
( ( ( c_Orderings_Oord__class_Oless(U_2307,hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2310))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2309,U_2310) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2309,U_2310)
| ~ c_Orderings_Oord__class_Oless(U_2307,hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2310)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2307,c_Groups_Oone__class_Oone(U_2307),U_2308)
| ~ class_Rings_Olinordered__semidom(U_2307) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
fof(f_732_3,plain,
( ! [U_2307,U_2308,U_2309,U_2310] :
( c_Orderings_Oord__class_Oless(U_2307,hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2310))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2309,U_2310)
| ~ sP232(U_2307,U_2308,U_2309,U_2310) )
& ! [U_2307,U_2308,U_2309,U_2310] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2309,U_2310)
| ~ c_Orderings_Oord__class_Oless(U_2307,hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2310))
| ~ sP232(U_2307,U_2308,U_2309,U_2310) )
& ! [U_2307,U_2308,U_2309,U_2310] :
( sP232(U_2307,U_2308,U_2309,U_2310)
| ~ c_Orderings_Oord__class_Oless(U_2307,c_Groups_Oone__class_Oone(U_2307),U_2308)
| ~ class_Rings_Olinordered__semidom(U_2307) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_732_2]) ).
cnf(f_732_4,plain,
( sP232(U_2307,U_2308,U_2309,U_2310)
| ~ c_Orderings_Oord__class_Oless(U_2307,c_Groups_Oone__class_Oone(U_2307),U_2308)
| ~ class_Rings_Olinordered__semidom(U_2307) ),
inference(clausify,[status(thm)],[f_732_3]) ).
cnf(f_732_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2309,U_2310)
| ~ c_Orderings_Oord__class_Oless(U_2307,hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2310))
| ~ sP232(U_2307,U_2308,U_2309,U_2310) ),
inference(clausify,[status(thm)],[f_732_3]) ).
cnf(f_732_6,plain,
( c_Orderings_Oord__class_Oless(U_2307,hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2307),U_2308),U_2310))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2309,U_2310)
| ~ sP232(U_2307,U_2308,U_2309,U_2310) ),
inference(clausify,[status(thm)],[f_732_3]) ).
fof(f_733_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ 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_733_2,plain,
! [U_2314,U_2313,U_2312,U_2311] :
( c_Orderings_Oord__class_Oless__eq(U_2311,hAPP(hAPP(c_Power_Opower__class_Opower(U_2311),U_2314),U_2312),hAPP(hAPP(c_Power_Opower__class_Opower(U_2311),U_2314),U_2313))
| ~ c_Orderings_Oord__class_Oless__eq(U_2311,c_Groups_Oone__class_Oone(U_2311),U_2314)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2312,U_2313)
| ~ class_Rings_Olinordered__semidom(U_2311) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
fof(f_733_3,plain,
! [U_2312,U_2311,U_2314,U_2313] :
( c_Orderings_Oord__class_Oless__eq(U_2311,hAPP(hAPP(c_Power_Opower__class_Opower(U_2311),U_2314),U_2312),hAPP(hAPP(c_Power_Opower__class_Opower(U_2311),U_2314),U_2313))
| ~ c_Orderings_Oord__class_Oless__eq(U_2311,c_Groups_Oone__class_Oone(U_2311),U_2314)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2312,U_2313)
| ~ class_Rings_Olinordered__semidom(U_2311) ),
inference(definitional_conversion,[status(esa)],[f_733_2]) ).
cnf(f_733_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2311,hAPP(hAPP(c_Power_Opower__class_Opower(U_2311),U_2314),U_2312),hAPP(hAPP(c_Power_Opower__class_Opower(U_2311),U_2314),U_2313))
| ~ c_Orderings_Oord__class_Oless__eq(U_2311,c_Groups_Oone__class_Oone(U_2311),U_2314)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2312,U_2313)
| ~ class_Rings_Olinordered__semidom(U_2311) ),
inference(clausify,[status(thm)],[f_733_3]) ).
fof(f_734_1,plain,
! [V_n,V_a,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ 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_734_2,plain,
! [U_2317,U_2316,U_2315] :
( c_Orderings_Oord__class_Oless(U_2315,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2315),U_2316),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317))
| ~ c_Orderings_Oord__class_Oless(U_2315,U_2316,c_Groups_Oone__class_Oone(U_2315))
| ~ c_Orderings_Oord__class_Oless(U_2315,c_Groups_Ozero__class_Ozero(U_2315),U_2316)
| ~ class_Rings_Olinordered__semidom(U_2315) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
fof(f_734_3,plain,
! [U_2315,U_2316,U_2317] :
( c_Orderings_Oord__class_Oless(U_2315,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2315),U_2316),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317))
| ~ c_Orderings_Oord__class_Oless(U_2315,U_2316,c_Groups_Oone__class_Oone(U_2315))
| ~ c_Orderings_Oord__class_Oless(U_2315,c_Groups_Ozero__class_Ozero(U_2315),U_2316)
| ~ class_Rings_Olinordered__semidom(U_2315) ),
inference(definitional_conversion,[status(esa)],[f_734_2]) ).
cnf(f_734_4,plain,
( c_Orderings_Oord__class_Oless(U_2315,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2315),U_2316),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317))
| ~ c_Orderings_Oord__class_Oless(U_2315,U_2316,c_Groups_Oone__class_Oone(U_2315))
| ~ c_Orderings_Oord__class_Oless(U_2315,c_Groups_Ozero__class_Ozero(U_2315),U_2316)
| ~ class_Rings_Olinordered__semidom(U_2315) ),
inference(clausify,[status(thm)],[f_734_3]) ).
fof(f_735_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ 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_735_2,plain,
! [U_2321,U_2320,U_2319,U_2318] :
( c_Orderings_Oord__class_Oless(U_2318,hAPP(hAPP(c_Power_Opower__class_Opower(U_2318),U_2321),U_2320),hAPP(hAPP(c_Power_Opower__class_Opower(U_2318),U_2321),U_2319))
| ~ c_Orderings_Oord__class_Oless(U_2318,U_2321,c_Groups_Oone__class_Oone(U_2318))
| ~ c_Orderings_Oord__class_Oless(U_2318,c_Groups_Ozero__class_Ozero(U_2318),U_2321)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2320)
| ~ class_Rings_Olinordered__semidom(U_2318) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
fof(f_735_3,plain,
! [U_2318,U_2319,U_2320,U_2321] :
( c_Orderings_Oord__class_Oless(U_2318,hAPP(hAPP(c_Power_Opower__class_Opower(U_2318),U_2321),U_2320),hAPP(hAPP(c_Power_Opower__class_Opower(U_2318),U_2321),U_2319))
| ~ c_Orderings_Oord__class_Oless(U_2318,U_2321,c_Groups_Oone__class_Oone(U_2318))
| ~ c_Orderings_Oord__class_Oless(U_2318,c_Groups_Ozero__class_Ozero(U_2318),U_2321)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2320)
| ~ class_Rings_Olinordered__semidom(U_2318) ),
inference(definitional_conversion,[status(esa)],[f_735_2]) ).
cnf(f_735_4,plain,
( c_Orderings_Oord__class_Oless(U_2318,hAPP(hAPP(c_Power_Opower__class_Opower(U_2318),U_2321),U_2320),hAPP(hAPP(c_Power_Opower__class_Opower(U_2318),U_2321),U_2319))
| ~ c_Orderings_Oord__class_Oless(U_2318,U_2321,c_Groups_Oone__class_Oone(U_2318))
| ~ c_Orderings_Oord__class_Oless(U_2318,c_Groups_Ozero__class_Ozero(U_2318),U_2321)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2320)
| ~ class_Rings_Olinordered__semidom(U_2318) ),
inference(clausify,[status(thm)],[f_735_3]) ).
fof(f_736_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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_736_2,plain,
! [U_2325,U_2324,U_2323,U_2322] :
( U_2323 = U_2325
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2324)
| ~ c_Orderings_Oord__class_Oless__eq(U_2322,c_Groups_Ozero__class_Ozero(U_2322),U_2325)
| ~ c_Orderings_Oord__class_Oless__eq(U_2322,c_Groups_Ozero__class_Ozero(U_2322),U_2323)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2322),U_2323),U_2324) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2322),U_2325),U_2324)
| ~ class_Rings_Olinordered__semidom(U_2322) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
fof(f_736_3,plain,
! [U_2322,U_2323,U_2324,U_2325] :
( U_2323 = U_2325
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2324)
| ~ c_Orderings_Oord__class_Oless__eq(U_2322,c_Groups_Ozero__class_Ozero(U_2322),U_2325)
| ~ c_Orderings_Oord__class_Oless__eq(U_2322,c_Groups_Ozero__class_Ozero(U_2322),U_2323)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2322),U_2323),U_2324) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2322),U_2325),U_2324)
| ~ class_Rings_Olinordered__semidom(U_2322) ),
inference(definitional_conversion,[status(esa)],[f_736_2]) ).
cnf(f_736_4,plain,
( U_2323 = U_2325
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2324)
| ~ c_Orderings_Oord__class_Oless__eq(U_2322,c_Groups_Ozero__class_Ozero(U_2322),U_2325)
| ~ c_Orderings_Oord__class_Oless__eq(U_2322,c_Groups_Ozero__class_Ozero(U_2322),U_2323)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2322),U_2323),U_2324) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2322),U_2325),U_2324)
| ~ class_Rings_Olinordered__semidom(U_2322) ),
inference(clausify,[status(thm)],[f_736_3]) ).
fof(f_737_1,plain,
! [V_a,V_N,V_n,T_a] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ 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_737_2,plain,
! [U_2329,U_2328,U_2327,U_2326] :
( c_Orderings_Oord__class_Oless__eq(U_2326,hAPP(hAPP(c_Power_Opower__class_Opower(U_2326),U_2329),U_2328),hAPP(hAPP(c_Power_Opower__class_Opower(U_2326),U_2329),U_2327))
| ~ c_Orderings_Oord__class_Oless__eq(U_2326,U_2329,c_Groups_Oone__class_Oone(U_2326))
| ~ c_Orderings_Oord__class_Oless__eq(U_2326,c_Groups_Ozero__class_Ozero(U_2326),U_2329)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2327,U_2328)
| ~ class_Rings_Olinordered__semidom(U_2326) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
fof(f_737_3,plain,
! [U_2327,U_2329,U_2328,U_2326] :
( c_Orderings_Oord__class_Oless__eq(U_2326,hAPP(hAPP(c_Power_Opower__class_Opower(U_2326),U_2329),U_2328),hAPP(hAPP(c_Power_Opower__class_Opower(U_2326),U_2329),U_2327))
| ~ c_Orderings_Oord__class_Oless__eq(U_2326,U_2329,c_Groups_Oone__class_Oone(U_2326))
| ~ c_Orderings_Oord__class_Oless__eq(U_2326,c_Groups_Ozero__class_Ozero(U_2326),U_2329)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2327,U_2328)
| ~ class_Rings_Olinordered__semidom(U_2326) ),
inference(definitional_conversion,[status(esa)],[f_737_2]) ).
cnf(f_737_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2326,hAPP(hAPP(c_Power_Opower__class_Opower(U_2326),U_2329),U_2328),hAPP(hAPP(c_Power_Opower__class_Opower(U_2326),U_2329),U_2327))
| ~ c_Orderings_Oord__class_Oless__eq(U_2326,U_2329,c_Groups_Oone__class_Oone(U_2326))
| ~ c_Orderings_Oord__class_Oless__eq(U_2326,c_Groups_Ozero__class_Ozero(U_2326),U_2329)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2327,U_2328)
| ~ class_Rings_Olinordered__semidom(U_2326) ),
inference(clausify,[status(thm)],[f_737_3]) ).
fof(f_738_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_738_2,plain,
! [U_2333,U_2332,U_2331,U_2330] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2330,hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2332),hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2333))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2332,U_2333) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2332,U_2333)
| ~ c_Orderings_Oord__class_Oless__eq(U_2330,hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2332),hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2333)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2330,c_Groups_Oone__class_Oone(U_2330),U_2331)
| ~ class_Rings_Olinordered__semidom(U_2330) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
( ! [U_2332,U_2331,U_2330,U_2333] :
( c_Orderings_Oord__class_Oless__eq(U_2330,hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2332),hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2333))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2332,U_2333)
| ~ sP233(U_2332,U_2331,U_2330,U_2333) )
& ! [U_2332,U_2331,U_2330,U_2333] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2332,U_2333)
| ~ c_Orderings_Oord__class_Oless__eq(U_2330,hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2332),hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2333))
| ~ sP233(U_2332,U_2331,U_2330,U_2333) )
& ! [U_2332,U_2331,U_2330,U_2333] :
( sP233(U_2332,U_2331,U_2330,U_2333)
| ~ c_Orderings_Oord__class_Oless(U_2330,c_Groups_Oone__class_Oone(U_2330),U_2331)
| ~ class_Rings_Olinordered__semidom(U_2330) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_738_2]) ).
cnf(f_738_4,plain,
( sP233(U_2332,U_2331,U_2330,U_2333)
| ~ c_Orderings_Oord__class_Oless(U_2330,c_Groups_Oone__class_Oone(U_2330),U_2331)
| ~ class_Rings_Olinordered__semidom(U_2330) ),
inference(clausify,[status(thm)],[f_738_3]) ).
cnf(f_738_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2332,U_2333)
| ~ c_Orderings_Oord__class_Oless__eq(U_2330,hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2332),hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2333))
| ~ sP233(U_2332,U_2331,U_2330,U_2333) ),
inference(clausify,[status(thm)],[f_738_3]) ).
cnf(f_738_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2330,hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2332),hAPP(hAPP(c_Power_Opower__class_Opower(U_2330),U_2331),U_2333))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2332,U_2333)
| ~ sP233(U_2332,U_2331,U_2330,U_2333) ),
inference(clausify,[status(thm)],[f_738_3]) ).
fof(f_739_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ 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))
| ~ 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_739_2,plain,
! [U_2337,U_2336,U_2335,U_2334] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Power_Opower__class_Opower(U_2334),U_2335),U_2336),hAPP(hAPP(c_Power_Opower__class_Opower(U_2334),U_2335),U_2337))
| ~ c_Orderings_Oord__class_Oless(U_2334,c_Groups_Oone__class_Oone(U_2334),U_2335)
| ~ class_Rings_Olinordered__semidom(U_2334) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
fof(f_739_3,plain,
! [U_2337,U_2335,U_2336,U_2334] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Power_Opower__class_Opower(U_2334),U_2335),U_2336),hAPP(hAPP(c_Power_Opower__class_Opower(U_2334),U_2335),U_2337))
| ~ c_Orderings_Oord__class_Oless(U_2334,c_Groups_Oone__class_Oone(U_2334),U_2335)
| ~ class_Rings_Olinordered__semidom(U_2334) ),
inference(definitional_conversion,[status(esa)],[f_739_2]) ).
cnf(f_739_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Power_Opower__class_Opower(U_2334),U_2335),U_2336),hAPP(hAPP(c_Power_Opower__class_Opower(U_2334),U_2335),U_2337))
| ~ c_Orderings_Oord__class_Oless(U_2334,c_Groups_Oone__class_Oone(U_2334),U_2335)
| ~ class_Rings_Olinordered__semidom(U_2334) ),
inference(clausify,[status(thm)],[f_739_3]) ).
fof(f_740_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_k] :
( ! [B_x] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) )
& ( ? [B_k] :
( ? [B_x] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) )
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff2]) ).
fof(f_740_2,plain,
! [U_2345,U_2344] :
( ( ( c_SEQ_OBseq(U_2344,U_2345)
| ! [U_2343] :
( ! [U_2342] :
? [U_2341] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2341),c_Groups_Ouminus__class_Ouminus(U_2344,U_2342))),U_2343)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2343) ) )
& ( ? [U_2340] :
( ? [U_2339] :
! [U_2338] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2338),c_Groups_Ouminus__class_Ouminus(U_2344,U_2339))),U_2340)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2340) )
| ~ c_SEQ_OBseq(U_2344,U_2345) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2344) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
fof(f_740_3,plain,
! [U_2345,U_2344] :
( ( ( c_SEQ_OBseq(U_2344,U_2345)
| ! [U_2343] :
( ! [U_2342] :
? [U_2341] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2341),c_Groups_Ouminus__class_Ouminus(U_2344,U_2342))),U_2343)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2343) ) )
& ( ( ? [U_2339] :
! [U_2338] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2338),c_Groups_Ouminus__class_Ouminus(U_2344,U_2339))),sK31(U_2345,U_2344))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK31(U_2345,U_2344)) )
| ~ c_SEQ_OBseq(U_2344,U_2345) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2344) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_2340,sK31(U_2345,U_2344))],[f_740_2]) ).
fof(f_740_4,plain,
! [U_2345,U_2344] :
( ( ( c_SEQ_OBseq(U_2344,U_2345)
| ! [U_2343] :
( ! [U_2342] :
? [U_2341] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2341),c_Groups_Ouminus__class_Ouminus(U_2344,U_2342))),U_2343)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2343) ) )
& ( ( ! [U_2338] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2338),c_Groups_Ouminus__class_Ouminus(U_2344,sK32(U_2345,U_2344)))),sK31(U_2345,U_2344))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK31(U_2345,U_2344)) )
| ~ c_SEQ_OBseq(U_2344,U_2345) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2344) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_2339,sK32(U_2345,U_2344))],[f_740_3]) ).
fof(f_740_5,plain,
! [U_2345,U_2344] :
( ( ( c_SEQ_OBseq(U_2344,U_2345)
| ! [U_2343] :
( ! [U_2342] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,sK33(U_2345,U_2344,U_2343,U_2342)),c_Groups_Ouminus__class_Ouminus(U_2344,U_2342))),U_2343)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2343) ) )
& ( ( ! [U_2338] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2338),c_Groups_Ouminus__class_Ouminus(U_2344,sK32(U_2345,U_2344)))),sK31(U_2345,U_2344))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK31(U_2345,U_2344)) )
| ~ c_SEQ_OBseq(U_2344,U_2345) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2344) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_2341,sK33(U_2345,U_2344,U_2343,U_2342))],[f_740_4]) ).
fof(f_740_6,plain,
( ! [U_2338,U_2344,U_2345] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2338),c_Groups_Ouminus__class_Ouminus(U_2344,sK32(U_2345,U_2344)))),sK31(U_2345,U_2344))
| ~ sP234(U_2338,U_2344,U_2345) )
& ! [U_2338,U_2344,U_2345] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK31(U_2345,U_2344))
| ~ sP234(U_2338,U_2344,U_2345) )
& ! [U_2338,U_2342,U_2343,U_2344,U_2345] :
( c_SEQ_OBseq(U_2344,U_2345)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,sK33(U_2345,U_2344,U_2343,U_2342)),c_Groups_Ouminus__class_Ouminus(U_2344,U_2342))),U_2343)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2343)
| ~ sP235(U_2338,U_2342,U_2343,U_2344,U_2345) )
& ! [U_2338,U_2342,U_2343,U_2344,U_2345] :
( sP234(U_2338,U_2344,U_2345)
| ~ c_SEQ_OBseq(U_2344,U_2345)
| ~ sP235(U_2338,U_2342,U_2343,U_2344,U_2345) )
& ! [U_2338,U_2342,U_2343,U_2344,U_2345] :
( sP235(U_2338,U_2342,U_2343,U_2344,U_2345)
| ~ class_RealVector_Oreal__normed__vector(U_2344) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234,sP235])],[f_740_5]) ).
cnf(f_740_7,plain,
( sP235(U_2338,U_2342,U_2343,U_2344,U_2345)
| ~ class_RealVector_Oreal__normed__vector(U_2344) ),
inference(clausify,[status(thm)],[f_740_6]) ).
cnf(f_740_8,plain,
( sP234(U_2338,U_2344,U_2345)
| ~ c_SEQ_OBseq(U_2344,U_2345)
| ~ sP235(U_2338,U_2342,U_2343,U_2344,U_2345) ),
inference(clausify,[status(thm)],[f_740_6]) ).
cnf(f_740_9,plain,
( c_SEQ_OBseq(U_2344,U_2345)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,sK33(U_2345,U_2344,U_2343,U_2342)),c_Groups_Ouminus__class_Ouminus(U_2344,U_2342))),U_2343)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2343)
| ~ sP235(U_2338,U_2342,U_2343,U_2344,U_2345) ),
inference(clausify,[status(thm)],[f_740_6]) ).
cnf(f_740_10,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK31(U_2345,U_2344))
| ~ sP234(U_2338,U_2344,U_2345) ),
inference(clausify,[status(thm)],[f_740_6]) ).
cnf(f_740_11,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2344,c_Groups_Oplus__class_Oplus(U_2344,hAPP(U_2345,U_2338),c_Groups_Ouminus__class_Ouminus(U_2344,sK32(U_2345,U_2344)))),sK31(U_2345,U_2344))
| ~ sP234(U_2338,U_2344,U_2345) ),
inference(clausify,[status(thm)],[f_740_6]) ).
fof(f_741_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_k] :
( ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) )
& ( ? [B_k] :
( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) )
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff3]) ).
fof(f_741_2,plain,
! [U_2353,U_2352] :
( ( ( c_SEQ_OBseq(U_2352,U_2353)
| ! [U_2351] :
( ! [U_2350] :
? [U_2349] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2349),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2350)))),U_2351)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2351) ) )
& ( ? [U_2348] :
( ? [U_2347] :
! [U_2346] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2346),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2347)))),U_2348)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2348) )
| ~ c_SEQ_OBseq(U_2352,U_2353) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2352) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
fof(f_741_3,plain,
! [U_2353,U_2352] :
( ( ( c_SEQ_OBseq(U_2352,U_2353)
| ! [U_2351] :
( ! [U_2350] :
? [U_2349] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2349),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2350)))),U_2351)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2351) ) )
& ( ( ? [U_2347] :
! [U_2346] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2346),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2347)))),sK34(U_2353,U_2352))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK34(U_2353,U_2352)) )
| ~ c_SEQ_OBseq(U_2352,U_2353) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2352) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_2348,sK34(U_2353,U_2352))],[f_741_2]) ).
fof(f_741_4,plain,
! [U_2353,U_2352] :
( ( ( c_SEQ_OBseq(U_2352,U_2353)
| ! [U_2351] :
( ! [U_2350] :
? [U_2349] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2349),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2350)))),U_2351)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2351) ) )
& ( ( ! [U_2346] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2346),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,sK35(U_2353,U_2352))))),sK34(U_2353,U_2352))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK34(U_2353,U_2352)) )
| ~ c_SEQ_OBseq(U_2352,U_2353) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2352) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_2347,sK35(U_2353,U_2352))],[f_741_3]) ).
fof(f_741_5,plain,
! [U_2353,U_2352] :
( ( ( c_SEQ_OBseq(U_2352,U_2353)
| ! [U_2351] :
( ! [U_2350] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,sK36(U_2353,U_2352,U_2351,U_2350)),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2350)))),U_2351)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2351) ) )
& ( ( ! [U_2346] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2346),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,sK35(U_2353,U_2352))))),sK34(U_2353,U_2352))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK34(U_2353,U_2352)) )
| ~ c_SEQ_OBseq(U_2352,U_2353) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2352) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_2349,sK36(U_2353,U_2352,U_2351,U_2350))],[f_741_4]) ).
fof(f_741_6,plain,
( ! [U_2346,U_2353,U_2352] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2346),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,sK35(U_2353,U_2352))))),sK34(U_2353,U_2352))
| ~ sP236(U_2346,U_2353,U_2352) )
& ! [U_2346,U_2353,U_2352] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK34(U_2353,U_2352))
| ~ sP236(U_2346,U_2353,U_2352) )
& ! [U_2351,U_2346,U_2353,U_2352,U_2350] :
( c_SEQ_OBseq(U_2352,U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,sK36(U_2353,U_2352,U_2351,U_2350)),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2350)))),U_2351)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2351)
| ~ sP237(U_2351,U_2346,U_2353,U_2352,U_2350) )
& ! [U_2351,U_2346,U_2353,U_2352,U_2350] :
( sP236(U_2346,U_2353,U_2352)
| ~ c_SEQ_OBseq(U_2352,U_2353)
| ~ sP237(U_2351,U_2346,U_2353,U_2352,U_2350) )
& ! [U_2351,U_2346,U_2353,U_2352,U_2350] :
( sP237(U_2351,U_2346,U_2353,U_2352,U_2350)
| ~ class_RealVector_Oreal__normed__vector(U_2352) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236,sP237])],[f_741_5]) ).
cnf(f_741_7,plain,
( sP237(U_2351,U_2346,U_2353,U_2352,U_2350)
| ~ class_RealVector_Oreal__normed__vector(U_2352) ),
inference(clausify,[status(thm)],[f_741_6]) ).
cnf(f_741_8,plain,
( sP236(U_2346,U_2353,U_2352)
| ~ c_SEQ_OBseq(U_2352,U_2353)
| ~ sP237(U_2351,U_2346,U_2353,U_2352,U_2350) ),
inference(clausify,[status(thm)],[f_741_6]) ).
cnf(f_741_9,plain,
( c_SEQ_OBseq(U_2352,U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,sK36(U_2353,U_2352,U_2351,U_2350)),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,U_2350)))),U_2351)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2351)
| ~ sP237(U_2351,U_2346,U_2353,U_2352,U_2350) ),
inference(clausify,[status(thm)],[f_741_6]) ).
cnf(f_741_10,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK34(U_2353,U_2352))
| ~ sP236(U_2346,U_2353,U_2352) ),
inference(clausify,[status(thm)],[f_741_6]) ).
cnf(f_741_11,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2352,c_Groups_Oplus__class_Oplus(U_2352,hAPP(U_2353,U_2346),c_Groups_Ouminus__class_Ouminus(U_2352,hAPP(U_2353,sK35(U_2353,U_2352))))),sK34(U_2353,U_2352))
| ~ sP236(U_2346,U_2353,U_2352) ),
inference(clausify,[status(thm)],[f_741_6]) ).
fof(f_742_1,plain,
! [T_a] :
( c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).
fof(f_742_2,plain,
! [U_2354] :
( c_Power_Opower__class_Opower(U_2354) = c_Power_Opower_Opower(U_2354,c_Groups_Oone__class_Oone(U_2354),c_Groups_Otimes__class_Otimes(U_2354))
| ~ class_Power_Opower(U_2354) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
fof(f_742_3,plain,
! [U_2354] :
( c_Power_Opower__class_Opower(U_2354) = c_Power_Opower_Opower(U_2354,c_Groups_Oone__class_Oone(U_2354),c_Groups_Otimes__class_Otimes(U_2354))
| ~ class_Power_Opower(U_2354) ),
inference(definitional_conversion,[status(esa)],[f_742_2]) ).
cnf(f_742_4,plain,
( c_Power_Opower__class_Opower(U_2354) = c_Power_Opower_Opower(U_2354,c_Groups_Oone__class_Oone(U_2354),c_Groups_Otimes__class_Otimes(U_2354))
| ~ class_Power_Opower(U_2354) ),
inference(clausify,[status(thm)],[f_742_3]) ).
fof(f_743_1,plain,
! [V_n,V_x] : 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)),
inference(fof_nnf,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(f_743_2,plain,
! [U_2356,U_2355] : 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2355)),U_2356)),
inference(variable_rename,[status(thm)],[f_743_1]) ).
fof(f_743_3,plain,
! [U_2355,U_2356] : 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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2355)),U_2356)),
inference(definitional_conversion,[status(esa)],[f_743_2]) ).
cnf(f_743_4,plain,
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),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2355)),U_2356)),
inference(clausify,[status(thm)],[f_743_3]) ).
fof(f_744_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,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_744_2,plain,
! [U_2358,U_2357] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2357,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2358,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2357,U_2358) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2357,U_2358)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2357,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2358,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
fof(f_744_3,plain,
( ! [U_2362,U_2360] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2360,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2362,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2360,U_2362) )
& ! [U_2361,U_2359] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2359,U_2361)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2359,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2361,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_744_2]) ).
fof(f_744_4,plain,
( ! [U_2360,U_2362] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2360,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2362,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2360,U_2362) )
& ! [U_2361,U_2359] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2359,U_2361)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2359,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2361,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_744_3]) ).
cnf(f_744_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2359,U_2361)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2359,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2361,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_744_4]) ).
cnf(f_744_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2360,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2362,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2360,U_2362) ),
inference(clausify,[status(thm)],[f_744_4]) ).
fof(f_745_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)
| ~ 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_745_2,plain,
! [U_2363] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2363)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2363) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2363)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2363) ) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
( ! [U_2365] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2365)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2365) )
& ! [U_2364] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2364) ) ),
inference(miniscope,[status(thm)],[f_745_2]) ).
fof(f_745_4,plain,
( ! [U_2365] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2365)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2365) )
& ! [U_2364] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2364) ) ),
inference(definitional_conversion,[status(esa)],[f_745_3]) ).
cnf(f_745_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2364)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2364) ),
inference(clausify,[status(thm)],[f_745_4]) ).
cnf(f_745_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2365)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2365) ),
inference(clausify,[status(thm)],[f_745_4]) ).
fof(f_746_1,plain,
! [V_w_2,V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
| V_z_2 = V_w_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
& ( ( V_z_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_746_2,plain,
! [U_2367,U_2366] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2366,U_2367)
| U_2366 = U_2367
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2366,U_2367) )
& ( ( U_2366 != U_2367
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2366,U_2367) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2366,U_2367) ) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
fof(f_746_3,plain,
( ! [U_2371,U_2369] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2369,U_2371)
| U_2369 = U_2371
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2369,U_2371) )
& ! [U_2370,U_2368] :
( ( U_2368 != U_2370
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2368,U_2370) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2368,U_2370) ) ),
inference(miniscope,[status(thm)],[f_746_2]) ).
fof(f_746_4,plain,
( ! [U_2368,U_2370] :
( U_2368 != U_2370
| ~ sP238(U_2368,U_2370) )
& ! [U_2368,U_2370] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2368,U_2370)
| ~ sP238(U_2368,U_2370) )
& ! [U_2369,U_2371] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2369,U_2371)
| U_2369 = U_2371
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2369,U_2371) )
& ! [U_2368,U_2370] :
( sP238(U_2368,U_2370)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2368,U_2370) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238])],[f_746_3]) ).
cnf(f_746_5,plain,
( sP238(U_2368,U_2370)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2368,U_2370) ),
inference(clausify,[status(thm)],[f_746_4]) ).
cnf(f_746_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2369,U_2371)
| U_2369 = U_2371
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2369,U_2371) ),
inference(clausify,[status(thm)],[f_746_4]) ).
cnf(f_746_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2368,U_2370)
| ~ sP238(U_2368,U_2370) ),
inference(clausify,[status(thm)],[f_746_4]) ).
cnf(f_746_8,plain,
( U_2368 != U_2370
| ~ sP238(U_2368,U_2370) ),
inference(clausify,[status(thm)],[f_746_4]) ).
fof(f_747_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,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_747_2,plain,
! [U_2373,U_2372] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2372,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2373,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2372,U_2373) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2372,U_2373)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2372,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2373,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
fof(f_747_3,plain,
( ! [U_2377,U_2375] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2375,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2377,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2375,U_2377) )
& ! [U_2376,U_2374] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2374,U_2376)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2374,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2376,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_747_2]) ).
fof(f_747_4,plain,
( ! [U_2377,U_2375] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2375,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2377,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2375,U_2377) )
& ! [U_2374,U_2376] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2374,U_2376)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2374,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2376,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_747_3]) ).
cnf(f_747_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2374,U_2376)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2374,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2376,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_747_4]) ).
cnf(f_747_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2375,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2377,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2375,U_2377) ),
inference(clausify,[status(thm)],[f_747_4]) ).
fof(f_748_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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_748_2,plain,
! [U_2379,U_2378] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2378,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2379)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2378,U_2379) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2378,U_2379)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2378,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2379) ) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
fof(f_748_3,plain,
( ! [U_2383,U_2381] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2381,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2383)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2381,U_2383) )
& ! [U_2382,U_2380] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2380,U_2382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2380,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2382) ) ),
inference(miniscope,[status(thm)],[f_748_2]) ).
fof(f_748_4,plain,
( ! [U_2381,U_2383] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2381,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2383)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2381,U_2383) )
& ! [U_2380,U_2382] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2380,U_2382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2380,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2382) ) ),
inference(definitional_conversion,[status(esa)],[f_748_3]) ).
cnf(f_748_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2380,U_2382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2380,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2382) ),
inference(clausify,[status(thm)],[f_748_4]) ).
cnf(f_748_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2381,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2383)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2381,U_2383) ),
inference(clausify,[status(thm)],[f_748_4]) ).
fof(f_749_1,plain,
! [V_z] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))
| ~ 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_749_2,plain,
! [U_2384] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2384))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2384) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
fof(f_749_3,plain,
! [U_2384] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2384))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2384) ),
inference(definitional_conversion,[status(esa)],[f_749_2]) ).
cnf(f_749_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2384))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2384) ),
inference(clausify,[status(thm)],[f_749_3]) ).
fof(f_750_1,plain,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) ),
inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).
fof(f_750_2,plain,
! [U_2386,U_2385] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2385,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2385,U_2386) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
fof(f_750_3,plain,
! [U_2385,U_2386] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2385,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2385,U_2386) ),
inference(definitional_conversion,[status(esa)],[f_750_2]) ).
cnf(f_750_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2385,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2385,U_2386) ),
inference(clausify,[status(thm)],[f_750_3]) ).
fof(f_751_1,plain,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).
fof(f_751_2,plain,
! [U_2390,U_2389,U_2388,U_2387] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2387,U_2389),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2388,U_2390))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2389,U_2390)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2387,U_2388) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
fof(f_751_3,plain,
! [U_2388,U_2387,U_2389,U_2390] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2387,U_2389),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2388,U_2390))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2389,U_2390)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2387,U_2388) ),
inference(definitional_conversion,[status(esa)],[f_751_2]) ).
cnf(f_751_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2387,U_2389),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2388,U_2390))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2389,U_2390)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2387,U_2388) ),
inference(clausify,[status(thm)],[f_751_3]) ).
fof(f_752_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_752_2,plain,
! [U_2391] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2391),U_2391) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_752_1]) ).
fof(f_752_3,plain,
! [U_2391] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2391),U_2391) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_752_2]) ).
cnf(f_752_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2391),U_2391) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_752_3]) ).
fof(f_753_1,plain,
! [V_z] : 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_753_2,plain,
! [U_2392] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2392) = U_2392,
inference(variable_rename,[status(thm)],[f_753_1]) ).
fof(f_753_3,plain,
! [U_2392] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2392) = U_2392,
inference(definitional_conversion,[status(esa)],[f_753_2]) ).
cnf(f_753_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2392) = U_2392,
inference(clausify,[status(thm)],[f_753_3]) ).
fof(f_754_1,plain,
! [V_z] : 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_754_2,plain,
! [U_2393] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2393,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2393,
inference(variable_rename,[status(thm)],[f_754_1]) ).
fof(f_754_3,plain,
! [U_2393] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2393,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2393,
inference(definitional_conversion,[status(esa)],[f_754_2]) ).
cnf(f_754_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2393,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2393,
inference(clausify,[status(thm)],[f_754_3]) ).
fof(f_755_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).
fof(f_755_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_755_1]) ).
cnf(f_755_3,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_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_756_2,plain,
! [U_2394] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2394) = U_2394,
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
! [U_2394] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2394) = U_2394,
inference(definitional_conversion,[status(esa)],[f_756_2]) ).
cnf(f_756_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2394) = U_2394,
inference(clausify,[status(thm)],[f_756_3]) ).
fof(f_757_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_757_2,plain,
! [U_2395] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2395),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2395,
inference(variable_rename,[status(thm)],[f_757_1]) ).
fof(f_757_3,plain,
! [U_2395] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2395),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2395,
inference(definitional_conversion,[status(esa)],[f_757_2]) ).
cnf(f_757_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2395),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2395,
inference(clausify,[status(thm)],[f_757_3]) ).
fof(f_758_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_758_2,plain,
! [U_2397,U_2396] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2396),U_2397) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2397),U_2396),
inference(variable_rename,[status(thm)],[f_758_1]) ).
fof(f_758_3,plain,
! [U_2396,U_2397] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2396),U_2397) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2397),U_2396),
inference(definitional_conversion,[status(esa)],[f_758_2]) ).
cnf(f_758_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2396),U_2397) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2397),U_2396),
inference(clausify,[status(thm)],[f_758_3]) ).
fof(f_759_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_759_2,plain,
! [U_2400,U_2399,U_2398] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2398),U_2399)),U_2400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2399),U_2400)),
inference(variable_rename,[status(thm)],[f_759_1]) ).
fof(f_759_3,plain,
! [U_2398,U_2399,U_2400] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2398),U_2399)),U_2400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2399),U_2400)),
inference(definitional_conversion,[status(esa)],[f_759_2]) ).
cnf(f_759_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2398),U_2399)),U_2400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2399),U_2400)),
inference(clausify,[status(thm)],[f_759_3]) ).
fof(f_760_1,plain,
! [V_n,V_m] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| 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_760_2,plain,
! [U_2402,U_2401] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2401) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2401),U_2402)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
! [U_2401,U_2402] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2401) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2401),U_2402)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_760_2]) ).
cnf(f_760_4,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2401) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2401),U_2402)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_760_3]) ).
fof(f_761_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = 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_761_2,plain,
! [U_2405,U_2404,U_2403] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2403,U_2404)),U_2405) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2403),U_2405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2404),U_2405)),
inference(variable_rename,[status(thm)],[f_761_1]) ).
fof(f_761_3,plain,
! [U_2403,U_2404,U_2405] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2403,U_2404)),U_2405) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2403),U_2405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2404),U_2405)),
inference(definitional_conversion,[status(esa)],[f_761_2]) ).
cnf(f_761_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2403,U_2404)),U_2405) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2403),U_2405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2404),U_2405)),
inference(clausify,[status(thm)],[f_761_3]) ).
fof(f_762_1,plain,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = 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_762_2,plain,
! [U_2408,U_2407,U_2406] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2407,U_2408)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2408)),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
! [U_2406,U_2407,U_2408] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2407,U_2408)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2408)),
inference(definitional_conversion,[status(esa)],[f_762_2]) ).
cnf(f_762_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2407,U_2408)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2408)),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,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
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) )
& ( V_w_2 = V_z_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,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_763_2,plain,
! [U_2410,U_2409] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2409,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2410,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_2409 != U_2410
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2409,U_2410) ) )
& ( U_2409 = U_2410
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2409,U_2410)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2409,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2410,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
fof(f_763_3,plain,
( ! [U_2414,U_2412] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2412,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2414,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_2412 != U_2414
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2412,U_2414) ) )
& ! [U_2413,U_2411] :
( U_2411 = U_2413
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2411,U_2413)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2411,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2413,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_763_2]) ).
fof(f_763_4,plain,
( ! [U_2414,U_2412] :
( U_2412 != U_2414
| ~ sP239(U_2414,U_2412) )
& ! [U_2414,U_2412] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2412,U_2414)
| ~ sP239(U_2414,U_2412) )
& ! [U_2414,U_2412] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2412,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2414,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| sP239(U_2414,U_2412) )
& ! [U_2411,U_2413] :
( U_2411 = U_2413
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2411,U_2413)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2411,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2413,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239])],[f_763_3]) ).
cnf(f_763_5,plain,
( U_2411 = U_2413
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2411,U_2413)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2411,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2413,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_763_4]) ).
cnf(f_763_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2412,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2414,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| sP239(U_2414,U_2412) ),
inference(clausify,[status(thm)],[f_763_4]) ).
cnf(f_763_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2412,U_2414)
| ~ sP239(U_2414,U_2412) ),
inference(clausify,[status(thm)],[f_763_4]) ).
cnf(f_763_8,plain,
( U_2412 != U_2414
| ~ sP239(U_2414,U_2412) ),
inference(clausify,[status(thm)],[f_763_4]) ).
fof(f_764_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).
fof(f_764_2,plain,
! [U_2417,U_2416,U_2415] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2415,U_2417),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2416,U_2417))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2415,U_2416) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
fof(f_764_3,plain,
! [U_2416,U_2417,U_2415] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2415,U_2417),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2416,U_2417))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2415,U_2416) ),
inference(definitional_conversion,[status(esa)],[f_764_2]) ).
cnf(f_764_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2415,U_2417),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2416,U_2417))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2415,U_2416) ),
inference(clausify,[status(thm)],[f_764_3]) ).
fof(f_765_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).
fof(f_765_2,plain,
! [U_2419,U_2418] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2419,U_2418)
| U_2418 = U_2419
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2418,U_2419) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
fof(f_765_3,plain,
! [U_2419,U_2418] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2419,U_2418)
| U_2418 = U_2419
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2418,U_2419) ),
inference(definitional_conversion,[status(esa)],[f_765_2]) ).
cnf(f_765_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2419,U_2418)
| U_2418 = U_2419
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2418,U_2419) ),
inference(clausify,[status(thm)],[f_765_3]) ).
fof(f_766_1,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).
fof(f_766_2,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_766_1]) ).
cnf(f_766_3,plain,
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_766_2]) ).
fof(f_767_1,plain,
! [V_n_2,V_ma_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_ma_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).
fof(f_767_2,plain,
! [U_2421,U_2420] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2420),U_2421) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2421 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2420 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_2421 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_2420 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2420),U_2421) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2420) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
fof(f_767_3,plain,
( ! [U_2421,U_2420] :
( U_2421 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP240(U_2421,U_2420) )
& ! [U_2421,U_2420] :
( U_2420 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP240(U_2421,U_2420) )
& ! [U_2421,U_2420] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2420),U_2421) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2421 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2420 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP241(U_2421,U_2420) )
& ! [U_2421,U_2420] :
( sP240(U_2421,U_2420)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2420),U_2421) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP241(U_2421,U_2420) )
& ! [U_2421,U_2420] :
( sP241(U_2421,U_2420)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2420) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240,sP241])],[f_767_2]) ).
cnf(f_767_4,plain,
( sP241(U_2421,U_2420)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2420) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_5,plain,
( sP240(U_2421,U_2420)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2420),U_2421) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP241(U_2421,U_2420) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2420),U_2421) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2421 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2420 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP241(U_2421,U_2420) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_7,plain,
( U_2420 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP240(U_2421,U_2420) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_8,plain,
( U_2421 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP240(U_2421,U_2420) ),
inference(clausify,[status(thm)],[f_767_3]) ).
fof(f_768_1,plain,
! [V_k,V_j,V_i] :
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).
fof(f_768_2,plain,
! [U_2424,U_2423,U_2422] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2424),U_2422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2424),U_2423))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2424)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2422,U_2423) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
fof(f_768_3,plain,
! [U_2423,U_2424,U_2422] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2424),U_2422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2424),U_2423))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2424)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2422,U_2423) ),
inference(definitional_conversion,[status(esa)],[f_768_2]) ).
cnf(f_768_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2424),U_2422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2424),U_2423))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2424)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2422,U_2423) ),
inference(clausify,[status(thm)],[f_768_3]) ).
fof(f_769_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_769_2,plain,
! [U_2425] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2425),U_2425),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2425,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2425,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2425),U_2425),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
fof(f_769_3,plain,
( ! [U_2427] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2427),U_2427),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2427,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2426] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2426,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2426),U_2426),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_769_2]) ).
fof(f_769_4,plain,
( ! [U_2427] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2427),U_2427),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2427,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2426] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2426,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2426),U_2426),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_769_3]) ).
cnf(f_769_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2426,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2426),U_2426),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_769_4]) ).
cnf(f_769_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2427),U_2427),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2427,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_769_4]) ).
fof(f_770_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,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)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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_770_2,plain,
! [U_2428] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2428),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2428 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_2428 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2428),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
fof(f_770_3,plain,
( ! [U_2430] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2430),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2430 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2429] :
( U_2429 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2429),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_770_2]) ).
fof(f_770_4,plain,
( ! [U_2430] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2430),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2430 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2429] :
( U_2429 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2429),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_770_3]) ).
cnf(f_770_5,plain,
( U_2429 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2429),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_770_4]) ).
cnf(f_770_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2430),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2430 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_770_4]) ).
fof(f_771_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = 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_771_2,plain,
! [U_2433,U_2432,U_2431] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2431,U_2432)),U_2433) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2431),U_2433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2432),U_2433)),
inference(variable_rename,[status(thm)],[f_771_1]) ).
fof(f_771_3,plain,
! [U_2432,U_2431,U_2433] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2431,U_2432)),U_2433) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2431),U_2433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2432),U_2433)),
inference(definitional_conversion,[status(esa)],[f_771_2]) ).
cnf(f_771_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2431,U_2432)),U_2433) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2431),U_2433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2432),U_2433)),
inference(clausify,[status(thm)],[f_771_3]) ).
fof(f_772_1,plain,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = 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_772_2,plain,
! [U_2435,U_2434] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2434)),U_2435) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2434),U_2435)),
inference(variable_rename,[status(thm)],[f_772_1]) ).
fof(f_772_3,plain,
! [U_2434,U_2435] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2434)),U_2435) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2434),U_2435)),
inference(definitional_conversion,[status(esa)],[f_772_2]) ).
cnf(f_772_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2434)),U_2435) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2434),U_2435)),
inference(clausify,[status(thm)],[f_772_3]) ).
fof(f_773_1,plain,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = 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_773_2,plain,
! [U_2438,U_2437,U_2436] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2437,U_2438)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),U_2437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),U_2438)),
inference(variable_rename,[status(thm)],[f_773_1]) ).
fof(f_773_3,plain,
! [U_2436,U_2437,U_2438] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2437,U_2438)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),U_2437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),U_2438)),
inference(definitional_conversion,[status(esa)],[f_773_2]) ).
cnf(f_773_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2437,U_2438)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),U_2437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2436),U_2438)),
inference(clausify,[status(thm)],[f_773_3]) ).
fof(f_774_1,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).
fof(f_774_2,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_774_1]) ).
cnf(f_774_3,plain,
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_774_2]) ).
fof(f_775_1,plain,
! [V_i] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| 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)
| ~ 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_775_2,plain,
! [U_2439] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2439) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2439) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2439) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2439) ) )
| U_2439 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2439) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2439 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
fof(f_775_3,plain,
( ! [U_2441] :
( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2441) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2441) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2441) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2441) ) )
| U_2441 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2440] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2440) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2440 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_775_2]) ).
fof(f_775_4,plain,
( ! [U_2441] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2441) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2441)
| ~ sP242(U_2441) )
& ! [U_2441] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2441) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2441)
| ~ sP242(U_2441) )
& ! [U_2441] :
( sP242(U_2441)
| U_2441 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2440] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2440) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2440 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_775_3]) ).
cnf(f_775_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2440) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2440 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_775_4]) ).
cnf(f_775_6,plain,
( sP242(U_2441)
| U_2441 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_775_4]) ).
cnf(f_775_7,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2441) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2441)
| ~ sP242(U_2441) ),
inference(clausify,[status(thm)],[f_775_4]) ).
cnf(f_775_8,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2441) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2441)
| ~ sP242(U_2441) ),
inference(clausify,[status(thm)],[f_775_4]) ).
fof(f_776_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ 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_776_2,plain,
! [U_2443,U_2442] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2442,U_2443)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2442,U_2443),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2442,U_2443),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2442,U_2443) ) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
fof(f_776_3,plain,
( ! [U_2447,U_2445] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2445,U_2447)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2445,U_2447),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2446,U_2444] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2444,U_2446),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2444,U_2446) ) ),
inference(miniscope,[status(thm)],[f_776_2]) ).
fof(f_776_4,plain,
( ! [U_2445,U_2447] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2445,U_2447)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2445,U_2447),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2444,U_2446] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2444,U_2446),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2444,U_2446) ) ),
inference(definitional_conversion,[status(esa)],[f_776_3]) ).
cnf(f_776_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2444,U_2446),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2444,U_2446) ),
inference(clausify,[status(thm)],[f_776_4]) ).
cnf(f_776_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2445,U_2447)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2445,U_2447),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_776_4]) ).
fof(f_777_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_777_2,plain,
! [U_2448] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2448),U_2448) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_777_1]) ).
fof(f_777_3,plain,
! [U_2448] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2448),U_2448) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_777_2]) ).
cnf(f_777_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2448),U_2448) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_777_3]) ).
fof(f_778_1,plain,
! [V_i] :
( ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i)
| ~ 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_778_2,plain,
! [U_2449] :
( ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2449) = U_2449
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2449,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2449) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2449)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2449,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
fof(f_778_3,plain,
( ! [U_2451] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2451) = U_2451
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2451,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2450] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2450) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2450)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2450,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_778_2]) ).
fof(f_778_4,plain,
( ! [U_2451] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2451) = U_2451
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2451,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2450] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2450) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2450)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2450,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_778_3]) ).
cnf(f_778_5,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2450) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2450)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2450,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_778_4]) ).
cnf(f_778_6,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2451) = U_2451
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2451,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_778_4]) ).
fof(f_779_1,plain,
! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,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_779_2,plain,
! [U_2455,U_2454,U_2453,U_2452] : hAPP(hAPP(c_Power_Opower_Opower(U_2452,U_2453,U_2454),U_2455),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2453,
inference(variable_rename,[status(thm)],[f_779_1]) ).
fof(f_779_3,plain,
! [U_2454,U_2452,U_2453,U_2455] : hAPP(hAPP(c_Power_Opower_Opower(U_2452,U_2453,U_2454),U_2455),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2453,
inference(definitional_conversion,[status(esa)],[f_779_2]) ).
cnf(f_779_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_2452,U_2453,U_2454),U_2455),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2453,
inference(clausify,[status(thm)],[f_779_3]) ).
fof(f_780_1,plain,
! [V_z,V_x,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z)
| ~ 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_780_2,plain,
! [U_2458,U_2457,U_2456] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2457,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2457,U_2458)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2456)),U_2458)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2456) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
fof(f_780_3,plain,
! [U_2457,U_2456,U_2458] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2457,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2457,U_2458)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2456)),U_2458)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2456) ),
inference(definitional_conversion,[status(esa)],[f_780_2]) ).
cnf(f_780_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2457,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2457,U_2458)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2456)),U_2458)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2456) ),
inference(clausify,[status(thm)],[f_780_3]) ).
fof(f_781_1,plain,
! [V_x,V_z,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))
| ~ 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_781_2,plain,
! [U_2461,U_2460,U_2459] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2460,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2461,U_2460)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2459)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2459) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
fof(f_781_3,plain,
! [U_2459,U_2460,U_2461] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2460,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2461,U_2460)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2459)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2459) ),
inference(definitional_conversion,[status(esa)],[f_781_2]) ).
cnf(f_781_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2460,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2461,U_2460)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2459)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2459) ),
inference(clausify,[status(thm)],[f_781_3]) ).
fof(f_782_1,plain,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(f_782_2,plain,
! [U_2463,U_2462] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2462,U_2463)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2462),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2463)),
inference(variable_rename,[status(thm)],[f_782_1]) ).
fof(f_782_3,plain,
! [U_2462,U_2463] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2462,U_2463)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2462),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2463)),
inference(definitional_conversion,[status(esa)],[f_782_2]) ).
cnf(f_782_4,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2462,U_2463)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2462),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2463)),
inference(clausify,[status(thm)],[f_782_3]) ).
fof(f_783_1,plain,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).
fof(f_783_2,plain,
! [U_2465,U_2464] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2464,U_2465) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2464,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2465)),
inference(variable_rename,[status(thm)],[f_783_1]) ).
fof(f_783_3,plain,
! [U_2465,U_2464] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2464,U_2465) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2464,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2465)),
inference(definitional_conversion,[status(esa)],[f_783_2]) ).
cnf(f_783_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2464,U_2465) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2464,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2465)),
inference(clausify,[status(thm)],[f_783_3]) ).
fof(f_784_1,plain,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(f_784_2,plain,
! [U_2467,U_2466] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2466,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2467)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2466,U_2467),
inference(variable_rename,[status(thm)],[f_784_1]) ).
fof(f_784_3,plain,
! [U_2466,U_2467] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2466,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2467)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2466,U_2467),
inference(definitional_conversion,[status(esa)],[f_784_2]) ).
cnf(f_784_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2466,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2467)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2466,U_2467),
inference(clausify,[status(thm)],[f_784_3]) ).
fof(f_785_1,plain,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).
fof(f_785_2,plain,
! [U_2468] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2468)) = U_2468,
inference(variable_rename,[status(thm)],[f_785_1]) ).
fof(f_785_3,plain,
! [U_2468] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2468)) = U_2468,
inference(definitional_conversion,[status(esa)],[f_785_2]) ).
cnf(f_785_4,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2468)) = U_2468,
inference(clausify,[status(thm)],[f_785_3]) ).
fof(f_786_1,plain,
! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).
fof(f_786_2,plain,
! [U_2471,U_2470,U_2469] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2469,U_2470),U_2471) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2469,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2470,U_2471)),
inference(variable_rename,[status(thm)],[f_786_1]) ).
fof(f_786_3,plain,
! [U_2470,U_2469,U_2471] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2469,U_2470),U_2471) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2469,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2470,U_2471)),
inference(definitional_conversion,[status(esa)],[f_786_2]) ).
cnf(f_786_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2469,U_2470),U_2471) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2469,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2470,U_2471)),
inference(clausify,[status(thm)],[f_786_3]) ).
fof(f_787_1,plain,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).
fof(f_787_2,plain,
! [U_2474,U_2473,U_2472] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2473,U_2474)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2473,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,U_2474)),
inference(variable_rename,[status(thm)],[f_787_1]) ).
fof(f_787_3,plain,
! [U_2472,U_2473,U_2474] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2473,U_2474)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2473,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,U_2474)),
inference(definitional_conversion,[status(esa)],[f_787_2]) ).
cnf(f_787_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2473,U_2474)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2473,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,U_2474)),
inference(clausify,[status(thm)],[f_787_3]) ).
fof(f_788_1,plain,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).
fof(f_788_2,plain,
! [U_2476,U_2475] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2475,U_2476) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2476,U_2475),
inference(variable_rename,[status(thm)],[f_788_1]) ).
fof(f_788_3,plain,
! [U_2476,U_2475] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2475,U_2476) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2476,U_2475),
inference(definitional_conversion,[status(esa)],[f_788_2]) ).
cnf(f_788_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2475,U_2476) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2476,U_2475),
inference(clausify,[status(thm)],[f_788_3]) ).
fof(f_789_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).
fof(f_789_2,plain,
! [U_2478,U_2477] :
( U_2477 = U_2478
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2478,U_2477)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2477,U_2478) ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
fof(f_789_3,plain,
! [U_2478,U_2477] :
( U_2477 = U_2478
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2478,U_2477)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2477,U_2478) ),
inference(definitional_conversion,[status(esa)],[f_789_2]) ).
cnf(f_789_4,plain,
( U_2477 = U_2478
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2478,U_2477)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2477,U_2478) ),
inference(clausify,[status(thm)],[f_789_3]) ).
fof(f_790_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).
fof(f_790_2,plain,
! [U_2481,U_2480,U_2479] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2479,U_2481)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2480,U_2481)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2479,U_2480) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
fof(f_790_3,plain,
! [U_2481,U_2480,U_2479] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2479,U_2481)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2480,U_2481)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2479,U_2480) ),
inference(definitional_conversion,[status(esa)],[f_790_2]) ).
cnf(f_790_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2479,U_2481)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2480,U_2481)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2479,U_2480) ),
inference(clausify,[status(thm)],[f_790_3]) ).
fof(f_791_1,plain,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).
fof(f_791_2,plain,
! [U_2483,U_2482] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,U_2482)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2483) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
fof(f_791_3,plain,
! [U_2483,U_2482] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,U_2482)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2483) ),
inference(definitional_conversion,[status(esa)],[f_791_2]) ).
cnf(f_791_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,U_2482)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2483) ),
inference(clausify,[status(thm)],[f_791_3]) ).
fof(f_792_1,plain,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).
fof(f_792_2,plain,
! [U_2484] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2484,U_2484),
inference(variable_rename,[status(thm)],[f_792_1]) ).
fof(f_792_3,plain,
! [U_2484] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2484,U_2484),
inference(definitional_conversion,[status(esa)],[f_792_2]) ).
cnf(f_792_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2484,U_2484),
inference(clausify,[status(thm)],[f_792_3]) ).
fof(f_793_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).
fof(f_793_2,plain,
! [U_2487,U_2486,U_2485] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,U_2485),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,U_2486))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2485,U_2486) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
fof(f_793_3,plain,
! [U_2486,U_2485,U_2487] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,U_2485),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,U_2486))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2485,U_2486) ),
inference(definitional_conversion,[status(esa)],[f_793_2]) ).
cnf(f_793_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,U_2485),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,U_2486))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2485,U_2486) ),
inference(clausify,[status(thm)],[f_793_3]) ).
fof(f_794_1,plain,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
| V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ 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_2490,U_2489,U_2488] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2490)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2489,U_2488)
| U_2488 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2488),U_2490))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2488) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
fof(f_794_3,plain,
! [U_2488,U_2489,U_2490] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2490)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2489,U_2488)
| U_2488 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2488),U_2490))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2488) ),
inference(definitional_conversion,[status(esa)],[f_794_2]) ).
cnf(f_794_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2490)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2489,U_2488)
| U_2488 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2488),U_2490))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2488) ),
inference(clausify,[status(thm)],[f_794_3]) ).
fof(f_795_1,plain,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
| V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ 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_795_2,plain,
! [U_2493,U_2492,U_2491] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2493,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2492)
| U_2491 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2492,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2491),U_2493))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2491) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
fof(f_795_3,plain,
! [U_2491,U_2492,U_2493] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2493,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2492)
| U_2491 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2492,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2491),U_2493))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2491) ),
inference(definitional_conversion,[status(esa)],[f_795_2]) ).
cnf(f_795_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2493,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2492)
| U_2491 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2492,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2491),U_2493))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2491) ),
inference(clausify,[status(thm)],[f_795_3]) ).
fof(f_796_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_796_2,plain,
! [U_2496,U_2495,U_2494] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2495)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2494)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2496,U_2494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2494),U_2495),U_2496)) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
fof(f_796_3,plain,
! [U_2494,U_2495,U_2496] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2495)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2494)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2496,U_2494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2494),U_2495),U_2496)) ),
inference(definitional_conversion,[status(esa)],[f_796_2]) ).
cnf(f_796_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2495)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2494)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2496,U_2494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2494),U_2495),U_2496)) ),
inference(clausify,[status(thm)],[f_796_3]) ).
fof(f_797_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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_797_2,plain,
! [U_2499,U_2498,U_2497] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2498,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2497)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2499)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2497),U_2498),U_2499),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
fof(f_797_3,plain,
! [U_2498,U_2499,U_2497] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2498,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2497)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2499)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2497),U_2498),U_2499),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(definitional_conversion,[status(esa)],[f_797_2]) ).
cnf(f_797_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2498,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2497)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2499)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2497),U_2498),U_2499),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_797_3]) ).
fof(f_798_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),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_798_2,plain,
! [U_2504,U_2503,U_2502,U_2501,U_2500] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2501,U_2503)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2504,U_2500)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2502,U_2500)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2502)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2500),U_2501),U_2502),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2500),U_2503),U_2504)) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
fof(f_798_3,plain,
! [U_2503,U_2502,U_2504,U_2500,U_2501] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2501,U_2503)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2504,U_2500)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2502,U_2500)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2502)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2500),U_2501),U_2502),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2500),U_2503),U_2504)) ),
inference(definitional_conversion,[status(esa)],[f_798_2]) ).
cnf(f_798_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2501,U_2503)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2504,U_2500)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2502,U_2500)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2502)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2500),U_2501),U_2502),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2500),U_2503),U_2504)) ),
inference(clausify,[status(thm)],[f_798_3]) ).
fof(f_799_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != 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_799_2,plain,
! [U_2510,U_2509,U_2508,U_2507,U_2506,U_2505] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2506,U_2509)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2508,U_2505)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2508)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2507)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2510,U_2508)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2508),U_2509),U_2510))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2505),U_2506),U_2507) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2508),U_2509),U_2510) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
fof(f_799_3,plain,
! [U_2506,U_2507,U_2508,U_2505,U_2509,U_2510] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2506,U_2509)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2508,U_2505)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2508)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2507)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2510,U_2508)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2508),U_2509),U_2510))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2505),U_2506),U_2507) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2508),U_2509),U_2510) ),
inference(definitional_conversion,[status(esa)],[f_799_2]) ).
cnf(f_799_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2506,U_2509)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2508,U_2505)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2508)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2507)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2510,U_2508)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2508),U_2509),U_2510))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2505),U_2506),U_2507) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2508),U_2509),U_2510) ),
inference(clausify,[status(thm)],[f_799_3]) ).
fof(f_800_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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),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_800_2,plain,
! [U_2515,U_2514,U_2513,U_2512,U_2511] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2514,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2511,U_2513)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2511,U_2515)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2515,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2511),U_2512),U_2513),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2511),U_2514),U_2515)) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
fof(f_800_3,plain,
! [U_2514,U_2515,U_2511,U_2512,U_2513] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2514,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2511,U_2513)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2511,U_2515)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2515,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2511),U_2512),U_2513),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2511),U_2514),U_2515)) ),
inference(definitional_conversion,[status(esa)],[f_800_2]) ).
cnf(f_800_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2514,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2511,U_2513)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2511,U_2515)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2515,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2511),U_2512),U_2513),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2511),U_2514),U_2515)) ),
inference(clausify,[status(thm)],[f_800_3]) ).
fof(f_801_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != 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_801_2,plain,
! [U_2521,U_2520,U_2519,U_2518,U_2517,U_2516] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2520,U_2517)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2519,U_2516)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2519)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2521)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2516)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2519),U_2520),U_2521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2516),U_2517),U_2518) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2519),U_2520),U_2521) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
fof(f_801_3,plain,
! [U_2519,U_2518,U_2521,U_2516,U_2517,U_2520] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2520,U_2517)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2519,U_2516)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2519)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2521)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2516)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2519),U_2520),U_2521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2516),U_2517),U_2518) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2519),U_2520),U_2521) ),
inference(definitional_conversion,[status(esa)],[f_801_2]) ).
cnf(f_801_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2520,U_2517)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2519,U_2516)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2519)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2521)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2516)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2519),U_2520),U_2521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2516),U_2517),U_2518) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2519),U_2520),U_2521) ),
inference(clausify,[status(thm)],[f_801_3]) ).
fof(f_802_1,plain,
! [V_n,V_x] :
( 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))
| ~ 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_802_2,plain,
! [U_2523,U_2522] :
( 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_2522),U_2523))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2522) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
fof(f_802_3,plain,
! [U_2523,U_2522] :
( 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_2522),U_2523))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2522) ),
inference(definitional_conversion,[status(esa)],[f_802_2]) ).
cnf(f_802_4,plain,
( 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_2522),U_2523))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2522) ),
inference(clausify,[status(thm)],[f_802_3]) ).
fof(f_803_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq]) ).
fof(f_803_2,plain,
! [U_2525,U_2524] :
( ( 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_2524),U_2525))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2524)
& U_2525 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2524)
| U_2525 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_2524),U_2525)) ) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
fof(f_803_3,plain,
( ! [U_2529,U_2527] :
( 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_2527),U_2529))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2527)
& U_2529 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2528,U_2526] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2526)
| U_2528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_2526),U_2528)) ) ),
inference(miniscope,[status(thm)],[f_803_2]) ).
fof(f_803_4,plain,
( ! [U_2529,U_2527] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2527)
| ~ sP243(U_2529,U_2527) )
& ! [U_2529,U_2527] :
( U_2529 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP243(U_2529,U_2527) )
& ! [U_2529,U_2527] :
( 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_2527),U_2529))
| sP243(U_2529,U_2527) )
& ! [U_2528,U_2526] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2526)
| U_2528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_2526),U_2528)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243])],[f_803_3]) ).
cnf(f_803_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2526)
| U_2528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_2526),U_2528)) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_6,plain,
( 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_2527),U_2529))
| sP243(U_2529,U_2527) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_7,plain,
( U_2529 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP243(U_2529,U_2527) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2527)
| ~ sP243(U_2529,U_2527) ),
inference(clausify,[status(thm)],[f_803_4]) ).
fof(f_804_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
fof(f_804_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_804_1]) ).
cnf(f_804_3,plain,
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_804_2]) ).
fof(f_805_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
fof(f_805_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_805_1]) ).
cnf(f_805_3,plain,
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_805_2]) ).
fof(f_806_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ 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_806_2,plain,
! [U_2531,U_2530] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2530,U_2531))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2531)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2530) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
fof(f_806_3,plain,
! [U_2530,U_2531] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2530,U_2531))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2531)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2530) ),
inference(definitional_conversion,[status(esa)],[f_806_2]) ).
cnf(f_806_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2530,U_2531))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2531)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2530) ),
inference(clausify,[status(thm)],[f_806_3]) ).
fof(f_807_1,plain,
! [V_y,V_x] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ 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_807_2,plain,
! [U_2533,U_2532] :
( 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_2532),U_2533))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2533)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2532) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
fof(f_807_3,plain,
! [U_2532,U_2533] :
( 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_2532),U_2533))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2533)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2532) ),
inference(definitional_conversion,[status(esa)],[f_807_2]) ).
cnf(f_807_4,plain,
( 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_2532),U_2533))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2533)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2532) ),
inference(clausify,[status(thm)],[f_807_3]) ).
fof(f_808_1,plain,
! [V_x,V_y] :
( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) )
& ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ) ),
inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).
fof(f_808_2,plain,
! [U_2535,U_2534] :
( ( c_Nat__Transfer_Otsub(U_2535,U_2534) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2534,U_2535) )
& ( c_Nat__Transfer_Otsub(U_2535,U_2534) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2535,U_2534)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2534,U_2535) ) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
fof(f_808_3,plain,
( ! [U_2539,U_2537] :
( c_Nat__Transfer_Otsub(U_2539,U_2537) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2537,U_2539) )
& ! [U_2538,U_2536] :
( c_Nat__Transfer_Otsub(U_2538,U_2536) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2538,U_2536)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2536,U_2538) ) ),
inference(miniscope,[status(thm)],[f_808_2]) ).
fof(f_808_4,plain,
( ! [U_2539,U_2537] :
( c_Nat__Transfer_Otsub(U_2539,U_2537) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2537,U_2539) )
& ! [U_2538,U_2536] :
( c_Nat__Transfer_Otsub(U_2538,U_2536) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2538,U_2536)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2536,U_2538) ) ),
inference(definitional_conversion,[status(esa)],[f_808_3]) ).
cnf(f_808_5,plain,
( c_Nat__Transfer_Otsub(U_2538,U_2536) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2538,U_2536)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2536,U_2538) ),
inference(clausify,[status(thm)],[f_808_4]) ).
cnf(f_808_6,plain,
( c_Nat__Transfer_Otsub(U_2539,U_2537) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2537,U_2539) ),
inference(clausify,[status(thm)],[f_808_4]) ).
fof(f_809_1,plain,
! [V_X_2,V_K_2,T_a] :
( c_SEQ_OBseq(T_a,V_X_2)
| ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_BseqI]) ).
fof(f_809_2,plain,
! [U_2543,U_2542,U_2541] :
( c_SEQ_OBseq(U_2541,U_2543)
| ? [U_2540] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2541,hAPP(U_2543,U_2540)),U_2542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2542)
| ~ class_RealVector_Oreal__normed__vector(U_2541) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
fof(f_809_3,plain,
! [U_2543,U_2542,U_2541] :
( c_SEQ_OBseq(U_2541,U_2543)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2541,hAPP(U_2543,sK37(U_2543,U_2542,U_2541))),U_2542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2542)
| ~ class_RealVector_Oreal__normed__vector(U_2541) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2540,sK37(U_2543,U_2542,U_2541))],[f_809_2]) ).
fof(f_809_4,plain,
! [U_2542,U_2543,U_2541] :
( c_SEQ_OBseq(U_2541,U_2543)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2541,hAPP(U_2543,sK37(U_2543,U_2542,U_2541))),U_2542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2542)
| ~ class_RealVector_Oreal__normed__vector(U_2541) ),
inference(definitional_conversion,[status(esa)],[f_809_3]) ).
cnf(f_809_5,plain,
( c_SEQ_OBseq(U_2541,U_2543)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2541,hAPP(U_2543,sK37(U_2543,U_2542,U_2541))),U_2542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2542)
| ~ class_RealVector_Oreal__normed__vector(U_2541) ),
inference(clausify,[status(thm)],[f_809_4]) ).
fof(f_810_1,plain,
! [V_y,V_x] :
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ 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_810_2,plain,
! [U_2545,U_2544] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_2544,U_2545))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2544) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
fof(f_810_3,plain,
! [U_2544,U_2545] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_2544,U_2545))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2544) ),
inference(definitional_conversion,[status(esa)],[f_810_2]) ).
cnf(f_810_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_2544,U_2545))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2544) ),
inference(clausify,[status(thm)],[f_810_3]) ).
fof(f_811_1,plain,
! [V_x,V_y] :
( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ),
inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).
fof(f_811_2,plain,
! [U_2547,U_2546] :
( c_Nat__Transfer_Otsub(U_2547,U_2546) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2547,U_2546)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2546,U_2547) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
fof(f_811_3,plain,
! [U_2547,U_2546] :
( c_Nat__Transfer_Otsub(U_2547,U_2546) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2547,U_2546)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2546,U_2547) ),
inference(definitional_conversion,[status(esa)],[f_811_2]) ).
cnf(f_811_4,plain,
( c_Nat__Transfer_Otsub(U_2547,U_2546) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2547,U_2546)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2546,U_2547) ),
inference(clausify,[status(thm)],[f_811_3]) ).
fof(f_812_1,plain,
! [V_X_2,T_a] :
( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ c_SEQ_OBseq(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_BseqD]) ).
fof(f_812_2,plain,
! [U_2551,U_2550] :
( ? [U_2549] :
( ! [U_2548] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2550,hAPP(U_2551,U_2548)),U_2549)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2549) )
| ~ c_SEQ_OBseq(U_2550,U_2551)
| ~ class_RealVector_Oreal__normed__vector(U_2550) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
fof(f_812_3,plain,
! [U_2551,U_2550] :
( ( ! [U_2548] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2550,hAPP(U_2551,U_2548)),sK38(U_2551,U_2550))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK38(U_2551,U_2550)) )
| ~ c_SEQ_OBseq(U_2550,U_2551)
| ~ class_RealVector_Oreal__normed__vector(U_2550) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2549,sK38(U_2551,U_2550))],[f_812_2]) ).
fof(f_812_4,plain,
( ! [U_2548,U_2550,U_2551] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2550,hAPP(U_2551,U_2548)),sK38(U_2551,U_2550))
| ~ sP244(U_2548,U_2550,U_2551) )
& ! [U_2548,U_2550,U_2551] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK38(U_2551,U_2550))
| ~ sP244(U_2548,U_2550,U_2551) )
& ! [U_2548,U_2550,U_2551] :
( sP244(U_2548,U_2550,U_2551)
| ~ c_SEQ_OBseq(U_2550,U_2551)
| ~ class_RealVector_Oreal__normed__vector(U_2550) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_812_3]) ).
cnf(f_812_5,plain,
( sP244(U_2548,U_2550,U_2551)
| ~ c_SEQ_OBseq(U_2550,U_2551)
| ~ class_RealVector_Oreal__normed__vector(U_2550) ),
inference(clausify,[status(thm)],[f_812_4]) ).
cnf(f_812_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK38(U_2551,U_2550))
| ~ sP244(U_2548,U_2550,U_2551) ),
inference(clausify,[status(thm)],[f_812_4]) ).
cnf(f_812_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2550,hAPP(U_2551,U_2548)),sK38(U_2551,U_2550))
| ~ sP244(U_2548,U_2550,U_2551) ),
inference(clausify,[status(thm)],[f_812_4]) ).
fof(f_813_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,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)) )
| ~ 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,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2)))
& hBOOL(hAPP(V_P_2,B_x)) )
| ~ 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_813_2,plain,
! [U_2556,U_2555,U_2554] :
( ! [U_2553] :
( hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2556),U_2554))))
| ~ hBOOL(hAPP(U_2555,U_2553)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2556)
| ? [U_2552] :
( ~ hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2552,U_2554)))
& hBOOL(hAPP(U_2555,U_2552)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2554) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
fof(f_813_3,plain,
! [U_2556,U_2555,U_2554] :
( ! [U_2553] :
( hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2556),U_2554))))
| ~ hBOOL(hAPP(U_2555,U_2553)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2556)
| ( ~ hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK39(U_2556,U_2555,U_2554),U_2554)))
& hBOOL(hAPP(U_2555,sK39(U_2556,U_2555,U_2554))) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2554) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2552,sK39(U_2556,U_2555,U_2554))],[f_813_2]) ).
fof(f_813_4,plain,
( ! [U_2554,U_2555,U_2556] :
( ~ hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK39(U_2556,U_2555,U_2554),U_2554)))
| ~ sP245(U_2554,U_2555,U_2556) )
& ! [U_2554,U_2555,U_2556] :
( hBOOL(hAPP(U_2555,sK39(U_2556,U_2555,U_2554)))
| ~ sP245(U_2554,U_2555,U_2556) )
& ! [U_2553,U_2554,U_2555,U_2556] :
( hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2556),U_2554))))
| ~ hBOOL(hAPP(U_2555,U_2553))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2556)
| sP245(U_2554,U_2555,U_2556)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2554) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245])],[f_813_3]) ).
cnf(f_813_5,plain,
( hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2556),U_2554))))
| ~ hBOOL(hAPP(U_2555,U_2553))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2556)
| sP245(U_2554,U_2555,U_2556)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2554) ),
inference(clausify,[status(thm)],[f_813_4]) ).
cnf(f_813_6,plain,
( hBOOL(hAPP(U_2555,sK39(U_2556,U_2555,U_2554)))
| ~ sP245(U_2554,U_2555,U_2556) ),
inference(clausify,[status(thm)],[f_813_4]) ).
cnf(f_813_7,plain,
( ~ hBOOL(hAPP(U_2555,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK39(U_2556,U_2555,U_2554),U_2554)))
| ~ sP245(U_2554,U_2555,U_2556) ),
inference(clausify,[status(thm)],[f_813_4]) ).
fof(f_814_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,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)) )
| ~ 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,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2)))
& hBOOL(hAPP(V_P_2,B_x)) )
| ~ 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_814_2,plain,
! [U_2561,U_2560,U_2559] :
( ! [U_2558] :
( hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2558,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2561),U_2559))))
| ~ hBOOL(hAPP(U_2560,U_2558)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2561)
| ? [U_2557] :
( ~ hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2557,U_2559)))
& hBOOL(hAPP(U_2560,U_2557)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2559) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
fof(f_814_3,plain,
! [U_2561,U_2560,U_2559] :
( ! [U_2558] :
( hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2558,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2561),U_2559))))
| ~ hBOOL(hAPP(U_2560,U_2558)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2561)
| ( ~ hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK40(U_2561,U_2560,U_2559),U_2559)))
& hBOOL(hAPP(U_2560,sK40(U_2561,U_2560,U_2559))) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2559) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2557,sK40(U_2561,U_2560,U_2559))],[f_814_2]) ).
fof(f_814_4,plain,
( ! [U_2559,U_2560,U_2561] :
( ~ hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK40(U_2561,U_2560,U_2559),U_2559)))
| ~ sP246(U_2559,U_2560,U_2561) )
& ! [U_2559,U_2560,U_2561] :
( hBOOL(hAPP(U_2560,sK40(U_2561,U_2560,U_2559)))
| ~ sP246(U_2559,U_2560,U_2561) )
& ! [U_2559,U_2560,U_2561,U_2558] :
( hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2558,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2561),U_2559))))
| ~ hBOOL(hAPP(U_2560,U_2558))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2561)
| sP246(U_2559,U_2560,U_2561)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2559) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246])],[f_814_3]) ).
cnf(f_814_5,plain,
( hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2558,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2561),U_2559))))
| ~ hBOOL(hAPP(U_2560,U_2558))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2561)
| sP246(U_2559,U_2560,U_2561)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2559) ),
inference(clausify,[status(thm)],[f_814_4]) ).
cnf(f_814_6,plain,
( hBOOL(hAPP(U_2560,sK40(U_2561,U_2560,U_2559)))
| ~ sP246(U_2559,U_2560,U_2561) ),
inference(clausify,[status(thm)],[f_814_4]) ).
cnf(f_814_7,plain,
( ~ hBOOL(hAPP(U_2560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK40(U_2561,U_2560,U_2559),U_2559)))
| ~ sP246(U_2559,U_2560,U_2561) ),
inference(clausify,[status(thm)],[f_814_4]) ).
fof(f_815_1,plain,
! [V_a,V_n] :
( ? [B_x] :
( ! [B_y] :
( B_y = B_x
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) != V_a
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth__unique]) ).
fof(f_815_2,plain,
! [U_2565,U_2564] :
( ? [U_2563] :
( ! [U_2562] :
( U_2562 = U_2563
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2562),U_2564) != U_2565
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2562) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2563),U_2564) = U_2565
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2563) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2565)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2564) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
fof(f_815_3,plain,
! [U_2565,U_2564] :
( ( ! [U_2562] :
( U_2562 = sK41(U_2565,U_2564)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2562),U_2564) != U_2565
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2562) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK41(U_2565,U_2564)),U_2564) = U_2565
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(U_2565,U_2564)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2565)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2564) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2563,sK41(U_2565,U_2564))],[f_815_2]) ).
fof(f_815_4,plain,
( ! [U_2564,U_2565,U_2562] :
( U_2562 = sK41(U_2565,U_2564)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2562),U_2564) != U_2565
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2562)
| ~ sP247(U_2564,U_2565,U_2562) )
& ! [U_2564,U_2565,U_2562] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK41(U_2565,U_2564)),U_2564) = U_2565
| ~ sP247(U_2564,U_2565,U_2562) )
& ! [U_2564,U_2565,U_2562] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(U_2565,U_2564))
| ~ sP247(U_2564,U_2565,U_2562) )
& ! [U_2564,U_2565,U_2562] :
( sP247(U_2564,U_2565,U_2562)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2565)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2564) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247])],[f_815_3]) ).
cnf(f_815_5,plain,
( sP247(U_2564,U_2565,U_2562)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2565)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2564) ),
inference(clausify,[status(thm)],[f_815_4]) ).
cnf(f_815_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(U_2565,U_2564))
| ~ sP247(U_2564,U_2565,U_2562) ),
inference(clausify,[status(thm)],[f_815_4]) ).
cnf(f_815_7,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK41(U_2565,U_2564)),U_2564) = U_2565
| ~ sP247(U_2564,U_2565,U_2562) ),
inference(clausify,[status(thm)],[f_815_4]) ).
cnf(f_815_8,plain,
( U_2562 = sK41(U_2565,U_2564)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2562),U_2564) != U_2565
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2562)
| ~ sP247(U_2564,U_2565,U_2562) ),
inference(clausify,[status(thm)],[f_815_4]) ).
fof(f_816_1,plain,
! [V_a,V_n] :
( ? [B_r] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth]) ).
fof(f_816_2,plain,
! [U_2568,U_2567] :
( ? [U_2566] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2566),U_2567) = U_2568
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2566) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2568)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2567) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
fof(f_816_3,plain,
! [U_2568,U_2567] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK42(U_2568,U_2567)),U_2567) = U_2568
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(U_2568,U_2567)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2568)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2567) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2566,sK42(U_2568,U_2567))],[f_816_2]) ).
fof(f_816_4,plain,
( ! [U_2568,U_2567] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK42(U_2568,U_2567)),U_2567) = U_2568
| ~ sP248(U_2568,U_2567) )
& ! [U_2568,U_2567] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(U_2568,U_2567))
| ~ sP248(U_2568,U_2567) )
& ! [U_2568,U_2567] :
( sP248(U_2568,U_2567)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2568)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2567) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248])],[f_816_3]) ).
cnf(f_816_5,plain,
( sP248(U_2568,U_2567)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2568)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2567) ),
inference(clausify,[status(thm)],[f_816_4]) ).
cnf(f_816_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(U_2568,U_2567))
| ~ sP248(U_2568,U_2567) ),
inference(clausify,[status(thm)],[f_816_4]) ).
cnf(f_816_7,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK42(U_2568,U_2567)),U_2567) = U_2568
| ~ sP248(U_2568,U_2567) ),
inference(clausify,[status(thm)],[f_816_4]) ).
fof(f_817_1,plain,
! [V_n,V_x] :
( c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Transcendental_Oln(V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__realpow]) ).
fof(f_817_2,plain,
! [U_2570,U_2569] :
( c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2569),U_2570)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2570)),c_Transcendental_Oln(U_2569))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2569) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
fof(f_817_3,plain,
! [U_2569,U_2570] :
( c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2569),U_2570)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2570)),c_Transcendental_Oln(U_2569))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2569) ),
inference(definitional_conversion,[status(esa)],[f_817_2]) ).
cnf(f_817_4,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2569),U_2570)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2570)),c_Transcendental_Oln(U_2569))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2569) ),
inference(clausify,[status(thm)],[f_817_3]) ).
fof(f_818_1,plain,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_ln__one]) ).
fof(f_818_2,plain,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_818_1]) ).
cnf(f_818_3,plain,
c_Transcendental_Oln(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__less__self]) ).
fof(f_819_2,plain,
! [U_2571] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2571),U_2571)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2571) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
fof(f_819_3,plain,
! [U_2571] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2571),U_2571)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2571) ),
inference(definitional_conversion,[status(esa)],[f_819_2]) ).
cnf(f_819_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2571),U_2571)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2571) ),
inference(clausify,[status(thm)],[f_819_3]) ).
fof(f_820_1,plain,
! [V_y_2,V_x_2] :
( ( ( c_Transcendental_Oln(V_x_2) = c_Transcendental_Oln(V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Transcendental_Oln(V_x_2) != c_Transcendental_Oln(V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__inj__iff]) ).
fof(f_820_2,plain,
! [U_2573,U_2572] :
( ( ( c_Transcendental_Oln(U_2572) = c_Transcendental_Oln(U_2573)
| U_2572 != U_2573 )
& ( U_2572 = U_2573
| c_Transcendental_Oln(U_2572) != c_Transcendental_Oln(U_2573) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2573)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2572) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
fof(f_820_3,plain,
( ! [U_2572,U_2573] :
( c_Transcendental_Oln(U_2572) = c_Transcendental_Oln(U_2573)
| U_2572 != U_2573
| ~ sP249(U_2572,U_2573) )
& ! [U_2572,U_2573] :
( U_2572 = U_2573
| c_Transcendental_Oln(U_2572) != c_Transcendental_Oln(U_2573)
| ~ sP249(U_2572,U_2573) )
& ! [U_2572,U_2573] :
( sP249(U_2572,U_2573)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2573)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2572) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249])],[f_820_2]) ).
cnf(f_820_4,plain,
( sP249(U_2572,U_2573)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2573)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2572) ),
inference(clausify,[status(thm)],[f_820_3]) ).
cnf(f_820_5,plain,
( U_2572 = U_2573
| c_Transcendental_Oln(U_2572) != c_Transcendental_Oln(U_2573)
| ~ sP249(U_2572,U_2573) ),
inference(clausify,[status(thm)],[f_820_3]) ).
cnf(f_820_6,plain,
( c_Transcendental_Oln(U_2572) = c_Transcendental_Oln(U_2573)
| U_2572 != U_2573
| ~ sP249(U_2572,U_2573) ),
inference(clausify,[status(thm)],[f_820_3]) ).
fof(f_821_1,plain,
! [V_y_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__less__cancel__iff]) ).
fof(f_821_2,plain,
! [U_2575,U_2574] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2574),c_Transcendental_Oln(U_2575))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2574,U_2575) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2574,U_2575)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2574),c_Transcendental_Oln(U_2575)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2575)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2574) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
fof(f_821_3,plain,
( ! [U_2575,U_2574] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2574),c_Transcendental_Oln(U_2575))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2574,U_2575)
| ~ sP250(U_2575,U_2574) )
& ! [U_2575,U_2574] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2574,U_2575)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2574),c_Transcendental_Oln(U_2575))
| ~ sP250(U_2575,U_2574) )
& ! [U_2575,U_2574] :
( sP250(U_2575,U_2574)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2575)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2574) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP250])],[f_821_2]) ).
cnf(f_821_4,plain,
( sP250(U_2575,U_2574)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2575)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2574) ),
inference(clausify,[status(thm)],[f_821_3]) ).
cnf(f_821_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2574,U_2575)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2574),c_Transcendental_Oln(U_2575))
| ~ sP250(U_2575,U_2574) ),
inference(clausify,[status(thm)],[f_821_3]) ).
cnf(f_821_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2574),c_Transcendental_Oln(U_2575))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2574,U_2575)
| ~ sP250(U_2575,U_2574) ),
inference(clausify,[status(thm)],[f_821_3]) ).
fof(f_822_1,plain,
! [V_y_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Transcendental_Oln(V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__le__cancel__iff]) ).
fof(f_822_2,plain,
! [U_2577,U_2576] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2576),c_Transcendental_Oln(U_2577))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2576,U_2577) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2576,U_2577)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2576),c_Transcendental_Oln(U_2577)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2577)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2576) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
fof(f_822_3,plain,
( ! [U_2577,U_2576] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2576),c_Transcendental_Oln(U_2577))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2576,U_2577)
| ~ sP251(U_2577,U_2576) )
& ! [U_2577,U_2576] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2576,U_2577)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2576),c_Transcendental_Oln(U_2577))
| ~ sP251(U_2577,U_2576) )
& ! [U_2577,U_2576] :
( sP251(U_2577,U_2576)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2577)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2576) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251])],[f_822_2]) ).
cnf(f_822_4,plain,
( sP251(U_2577,U_2576)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2577)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2576) ),
inference(clausify,[status(thm)],[f_822_3]) ).
cnf(f_822_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2576,U_2577)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2576),c_Transcendental_Oln(U_2577))
| ~ sP251(U_2577,U_2576) ),
inference(clausify,[status(thm)],[f_822_3]) ).
cnf(f_822_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2576),c_Transcendental_Oln(U_2577))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2576,U_2577)
| ~ sP251(U_2577,U_2576) ),
inference(clausify,[status(thm)],[f_822_3]) ).
fof(f_823_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__ge__zero]) ).
fof(f_823_2,plain,
! [U_2578] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2578))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2578) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
fof(f_823_3,plain,
! [U_2578] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2578))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2578) ),
inference(definitional_conversion,[status(esa)],[f_823_2]) ).
cnf(f_823_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2578))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2578) ),
inference(clausify,[status(thm)],[f_823_3]) ).
fof(f_824_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__gt__zero]) ).
fof(f_824_2,plain,
! [U_2579] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2579))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2579) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
fof(f_824_3,plain,
! [U_2579] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2579))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2579) ),
inference(definitional_conversion,[status(esa)],[f_824_2]) ).
cnf(f_824_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2579))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2579) ),
inference(clausify,[status(thm)],[f_824_3]) ).
fof(f_825_1,plain,
! [V_x_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__gt__zero__iff]) ).
fof(f_825_2,plain,
! [U_2580] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2580))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2580) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2580)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2580)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2580) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
fof(f_825_3,plain,
( ! [U_2580] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2580))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2580)
| ~ sP252(U_2580) )
& ! [U_2580] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2580)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2580))
| ~ sP252(U_2580) )
& ! [U_2580] :
( sP252(U_2580)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2580) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_825_2]) ).
cnf(f_825_4,plain,
( sP252(U_2580)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2580) ),
inference(clausify,[status(thm)],[f_825_3]) ).
cnf(f_825_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2580)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2580))
| ~ sP252(U_2580) ),
inference(clausify,[status(thm)],[f_825_3]) ).
cnf(f_825_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2580))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2580)
| ~ sP252(U_2580) ),
inference(clausify,[status(thm)],[f_825_3]) ).
fof(f_826_1,plain,
! [V_x_2] :
( ( ( c_Transcendental_Oln(V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(V_x_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__eq__zero__iff]) ).
fof(f_826_2,plain,
! [U_2581] :
( ( ( c_Transcendental_Oln(U_2581) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2581 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( U_2581 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(U_2581) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2581) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
fof(f_826_3,plain,
( ! [U_2581] :
( c_Transcendental_Oln(U_2581) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2581 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ sP253(U_2581) )
& ! [U_2581] :
( U_2581 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(U_2581) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP253(U_2581) )
& ! [U_2581] :
( sP253(U_2581)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2581) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253])],[f_826_2]) ).
cnf(f_826_4,plain,
( sP253(U_2581)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2581) ),
inference(clausify,[status(thm)],[f_826_3]) ).
cnf(f_826_5,plain,
( U_2581 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(U_2581) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP253(U_2581) ),
inference(clausify,[status(thm)],[f_826_3]) ).
cnf(f_826_6,plain,
( c_Transcendental_Oln(U_2581) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2581 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ sP253(U_2581) ),
inference(clausify,[status(thm)],[f_826_3]) ).
fof(f_827_1,plain,
! [V_x_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__less__zero__iff]) ).
fof(f_827_2,plain,
! [U_2582] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2582),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2582,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2582,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2582),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2582) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
fof(f_827_3,plain,
( ! [U_2582] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2582),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2582,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ sP254(U_2582) )
& ! [U_2582] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2582,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2582),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP254(U_2582) )
& ! [U_2582] :
( sP254(U_2582)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2582) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_827_2]) ).
cnf(f_827_4,plain,
( sP254(U_2582)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2582) ),
inference(clausify,[status(thm)],[f_827_3]) ).
cnf(f_827_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2582,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2582),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP254(U_2582) ),
inference(clausify,[status(thm)],[f_827_3]) ).
cnf(f_827_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2582),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2582,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ sP254(U_2582) ),
inference(clausify,[status(thm)],[f_827_3]) ).
fof(f_828_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__less__zero]) ).
fof(f_828_2,plain,
! [U_2583] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2583),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2583,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2583) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
fof(f_828_3,plain,
! [U_2583] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2583),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2583,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2583) ),
inference(definitional_conversion,[status(esa)],[f_828_2]) ).
cnf(f_828_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2583),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2583,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2583) ),
inference(clausify,[status(thm)],[f_828_3]) ).
fof(f_829_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)) ),
inference(fof_nnf,[status(thm)],[fact_ln__gt__zero__imp__gt__one]) ).
fof(f_829_2,plain,
! [U_2584] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2584)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2584)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2584)) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
fof(f_829_3,plain,
! [U_2584] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2584)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2584)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2584)) ),
inference(definitional_conversion,[status(esa)],[f_829_2]) ).
cnf(f_829_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2584)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2584)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2584)) ),
inference(clausify,[status(thm)],[f_829_3]) ).
fof(f_830_1,plain,
! [V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__ge__zero__iff]) ).
fof(f_830_2,plain,
! [U_2585] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2585))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2585) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2585)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2585)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2585) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
fof(f_830_3,plain,
( ! [U_2585] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2585))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2585)
| ~ sP255(U_2585) )
& ! [U_2585] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2585)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2585))
| ~ sP255(U_2585) )
& ! [U_2585] :
( sP255(U_2585)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2585) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255])],[f_830_2]) ).
cnf(f_830_4,plain,
( sP255(U_2585)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2585) ),
inference(clausify,[status(thm)],[f_830_3]) ).
cnf(f_830_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2585)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2585))
| ~ sP255(U_2585) ),
inference(clausify,[status(thm)],[f_830_3]) ).
cnf(f_830_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2585))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2585)
| ~ sP255(U_2585) ),
inference(clausify,[status(thm)],[f_830_3]) ).
fof(f_831_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)) ),
inference(fof_nnf,[status(thm)],[fact_ln__ge__zero__imp__ge__one]) ).
fof(f_831_2,plain,
! [U_2586] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2586)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2586)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2586)) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
fof(f_831_3,plain,
! [U_2586] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2586)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2586)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2586)) ),
inference(definitional_conversion,[status(esa)],[f_831_2]) ).
cnf(f_831_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2586)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2586)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(U_2586)) ),
inference(clausify,[status(thm)],[f_831_3]) ).
fof(f_832_1,plain,
! [V_y,V_x] :
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__mult]) ).
fof(f_832_2,plain,
! [U_2588,U_2587] :
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2587),U_2588)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(U_2587),c_Transcendental_Oln(U_2588))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2588)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2587) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
fof(f_832_3,plain,
! [U_2587,U_2588] :
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2587),U_2588)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(U_2587),c_Transcendental_Oln(U_2588))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2588)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2587) ),
inference(definitional_conversion,[status(esa)],[f_832_2]) ).
cnf(f_832_4,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2587),U_2588)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oln(U_2587),c_Transcendental_Oln(U_2588))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2588)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2587) ),
inference(clausify,[status(thm)],[f_832_3]) ).
fof(f_833_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__add__one__self__le__self]) ).
fof(f_833_2,plain,
! [U_2589] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2589)),U_2589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2589) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
fof(f_833_3,plain,
! [U_2589] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2589)),U_2589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2589) ),
inference(definitional_conversion,[status(esa)],[f_833_2]) ).
cnf(f_833_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2589)),U_2589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2589) ),
inference(clausify,[status(thm)],[f_833_3]) ).
fof(f_834_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Oincseq(T_a,V_X_2)
| ? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) )
& ( ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
| ~ c_SEQ_Oincseq(T_a,V_X_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_incseq__def]) ).
fof(f_834_2,plain,
! [U_2595,U_2594] :
( ( ( c_SEQ_Oincseq(U_2594,U_2595)
| ? [U_2593,U_2592] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,U_2593),hAPP(U_2595,U_2592))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2593,U_2592) ) )
& ( ! [U_2591,U_2590] :
( c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,U_2591),hAPP(U_2595,U_2590))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2591,U_2590) )
| ~ c_SEQ_Oincseq(U_2594,U_2595) ) )
| ~ class_Orderings_Oorder(U_2594) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
fof(f_834_3,plain,
! [U_2595,U_2594] :
( ( ( c_SEQ_Oincseq(U_2594,U_2595)
| ? [U_2592] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,sK43(U_2595,U_2594)),hAPP(U_2595,U_2592))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK43(U_2595,U_2594),U_2592) ) )
& ( ! [U_2591,U_2590] :
( c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,U_2591),hAPP(U_2595,U_2590))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2591,U_2590) )
| ~ c_SEQ_Oincseq(U_2594,U_2595) ) )
| ~ class_Orderings_Oorder(U_2594) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2593,sK43(U_2595,U_2594))],[f_834_2]) ).
fof(f_834_4,plain,
! [U_2595,U_2594] :
( ( ( c_SEQ_Oincseq(U_2594,U_2595)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,sK43(U_2595,U_2594)),hAPP(U_2595,sK44(U_2595,U_2594)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK43(U_2595,U_2594),sK44(U_2595,U_2594)) ) )
& ( ! [U_2591,U_2590] :
( c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,U_2591),hAPP(U_2595,U_2590))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2591,U_2590) )
| ~ c_SEQ_Oincseq(U_2594,U_2595) ) )
| ~ class_Orderings_Oorder(U_2594) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2592,sK44(U_2595,U_2594))],[f_834_3]) ).
fof(f_834_5,plain,
( ! [U_2594,U_2595] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,sK43(U_2595,U_2594)),hAPP(U_2595,sK44(U_2595,U_2594)))
| ~ sP256(U_2594,U_2595) )
& ! [U_2594,U_2595] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK43(U_2595,U_2594),sK44(U_2595,U_2594))
| ~ sP256(U_2594,U_2595) )
& ! [U_2590,U_2591,U_2594,U_2595] :
( c_SEQ_Oincseq(U_2594,U_2595)
| sP256(U_2594,U_2595)
| ~ sP257(U_2590,U_2591,U_2594,U_2595) )
& ! [U_2590,U_2591,U_2594,U_2595] :
( c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,U_2591),hAPP(U_2595,U_2590))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2591,U_2590)
| ~ c_SEQ_Oincseq(U_2594,U_2595)
| ~ sP257(U_2590,U_2591,U_2594,U_2595) )
& ! [U_2590,U_2591,U_2594,U_2595] :
( sP257(U_2590,U_2591,U_2594,U_2595)
| ~ class_Orderings_Oorder(U_2594) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256,sP257])],[f_834_4]) ).
cnf(f_834_6,plain,
( sP257(U_2590,U_2591,U_2594,U_2595)
| ~ class_Orderings_Oorder(U_2594) ),
inference(clausify,[status(thm)],[f_834_5]) ).
cnf(f_834_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,U_2591),hAPP(U_2595,U_2590))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2591,U_2590)
| ~ c_SEQ_Oincseq(U_2594,U_2595)
| ~ sP257(U_2590,U_2591,U_2594,U_2595) ),
inference(clausify,[status(thm)],[f_834_5]) ).
cnf(f_834_8,plain,
( c_SEQ_Oincseq(U_2594,U_2595)
| sP256(U_2594,U_2595)
| ~ sP257(U_2590,U_2591,U_2594,U_2595) ),
inference(clausify,[status(thm)],[f_834_5]) ).
cnf(f_834_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK43(U_2595,U_2594),sK44(U_2595,U_2594))
| ~ sP256(U_2594,U_2595) ),
inference(clausify,[status(thm)],[f_834_5]) ).
cnf(f_834_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2594,hAPP(U_2595,sK43(U_2595,U_2594)),hAPP(U_2595,sK44(U_2595,U_2594)))
| ~ sP256(U_2594,U_2595) ),
inference(clausify,[status(thm)],[f_834_5]) ).
fof(f_835_1,plain,
! [V_k_2,V_f_2,V_n_2] :
( ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,V_n_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,hAPP(V_f_2,V_n_2))
| ~ 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] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_f_2,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))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_int__val__lemma]) ).
fof(f_835_2,plain,
! [U_2600,U_2599,U_2598] :
( ? [U_2597] :
( hAPP(U_2599,U_2597) = U_2600
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2597,U_2598) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2600,hAPP(U_2599,U_2598))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2600)
| ? [U_2596] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2599,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2596,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2599,U_2596))),c_Groups_Oone__class_Oone(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2596,U_2598) ) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
fof(f_835_3,plain,
! [U_2600,U_2599,U_2598] :
( ? [U_2597] :
( hAPP(U_2599,U_2597) = U_2600
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2597,U_2598) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2600,hAPP(U_2599,U_2598))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2600)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2599,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2599,sK45(U_2600,U_2599,U_2598)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),U_2598) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_2596,sK45(U_2600,U_2599,U_2598))],[f_835_2]) ).
fof(f_835_4,plain,
! [U_2600,U_2599,U_2598] :
( ( hAPP(U_2599,sK46(U_2600,U_2599,U_2598)) = U_2600
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK46(U_2600,U_2599,U_2598),U_2598) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2600,hAPP(U_2599,U_2598))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2600)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2599,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2599,sK45(U_2600,U_2599,U_2598)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),U_2598) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_2597,sK46(U_2600,U_2599,U_2598))],[f_835_3]) ).
fof(f_835_5,plain,
( ! [U_2599,U_2600,U_2598] :
( hAPP(U_2599,sK46(U_2600,U_2599,U_2598)) = U_2600
| ~ sP259(U_2599,U_2600,U_2598) )
& ! [U_2599,U_2600,U_2598] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK46(U_2600,U_2599,U_2598),U_2598)
| ~ sP259(U_2599,U_2600,U_2598) )
& ! [U_2599,U_2600,U_2598] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2599,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2599,sK45(U_2600,U_2599,U_2598)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ sP258(U_2599,U_2600,U_2598) )
& ! [U_2599,U_2600,U_2598] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),U_2598)
| ~ sP258(U_2599,U_2600,U_2598) )
& ! [U_2599,U_2600,U_2598] :
( sP259(U_2599,U_2600,U_2598)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2600,hAPP(U_2599,U_2598))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2600)
| sP258(U_2599,U_2600,U_2598) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258,sP259])],[f_835_4]) ).
cnf(f_835_6,plain,
( sP259(U_2599,U_2600,U_2598)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2600,hAPP(U_2599,U_2598))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2599,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2600)
| sP258(U_2599,U_2600,U_2598) ),
inference(clausify,[status(thm)],[f_835_5]) ).
cnf(f_835_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),U_2598)
| ~ sP258(U_2599,U_2600,U_2598) ),
inference(clausify,[status(thm)],[f_835_5]) ).
cnf(f_835_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2599,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK45(U_2600,U_2599,U_2598),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2599,sK45(U_2600,U_2599,U_2598)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ sP258(U_2599,U_2600,U_2598) ),
inference(clausify,[status(thm)],[f_835_5]) ).
cnf(f_835_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK46(U_2600,U_2599,U_2598),U_2598)
| ~ sP259(U_2599,U_2600,U_2598) ),
inference(clausify,[status(thm)],[f_835_5]) ).
cnf(f_835_10,plain,
( hAPP(U_2599,sK46(U_2600,U_2599,U_2598)) = U_2600
| ~ sP259(U_2599,U_2600,U_2598) ),
inference(clausify,[status(thm)],[f_835_5]) ).
fof(f_836_1,plain,
! [V_k_2,V_f_2,V_n_2] :
( ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,V_n_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,hAPP(V_f_2,V_n_2))
| ~ 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] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(V_f_2,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))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_i,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat0__intermed__int__val]) ).
fof(f_836_2,plain,
! [U_2605,U_2604,U_2603] :
( ? [U_2602] :
( hAPP(U_2604,U_2602) = U_2605
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2602,U_2603) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2605,hAPP(U_2604,U_2603))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2604,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2605)
| ? [U_2601] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2601,c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2604,U_2601))),c_Groups_Oone__class_Oone(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2601,U_2603) ) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
! [U_2605,U_2604,U_2603] :
( ? [U_2602] :
( hAPP(U_2604,U_2602) = U_2605
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2602,U_2603) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2605,hAPP(U_2604,U_2603))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2604,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2605)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2604,sK47(U_2605,U_2604,U_2603)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),U_2603) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_2601,sK47(U_2605,U_2604,U_2603))],[f_836_2]) ).
fof(f_836_4,plain,
! [U_2605,U_2604,U_2603] :
( ( hAPP(U_2604,sK48(U_2605,U_2604,U_2603)) = U_2605
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK48(U_2605,U_2604,U_2603),U_2603) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2605,hAPP(U_2604,U_2603))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2604,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2605)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2604,sK47(U_2605,U_2604,U_2603)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),U_2603) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_2602,sK48(U_2605,U_2604,U_2603))],[f_836_3]) ).
fof(f_836_5,plain,
( ! [U_2605,U_2603,U_2604] :
( hAPP(U_2604,sK48(U_2605,U_2604,U_2603)) = U_2605
| ~ sP261(U_2605,U_2603,U_2604) )
& ! [U_2605,U_2603,U_2604] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK48(U_2605,U_2604,U_2603),U_2603)
| ~ sP261(U_2605,U_2603,U_2604) )
& ! [U_2605,U_2603,U_2604] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2604,sK47(U_2605,U_2604,U_2603)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ sP260(U_2605,U_2603,U_2604) )
& ! [U_2605,U_2603,U_2604] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),U_2603)
| ~ sP260(U_2605,U_2603,U_2604) )
& ! [U_2605,U_2603,U_2604] :
( sP261(U_2605,U_2603,U_2604)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2605,hAPP(U_2604,U_2603))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2604,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2605)
| sP260(U_2605,U_2603,U_2604) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260,sP261])],[f_836_4]) ).
cnf(f_836_6,plain,
( sP261(U_2605,U_2603,U_2604)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2605,hAPP(U_2604,U_2603))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(U_2604,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2605)
| sP260(U_2605,U_2603,U_2604) ),
inference(clausify,[status(thm)],[f_836_5]) ).
cnf(f_836_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),U_2603)
| ~ sP260(U_2605,U_2603,U_2604) ),
inference(clausify,[status(thm)],[f_836_5]) ).
cnf(f_836_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(U_2604,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK47(U_2605,U_2604,U_2603),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(U_2604,sK47(U_2605,U_2604,U_2603)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ sP260(U_2605,U_2603,U_2604) ),
inference(clausify,[status(thm)],[f_836_5]) ).
cnf(f_836_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK48(U_2605,U_2604,U_2603),U_2603)
| ~ sP261(U_2605,U_2603,U_2604) ),
inference(clausify,[status(thm)],[f_836_5]) ).
cnf(f_836_10,plain,
( hAPP(U_2604,sK48(U_2605,U_2604,U_2603)) = U_2605
| ~ sP261(U_2605,U_2603,U_2604) ),
inference(clausify,[status(thm)],[f_836_5]) ).
fof(f_837_1,plain,
! [V_K_2,V_X_2,V_N_2,T_a] :
( c_SEQ_OBseq(T_a,V_X_2)
| ? [B_n] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2,B_n) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_BseqI2_H]) ).
fof(f_837_2,plain,
! [U_2610,U_2609,U_2608,U_2607] :
( c_SEQ_OBseq(U_2607,U_2609)
| ? [U_2606] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2607,hAPP(U_2609,U_2606)),U_2610)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2608,U_2606) )
| ~ class_RealVector_Oreal__normed__vector(U_2607) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
fof(f_837_3,plain,
! [U_2610,U_2609,U_2608,U_2607] :
( c_SEQ_OBseq(U_2607,U_2609)
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2607,hAPP(U_2609,sK49(U_2610,U_2609,U_2608,U_2607))),U_2610)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2608,sK49(U_2610,U_2609,U_2608,U_2607)) )
| ~ class_RealVector_Oreal__normed__vector(U_2607) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_2606,sK49(U_2610,U_2609,U_2608,U_2607))],[f_837_2]) ).
fof(f_837_4,plain,
( ! [U_2609,U_2608,U_2607,U_2610] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2607,hAPP(U_2609,sK49(U_2610,U_2609,U_2608,U_2607))),U_2610)
| ~ sP262(U_2609,U_2608,U_2607,U_2610) )
& ! [U_2609,U_2608,U_2607,U_2610] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2608,sK49(U_2610,U_2609,U_2608,U_2607))
| ~ sP262(U_2609,U_2608,U_2607,U_2610) )
& ! [U_2609,U_2608,U_2607,U_2610] :
( c_SEQ_OBseq(U_2607,U_2609)
| sP262(U_2609,U_2608,U_2607,U_2610)
| ~ class_RealVector_Oreal__normed__vector(U_2607) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262])],[f_837_3]) ).
cnf(f_837_5,plain,
( c_SEQ_OBseq(U_2607,U_2609)
| sP262(U_2609,U_2608,U_2607,U_2610)
| ~ class_RealVector_Oreal__normed__vector(U_2607) ),
inference(clausify,[status(thm)],[f_837_4]) ).
cnf(f_837_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2608,sK49(U_2610,U_2609,U_2608,U_2607))
| ~ sP262(U_2609,U_2608,U_2607,U_2610) ),
inference(clausify,[status(thm)],[f_837_4]) ).
cnf(f_837_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2607,hAPP(U_2609,sK49(U_2610,U_2609,U_2608,U_2607))),U_2610)
| ~ sP262(U_2609,U_2608,U_2607,U_2610) ),
inference(clausify,[status(thm)],[f_837_4]) ).
fof(f_838_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def]) ).
fof(f_838_2,plain,
! [U_2620,U_2619] :
( ( ( ? [U_2618] :
( ! [U_2617] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2617)),U_2618)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2618) )
| ! [U_2616] :
? [U_2615] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2615)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2616))) )
& ( ? [U_2614] :
! [U_2613] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2613)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2614)))
| ! [U_2612] :
( ? [U_2611] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2611)),U_2612)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2612) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2619) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
fof(f_838_3,plain,
! [U_2620,U_2619] :
( ( ( ? [U_2618] :
( ! [U_2617] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2617)),U_2618)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2618) )
| ! [U_2616] :
? [U_2615] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2615)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2616))) )
& ( ? [U_2614] :
! [U_2613] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2613)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2614)))
| ! [U_2612] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK50(U_2620,U_2619,U_2612))),U_2612)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2612) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_2611,sK50(U_2620,U_2619,U_2612))],[f_838_2]) ).
fof(f_838_4,plain,
! [U_2620,U_2619] :
( ( ( ? [U_2618] :
( ! [U_2617] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2617)),U_2618)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2618) )
| ! [U_2616] :
? [U_2615] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2615)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2616))) )
& ( ! [U_2613] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2613)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK51(U_2620,U_2619))))
| ! [U_2612] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK50(U_2620,U_2619,U_2612))),U_2612)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2612) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_2614,sK51(U_2620,U_2619))],[f_838_3]) ).
fof(f_838_5,plain,
! [U_2620,U_2619] :
( ( ( ? [U_2618] :
( ! [U_2617] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2617)),U_2618)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2618) )
| ! [U_2616] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK52(U_2620,U_2619,U_2616))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2616))) )
& ( ! [U_2613] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2613)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK51(U_2620,U_2619))))
| ! [U_2612] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK50(U_2620,U_2619,U_2612))),U_2612)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2612) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_2615,sK52(U_2620,U_2619,U_2616))],[f_838_4]) ).
fof(f_838_6,plain,
! [U_2620,U_2619] :
( ( ( ( ! [U_2617] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2617)),sK53(U_2620,U_2619))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK53(U_2620,U_2619)) )
| ! [U_2616] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK52(U_2620,U_2619,U_2616))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2616))) )
& ( ! [U_2613] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2613)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK51(U_2620,U_2619))))
| ! [U_2612] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK50(U_2620,U_2619,U_2612))),U_2612)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2612) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2619) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_2618,sK53(U_2620,U_2619))],[f_838_5]) ).
fof(f_838_7,plain,
( ! [U_2617,U_2619,U_2620] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2617)),sK53(U_2620,U_2619))
| ~ sP263(U_2617,U_2619,U_2620) )
& ! [U_2617,U_2619,U_2620] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK53(U_2620,U_2619))
| ~ sP263(U_2617,U_2619,U_2620) )
& ! [U_2613,U_2612,U_2616,U_2617,U_2619,U_2620] :
( sP263(U_2617,U_2619,U_2620)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK52(U_2620,U_2619,U_2616))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2616)))
| ~ sP264(U_2613,U_2612,U_2616,U_2617,U_2619,U_2620) )
& ! [U_2613,U_2612,U_2616,U_2617,U_2619,U_2620] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2613)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK51(U_2620,U_2619))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK50(U_2620,U_2619,U_2612))),U_2612)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2612)
| ~ sP264(U_2613,U_2612,U_2616,U_2617,U_2619,U_2620) )
& ! [U_2613,U_2612,U_2616,U_2617,U_2619,U_2620] :
( sP264(U_2613,U_2612,U_2616,U_2617,U_2619,U_2620)
| ~ class_RealVector_Oreal__normed__vector(U_2619) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263,sP264])],[f_838_6]) ).
cnf(f_838_8,plain,
( sP264(U_2613,U_2612,U_2616,U_2617,U_2619,U_2620)
| ~ class_RealVector_Oreal__normed__vector(U_2619) ),
inference(clausify,[status(thm)],[f_838_7]) ).
cnf(f_838_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2613)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK51(U_2620,U_2619))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK50(U_2620,U_2619,U_2612))),U_2612)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2612)
| ~ sP264(U_2613,U_2612,U_2616,U_2617,U_2619,U_2620) ),
inference(clausify,[status(thm)],[f_838_7]) ).
cnf(f_838_10,plain,
( sP263(U_2617,U_2619,U_2620)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,sK52(U_2620,U_2619,U_2616))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2616)))
| ~ sP264(U_2613,U_2612,U_2616,U_2617,U_2619,U_2620) ),
inference(clausify,[status(thm)],[f_838_7]) ).
cnf(f_838_11,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK53(U_2620,U_2619))
| ~ sP263(U_2617,U_2619,U_2620) ),
inference(clausify,[status(thm)],[f_838_7]) ).
cnf(f_838_12,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2619,hAPP(U_2620,U_2617)),sK53(U_2620,U_2619))
| ~ sP263(U_2617,U_2619,U_2620) ),
inference(clausify,[status(thm)],[f_838_7]) ).
fof(f_839_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def2]) ).
fof(f_839_2,plain,
! [U_2630,U_2629] :
( ( ( ? [U_2628] :
( ! [U_2627] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2627)),U_2628)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2628) )
| ! [U_2626] :
? [U_2625] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2625)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2626))) )
& ( ? [U_2624] :
! [U_2623] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2623)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2624)))
| ! [U_2622] :
( ? [U_2621] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2621)),U_2622)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2622) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2629) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
fof(f_839_3,plain,
! [U_2630,U_2629] :
( ( ( ? [U_2628] :
( ! [U_2627] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2627)),U_2628)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2628) )
| ! [U_2626] :
? [U_2625] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2625)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2626))) )
& ( ? [U_2624] :
! [U_2623] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2623)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2624)))
| ! [U_2622] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK54(U_2630,U_2629,U_2622))),U_2622)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2622) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2629) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_2621,sK54(U_2630,U_2629,U_2622))],[f_839_2]) ).
fof(f_839_4,plain,
! [U_2630,U_2629] :
( ( ( ? [U_2628] :
( ! [U_2627] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2627)),U_2628)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2628) )
| ! [U_2626] :
? [U_2625] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2625)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2626))) )
& ( ! [U_2623] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2623)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK55(U_2630,U_2629))))
| ! [U_2622] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK54(U_2630,U_2629,U_2622))),U_2622)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2622) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2629) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_2624,sK55(U_2630,U_2629))],[f_839_3]) ).
fof(f_839_5,plain,
! [U_2630,U_2629] :
( ( ( ? [U_2628] :
( ! [U_2627] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2627)),U_2628)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2628) )
| ! [U_2626] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK56(U_2630,U_2629,U_2626))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2626))) )
& ( ! [U_2623] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2623)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK55(U_2630,U_2629))))
| ! [U_2622] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK54(U_2630,U_2629,U_2622))),U_2622)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2622) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2629) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_2625,sK56(U_2630,U_2629,U_2626))],[f_839_4]) ).
fof(f_839_6,plain,
! [U_2630,U_2629] :
( ( ( ( ! [U_2627] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2627)),sK57(U_2630,U_2629))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK57(U_2630,U_2629)) )
| ! [U_2626] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK56(U_2630,U_2629,U_2626))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2626))) )
& ( ! [U_2623] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2623)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK55(U_2630,U_2629))))
| ! [U_2622] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK54(U_2630,U_2629,U_2622))),U_2622)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2622) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2629) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_2628,sK57(U_2630,U_2629))],[f_839_5]) ).
fof(f_839_7,plain,
( ! [U_2627,U_2629,U_2630] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2627)),sK57(U_2630,U_2629))
| ~ sP265(U_2627,U_2629,U_2630) )
& ! [U_2627,U_2629,U_2630] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK57(U_2630,U_2629))
| ~ sP265(U_2627,U_2629,U_2630) )
& ! [U_2622,U_2623,U_2626,U_2627,U_2629,U_2630] :
( sP265(U_2627,U_2629,U_2630)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK56(U_2630,U_2629,U_2626))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2626)))
| ~ sP266(U_2622,U_2623,U_2626,U_2627,U_2629,U_2630) )
& ! [U_2622,U_2623,U_2626,U_2627,U_2629,U_2630] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2623)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK55(U_2630,U_2629))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK54(U_2630,U_2629,U_2622))),U_2622)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2622)
| ~ sP266(U_2622,U_2623,U_2626,U_2627,U_2629,U_2630) )
& ! [U_2622,U_2623,U_2626,U_2627,U_2629,U_2630] :
( sP266(U_2622,U_2623,U_2626,U_2627,U_2629,U_2630)
| ~ class_RealVector_Oreal__normed__vector(U_2629) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265,sP266])],[f_839_6]) ).
cnf(f_839_8,plain,
( sP266(U_2622,U_2623,U_2626,U_2627,U_2629,U_2630)
| ~ class_RealVector_Oreal__normed__vector(U_2629) ),
inference(clausify,[status(thm)],[f_839_7]) ).
cnf(f_839_9,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2623)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK55(U_2630,U_2629))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK54(U_2630,U_2629,U_2622))),U_2622)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2622)
| ~ sP266(U_2622,U_2623,U_2626,U_2627,U_2629,U_2630) ),
inference(clausify,[status(thm)],[f_839_7]) ).
cnf(f_839_10,plain,
( sP265(U_2627,U_2629,U_2630)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,sK56(U_2630,U_2629,U_2626))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2626)))
| ~ sP266(U_2622,U_2623,U_2626,U_2627,U_2629,U_2630) ),
inference(clausify,[status(thm)],[f_839_7]) ).
cnf(f_839_11,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK57(U_2630,U_2629))
| ~ sP265(U_2627,U_2629,U_2630) ),
inference(clausify,[status(thm)],[f_839_7]) ).
cnf(f_839_12,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2629,hAPP(U_2630,U_2627)),sK57(U_2630,U_2629))
| ~ sP265(U_2627,U_2629,U_2630) ),
inference(clausify,[status(thm)],[f_839_7]) ).
fof(f_840_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_lessI]) ).
fof(f_840_2,plain,
! [U_2631] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2631,c_Nat_OSuc(U_2631)),
inference(variable_rename,[status(thm)],[f_840_1]) ).
fof(f_840_3,plain,
! [U_2631] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2631,c_Nat_OSuc(U_2631)),
inference(definitional_conversion,[status(esa)],[f_840_2]) ).
cnf(f_840_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2631,c_Nat_OSuc(U_2631)),
inference(clausify,[status(thm)],[f_840_3]) ).
fof(f_841_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).
fof(f_841_2,plain,
! [U_2633,U_2632] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2632),c_Nat_OSuc(U_2633))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2632,U_2633) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
fof(f_841_3,plain,
! [U_2633,U_2632] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2632),c_Nat_OSuc(U_2633))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2632,U_2633) ),
inference(definitional_conversion,[status(esa)],[f_841_2]) ).
cnf(f_841_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2632),c_Nat_OSuc(U_2633))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2632,U_2633) ),
inference(clausify,[status(thm)],[f_841_3]) ).
fof(f_842_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_zero__less__Suc]) ).
fof(f_842_2,plain,
! [U_2634] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2634)),
inference(variable_rename,[status(thm)],[f_842_1]) ).
fof(f_842_3,plain,
! [U_2634] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2634)),
inference(definitional_conversion,[status(esa)],[f_842_2]) ).
cnf(f_842_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2634)),
inference(clausify,[status(thm)],[f_842_3]) ).
fof(f_843_1,plain,
! [V_x] :
( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one]) ).
fof(f_843_2,plain,
! [U_2635] :
( U_2635 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2635,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
fof(f_843_3,plain,
! [U_2635] :
( U_2635 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2635,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(definitional_conversion,[status(esa)],[f_843_2]) ).
cnf(f_843_4,plain,
( U_2635 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2635 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2635,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_843_3]) ).
fof(f_844_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ! [B_k] : V_n_2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)) )
& ( ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).
fof(f_844_2,plain,
! [U_2639,U_2638] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2638,U_2639)
| ! [U_2637] : U_2639 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2638,U_2637)) )
& ( ? [U_2636] : U_2639 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2638,U_2636))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2638,U_2639) ) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
fof(f_844_3,plain,
( ! [U_2643,U_2641] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2641,U_2643)
| ! [U_2637] : U_2643 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2641,U_2637)) )
& ! [U_2642,U_2640] :
( ? [U_2636] : U_2642 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2640,U_2636))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2640,U_2642) ) ),
inference(miniscope,[status(thm)],[f_844_2]) ).
fof(f_844_4,plain,
( ! [U_2643,U_2641] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2641,U_2643)
| ! [U_2637] : U_2643 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2641,U_2637)) )
& ! [U_2642,U_2640] :
( U_2642 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2640,sK58(U_2642,U_2640)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2640,U_2642) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_2636,sK58(U_2642,U_2640))],[f_844_3]) ).
fof(f_844_5,plain,
( ! [U_2637,U_2643,U_2641] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2641,U_2643)
| U_2643 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2641,U_2637)) )
& ! [U_2642,U_2640] :
( U_2642 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2640,sK58(U_2642,U_2640)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2640,U_2642) ) ),
inference(definitional_conversion,[status(esa)],[f_844_4]) ).
cnf(f_844_6,plain,
( U_2642 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2640,sK58(U_2642,U_2640)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2640,U_2642) ),
inference(clausify,[status(thm)],[f_844_5]) ).
cnf(f_844_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2641,U_2643)
| U_2643 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2641,U_2637)) ),
inference(clausify,[status(thm)],[f_844_5]) ).
fof(f_845_1,plain,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).
fof(f_845_2,plain,
! [U_2645,U_2644] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2644,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2645,U_2644))),
inference(variable_rename,[status(thm)],[f_845_1]) ).
fof(f_845_3,plain,
! [U_2644,U_2645] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2644,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2645,U_2644))),
inference(definitional_conversion,[status(esa)],[f_845_2]) ).
cnf(f_845_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2644,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2645,U_2644))),
inference(clausify,[status(thm)],[f_845_3]) ).
fof(f_846_1,plain,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).
fof(f_846_2,plain,
! [U_2647,U_2646] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2646,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2646,U_2647))),
inference(variable_rename,[status(thm)],[f_846_1]) ).
fof(f_846_3,plain,
! [U_2646,U_2647] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2646,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2646,U_2647))),
inference(definitional_conversion,[status(esa)],[f_846_2]) ).
cnf(f_846_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2646,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2646,U_2647))),
inference(clausify,[status(thm)],[f_846_3]) ).
fof(f_847_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD]) ).
fof(f_847_2,plain,
! [U_2649,U_2648] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2648,U_2649)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2648),U_2649) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
fof(f_847_3,plain,
! [U_2648,U_2649] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2648,U_2649)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2648),U_2649) ),
inference(definitional_conversion,[status(esa)],[f_847_2]) ).
cnf(f_847_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2648,U_2649)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2648),U_2649) ),
inference(clausify,[status(thm)],[f_847_3]) ).
fof(f_848_1,plain,
! [V_n_2,V_ma_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
| V_n_2 != V_ma_2 )
& ( V_n_2 = V_ma_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).
fof(f_848_2,plain,
! [U_2651,U_2650] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2651,c_Nat_OSuc(U_2650))
| U_2651 != U_2650 )
& ( U_2651 = U_2650
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2651,c_Nat_OSuc(U_2650)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2650,U_2651) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
( ! [U_2650,U_2651] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2651,c_Nat_OSuc(U_2650))
| U_2651 != U_2650
| ~ sP267(U_2650,U_2651) )
& ! [U_2650,U_2651] :
( U_2651 = U_2650
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2651,c_Nat_OSuc(U_2650))
| ~ sP267(U_2650,U_2651) )
& ! [U_2650,U_2651] :
( sP267(U_2650,U_2651)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2650,U_2651) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_848_2]) ).
cnf(f_848_4,plain,
( sP267(U_2650,U_2651)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2650,U_2651) ),
inference(clausify,[status(thm)],[f_848_3]) ).
cnf(f_848_5,plain,
( U_2651 = U_2650
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2651,c_Nat_OSuc(U_2650))
| ~ sP267(U_2650,U_2651) ),
inference(clausify,[status(thm)],[f_848_3]) ).
cnf(f_848_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2651,c_Nat_OSuc(U_2650))
| U_2651 != U_2650
| ~ sP267(U_2650,U_2651) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).
fof(f_849_2,plain,
! [U_2653,U_2652] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2652),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2652,U_2653) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
! [U_2652,U_2653] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2652),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2652,U_2653) ),
inference(definitional_conversion,[status(esa)],[f_849_2]) ).
cnf(f_849_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2652),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2652,U_2653) ),
inference(clausify,[status(thm)],[f_849_3]) ).
fof(f_850_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ 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_850_2,plain,
! [U_2655,U_2654] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2654,c_Nat_OSuc(U_2655))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2654,U_2655) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
fof(f_850_3,plain,
! [U_2654,U_2655] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2654,c_Nat_OSuc(U_2655))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2654,U_2655) ),
inference(definitional_conversion,[status(esa)],[f_850_2]) ).
cnf(f_850_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2654,c_Nat_OSuc(U_2655))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2654,U_2655) ),
inference(clausify,[status(thm)],[f_850_3]) ).
fof(f_851_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).
fof(f_851_2,plain,
! [U_2657,U_2656] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2656),U_2657)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2656,U_2657) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2656,U_2657)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2656),U_2657) ) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
fof(f_851_3,plain,
( ! [U_2661,U_2659] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2659),U_2661)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2659,U_2661) )
& ! [U_2660,U_2658] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2658,U_2660)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2658),U_2660) ) ),
inference(miniscope,[status(thm)],[f_851_2]) ).
fof(f_851_4,plain,
( ! [U_2661,U_2659] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2659),U_2661)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2659,U_2661) )
& ! [U_2660,U_2658] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2658,U_2660)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2658),U_2660) ) ),
inference(definitional_conversion,[status(esa)],[f_851_3]) ).
cnf(f_851_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2658,U_2660)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2658),U_2660) ),
inference(clausify,[status(thm)],[f_851_4]) ).
cnf(f_851_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2659),U_2661)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2659,U_2661) ),
inference(clausify,[status(thm)],[f_851_4]) ).
fof(f_852_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).
fof(f_852_2,plain,
! [U_2663,U_2662] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2662,c_Nat_OSuc(U_2663))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2662,U_2663) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2662,U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2662,c_Nat_OSuc(U_2663)) ) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
fof(f_852_3,plain,
( ! [U_2667,U_2665] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2665,c_Nat_OSuc(U_2667))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2667) )
& ! [U_2666,U_2664] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2664,U_2666)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2664,c_Nat_OSuc(U_2666)) ) ),
inference(miniscope,[status(thm)],[f_852_2]) ).
fof(f_852_4,plain,
( ! [U_2665,U_2667] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2665,c_Nat_OSuc(U_2667))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2667) )
& ! [U_2664,U_2666] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2664,U_2666)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2664,c_Nat_OSuc(U_2666)) ) ),
inference(definitional_conversion,[status(esa)],[f_852_3]) ).
cnf(f_852_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2664,U_2666)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2664,c_Nat_OSuc(U_2666)) ),
inference(clausify,[status(thm)],[f_852_4]) ).
cnf(f_852_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2665,c_Nat_OSuc(U_2667))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2667) ),
inference(clausify,[status(thm)],[f_852_4]) ).
fof(f_853_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).
fof(f_853_2,plain,
! [U_2669,U_2668] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2668,U_2669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2668),U_2669) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2668),U_2669)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2668,U_2669) ) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
fof(f_853_3,plain,
( ! [U_2673,U_2671] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2671,U_2673)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2671),U_2673) )
& ! [U_2672,U_2670] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2670),U_2672)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2670,U_2672) ) ),
inference(miniscope,[status(thm)],[f_853_2]) ).
fof(f_853_4,plain,
( ! [U_2673,U_2671] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2671,U_2673)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2671),U_2673) )
& ! [U_2672,U_2670] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2670),U_2672)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2670,U_2672) ) ),
inference(definitional_conversion,[status(esa)],[f_853_3]) ).
cnf(f_853_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2670),U_2672)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2670,U_2672) ),
inference(clausify,[status(thm)],[f_853_4]) ).
cnf(f_853_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2671,U_2673)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2671),U_2673) ),
inference(clausify,[status(thm)],[f_853_4]) ).
fof(f_854_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_One__nat__def]) ).
fof(f_854_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_854_1]) ).
cnf(f_854_3,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_854_2]) ).
fof(f_855_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).
fof(f_855_2,plain,
! [U_2675,U_2674] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2674,U_2675),c_Nat_OSuc(U_2674)),
inference(variable_rename,[status(thm)],[f_855_1]) ).
fof(f_855_3,plain,
! [U_2674,U_2675] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2674,U_2675),c_Nat_OSuc(U_2674)),
inference(definitional_conversion,[status(esa)],[f_855_2]) ).
cnf(f_855_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2674,U_2675),c_Nat_OSuc(U_2674)),
inference(clausify,[status(thm)],[f_855_3]) ).
fof(f_856_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = 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_856_2,plain,
! [U_2677,U_2676] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2676),c_Nat_OSuc(U_2677)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2676),U_2677)),
inference(variable_rename,[status(thm)],[f_856_1]) ).
fof(f_856_3,plain,
! [U_2676,U_2677] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2676),c_Nat_OSuc(U_2677)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2676),U_2677)),
inference(definitional_conversion,[status(esa)],[f_856_2]) ).
cnf(f_856_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2676),c_Nat_OSuc(U_2677)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2676),U_2677)),
inference(clausify,[status(thm)],[f_856_3]) ).
fof(f_857_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = 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_857_2,plain,
! [U_2679,U_2678] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2678)),U_2679) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2678),U_2679)),
inference(variable_rename,[status(thm)],[f_857_1]) ).
fof(f_857_3,plain,
! [U_2678,U_2679] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2678)),U_2679) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2678),U_2679)),
inference(definitional_conversion,[status(esa)],[f_857_2]) ).
cnf(f_857_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2678)),U_2679) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2678),U_2679)),
inference(clausify,[status(thm)],[f_857_3]) ).
fof(f_858_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).
fof(f_858_2,plain,
! [U_2682,U_2681,U_2680] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2680)),U_2681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2680)),U_2682))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2681,U_2682) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2681,U_2682)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2680)),U_2681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2680)),U_2682)) ) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
fof(f_858_3,plain,
( ! [U_2688,U_2686] :
( ! [U_2684] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2684)),U_2686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2684)),U_2688))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2686,U_2688) )
& ! [U_2687,U_2685] :
( ! [U_2683] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2683)),U_2685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2683)),U_2687))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2685,U_2687) ) ),
inference(miniscope,[status(thm)],[f_858_2]) ).
fof(f_858_4,plain,
( ! [U_2688,U_2684,U_2686] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2684)),U_2686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2684)),U_2688))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2686,U_2688) )
& ! [U_2685,U_2683,U_2687] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2683)),U_2685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2683)),U_2687))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2685,U_2687) ) ),
inference(definitional_conversion,[status(esa)],[f_858_3]) ).
cnf(f_858_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2683)),U_2685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2683)),U_2687))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2685,U_2687) ),
inference(clausify,[status(thm)],[f_858_4]) ).
cnf(f_858_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2684)),U_2686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2684)),U_2688))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2686,U_2688) ),
inference(clausify,[status(thm)],[f_858_4]) ).
fof(f_859_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)
| ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).
fof(f_859_2,plain,
! [U_2690,U_2689] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2689,U_2690)
| ( ( U_2690 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2689 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2690 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2689 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2690 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2689 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2689,U_2690) ) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
fof(f_859_3,plain,
( ! [U_2694,U_2692] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2692,U_2694)
| ( ( U_2694 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2692 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2694 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2692 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2693,U_2691] :
( ( U_2693 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2691 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2691,U_2693) ) ),
inference(miniscope,[status(thm)],[f_859_2]) ).
fof(f_859_4,plain,
( ! [U_2692,U_2694] :
( U_2694 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2692 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP270(U_2692,U_2694) )
& ! [U_2692,U_2694] :
( U_2694 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2692 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP270(U_2692,U_2694) )
& ! [U_2693,U_2691] :
( U_2693 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP269(U_2693,U_2691) )
& ! [U_2693,U_2691] :
( U_2691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP269(U_2693,U_2691) )
& ! [U_2693,U_2691] :
( U_2693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP268(U_2693,U_2691) )
& ! [U_2693,U_2691] :
( U_2691 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP268(U_2693,U_2691) )
& ! [U_2692,U_2694] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2692,U_2694)
| sP270(U_2692,U_2694) )
& ! [U_2693,U_2691] :
( sP269(U_2693,U_2691)
| sP268(U_2693,U_2691)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2691,U_2693) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268,sP269,sP270])],[f_859_3]) ).
cnf(f_859_5,plain,
( sP269(U_2693,U_2691)
| sP268(U_2693,U_2691)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2691,U_2693) ),
inference(clausify,[status(thm)],[f_859_4]) ).
cnf(f_859_6,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2692,U_2694)
| sP270(U_2692,U_2694) ),
inference(clausify,[status(thm)],[f_859_4]) ).
cnf(f_859_7,plain,
( U_2691 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP268(U_2693,U_2691) ),
inference(clausify,[status(thm)],[f_859_4]) ).
cnf(f_859_8,plain,
( U_2693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP268(U_2693,U_2691) ),
inference(clausify,[status(thm)],[f_859_4]) ).
cnf(f_859_9,plain,
( U_2691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP269(U_2693,U_2691) ),
inference(clausify,[status(thm)],[f_859_4]) ).
cnf(f_859_10,plain,
( U_2693 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP269(U_2693,U_2691) ),
inference(clausify,[status(thm)],[f_859_4]) ).
cnf(f_859_11,plain,
( U_2694 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2692 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP270(U_2692,U_2694) ),
inference(clausify,[status(thm)],[f_859_4]) ).
cnf(f_859_12,plain,
( U_2694 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2692 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP270(U_2692,U_2694) ),
inference(clausify,[status(thm)],[f_859_4]) ).
fof(f_860_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).
fof(f_860_2,plain,
! [U_2696,U_2695] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2695,U_2696) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2696 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2695 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2696 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2695 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2696 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2695 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2695 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2695,U_2696) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
fof(f_860_3,plain,
( ! [U_2700,U_2698] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2698,U_2700) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2700 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2698 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2700 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2698 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2699,U_2697] :
( ( U_2699 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2697 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2697,U_2699) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_860_2]) ).
fof(f_860_4,plain,
( ! [U_2698,U_2700] :
( U_2700 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2698 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP273(U_2698,U_2700) )
& ! [U_2698,U_2700] :
( U_2700 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2698 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP273(U_2698,U_2700) )
& ! [U_2699,U_2697] :
( U_2699 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP272(U_2699,U_2697) )
& ! [U_2699,U_2697] :
( U_2697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP272(U_2699,U_2697) )
& ! [U_2699,U_2697] :
( U_2699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP271(U_2699,U_2697) )
& ! [U_2699,U_2697] :
( U_2697 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP271(U_2699,U_2697) )
& ! [U_2698,U_2700] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2698,U_2700) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP273(U_2698,U_2700) )
& ! [U_2699,U_2697] :
( sP272(U_2699,U_2697)
| sP271(U_2699,U_2697)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2697,U_2699) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271,sP272,sP273])],[f_860_3]) ).
cnf(f_860_5,plain,
( sP272(U_2699,U_2697)
| sP271(U_2699,U_2697)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2697,U_2699) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_860_4]) ).
cnf(f_860_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2698,U_2700) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP273(U_2698,U_2700) ),
inference(clausify,[status(thm)],[f_860_4]) ).
cnf(f_860_7,plain,
( U_2697 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP271(U_2699,U_2697) ),
inference(clausify,[status(thm)],[f_860_4]) ).
cnf(f_860_8,plain,
( U_2699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP271(U_2699,U_2697) ),
inference(clausify,[status(thm)],[f_860_4]) ).
cnf(f_860_9,plain,
( U_2697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP272(U_2699,U_2697) ),
inference(clausify,[status(thm)],[f_860_4]) ).
cnf(f_860_10,plain,
( U_2699 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP272(U_2699,U_2697) ),
inference(clausify,[status(thm)],[f_860_4]) ).
cnf(f_860_11,plain,
( U_2700 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2698 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP273(U_2698,U_2700) ),
inference(clausify,[status(thm)],[f_860_4]) ).
cnf(f_860_12,plain,
( U_2700 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2698 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP273(U_2698,U_2700) ),
inference(clausify,[status(thm)],[f_860_4]) ).
fof(f_861_1,plain,
! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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_861_2,plain,
! [U_2701] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2701),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2701,
inference(variable_rename,[status(thm)],[f_861_1]) ).
fof(f_861_3,plain,
! [U_2701] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2701),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2701,
inference(definitional_conversion,[status(esa)],[f_861_2]) ).
cnf(f_861_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2701),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2701,
inference(clausify,[status(thm)],[f_861_3]) ).
fof(f_862_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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_862_2,plain,
! [U_2703,U_2702] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2702,c_Nat_OSuc(U_2703)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2702,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2703),
inference(variable_rename,[status(thm)],[f_862_1]) ).
fof(f_862_3,plain,
! [U_2703,U_2702] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2702,c_Nat_OSuc(U_2703)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2702,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2703),
inference(definitional_conversion,[status(esa)],[f_862_2]) ).
cnf(f_862_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2702,c_Nat_OSuc(U_2703)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2702,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2703),
inference(clausify,[status(thm)],[f_862_3]) ).
fof(f_863_1,plain,
! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,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_863_2,plain,
! [U_2706,U_2705,U_2704] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2704),U_2705),c_Nat_OSuc(U_2706)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2704,U_2705),U_2706),
inference(variable_rename,[status(thm)],[f_863_1]) ).
fof(f_863_3,plain,
! [U_2706,U_2704,U_2705] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2704),U_2705),c_Nat_OSuc(U_2706)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2704,U_2705),U_2706),
inference(definitional_conversion,[status(esa)],[f_863_2]) ).
cnf(f_863_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2704),U_2705),c_Nat_OSuc(U_2706)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2704,U_2705),U_2706),
inference(clausify,[status(thm)],[f_863_3]) ).
fof(f_864_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(f_864_2,plain,
! [U_2708,U_2707] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2707),c_Nat_OSuc(U_2708)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2707,U_2708),
inference(variable_rename,[status(thm)],[f_864_1]) ).
fof(f_864_3,plain,
! [U_2707,U_2708] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2707),c_Nat_OSuc(U_2708)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2707,U_2708),
inference(definitional_conversion,[status(esa)],[f_864_2]) ).
cnf(f_864_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2707),c_Nat_OSuc(U_2708)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2707,U_2708),
inference(clausify,[status(thm)],[f_864_3]) ).
fof(f_865_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).
fof(f_865_2,plain,
! [U_2710,U_2709] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2709,c_Nat_OSuc(U_2710)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2709,U_2710)),
inference(variable_rename,[status(thm)],[f_865_1]) ).
fof(f_865_3,plain,
! [U_2709,U_2710] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2709,c_Nat_OSuc(U_2710)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2709,U_2710)),
inference(definitional_conversion,[status(esa)],[f_865_2]) ).
cnf(f_865_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2709,c_Nat_OSuc(U_2710)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2709,U_2710)),
inference(clausify,[status(thm)],[f_865_3]) ).
fof(f_866_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).
fof(f_866_2,plain,
! [U_2712,U_2711] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2711),U_2712) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2711,U_2712)),
inference(variable_rename,[status(thm)],[f_866_1]) ).
fof(f_866_3,plain,
! [U_2711,U_2712] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2711),U_2712) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2711,U_2712)),
inference(definitional_conversion,[status(esa)],[f_866_2]) ).
cnf(f_866_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2711),U_2712) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2711,U_2712)),
inference(clausify,[status(thm)],[f_866_3]) ).
fof(f_867_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__shift]) ).
fof(f_867_2,plain,
! [U_2714,U_2713] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2713),U_2714) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2713,c_Nat_OSuc(U_2714)),
inference(variable_rename,[status(thm)],[f_867_1]) ).
fof(f_867_3,plain,
! [U_2713,U_2714] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2713),U_2714) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2713,c_Nat_OSuc(U_2714)),
inference(definitional_conversion,[status(esa)],[f_867_2]) ).
cnf(f_867_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2713),U_2714) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2713,c_Nat_OSuc(U_2714)),
inference(clausify,[status(thm)],[f_867_3]) ).
fof(f_868_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(f_868_2,plain,
! [U_2715] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2715),U_2715),
inference(variable_rename,[status(thm)],[f_868_1]) ).
fof(f_868_3,plain,
! [U_2715] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2715),U_2715),
inference(definitional_conversion,[status(esa)],[f_868_2]) ).
cnf(f_868_4,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2715),U_2715),
inference(clausify,[status(thm)],[f_868_3]) ).
fof(f_869_1,plain,
! [V_n_2,V_ma_2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).
fof(f_869_2,plain,
! [U_2717,U_2716] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2716,U_2717)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2717),U_2716) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2717),U_2716)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2716,U_2717) ) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
fof(f_869_3,plain,
( ! [U_2721,U_2719] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2719,U_2721)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2721),U_2719) )
& ! [U_2720,U_2718] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2720),U_2718)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2718,U_2720) ) ),
inference(miniscope,[status(thm)],[f_869_2]) ).
fof(f_869_4,plain,
( ! [U_2719,U_2721] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2719,U_2721)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2721),U_2719) )
& ! [U_2718,U_2720] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2720),U_2718)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2718,U_2720) ) ),
inference(definitional_conversion,[status(esa)],[f_869_3]) ).
cnf(f_869_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2720),U_2718)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2718,U_2720) ),
inference(clausify,[status(thm)],[f_869_4]) ).
cnf(f_869_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2719,U_2721)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2721),U_2719) ),
inference(clausify,[status(thm)],[f_869_4]) ).
fof(f_870_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ( V_ma_2 != c_Nat_OSuc(V_n_2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( V_ma_2 = c_Nat_OSuc(V_n_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).
fof(f_870_2,plain,
! [U_2723,U_2722] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2722,c_Nat_OSuc(U_2723))
| ( U_2722 != c_Nat_OSuc(U_2723)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2722,U_2723) ) )
& ( U_2722 = c_Nat_OSuc(U_2723)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2722,U_2723)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2722,c_Nat_OSuc(U_2723)) ) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
fof(f_870_3,plain,
( ! [U_2727,U_2725] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,c_Nat_OSuc(U_2727))
| ( U_2725 != c_Nat_OSuc(U_2727)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,U_2727) ) )
& ! [U_2726,U_2724] :
( U_2724 = c_Nat_OSuc(U_2726)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2724,U_2726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2724,c_Nat_OSuc(U_2726)) ) ),
inference(miniscope,[status(thm)],[f_870_2]) ).
fof(f_870_4,plain,
( ! [U_2725,U_2727] :
( U_2725 != c_Nat_OSuc(U_2727)
| ~ sP274(U_2725,U_2727) )
& ! [U_2725,U_2727] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,U_2727)
| ~ sP274(U_2725,U_2727) )
& ! [U_2725,U_2727] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,c_Nat_OSuc(U_2727))
| sP274(U_2725,U_2727) )
& ! [U_2726,U_2724] :
( U_2724 = c_Nat_OSuc(U_2726)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2724,U_2726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2724,c_Nat_OSuc(U_2726)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274])],[f_870_3]) ).
cnf(f_870_5,plain,
( U_2724 = c_Nat_OSuc(U_2726)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2724,U_2726)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2724,c_Nat_OSuc(U_2726)) ),
inference(clausify,[status(thm)],[f_870_4]) ).
cnf(f_870_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,c_Nat_OSuc(U_2727))
| sP274(U_2725,U_2727) ),
inference(clausify,[status(thm)],[f_870_4]) ).
cnf(f_870_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,U_2727)
| ~ sP274(U_2725,U_2727) ),
inference(clausify,[status(thm)],[f_870_4]) ).
cnf(f_870_8,plain,
( U_2725 != c_Nat_OSuc(U_2727)
| ~ sP274(U_2725,U_2727) ),
inference(clausify,[status(thm)],[f_870_4]) ).
fof(f_871_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).
fof(f_871_2,plain,
! [U_2729,U_2728] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2728),c_Nat_OSuc(U_2729))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2728,U_2729) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2728,U_2729)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2728),c_Nat_OSuc(U_2729)) ) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
fof(f_871_3,plain,
( ! [U_2733,U_2731] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2731),c_Nat_OSuc(U_2733))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2731,U_2733) )
& ! [U_2732,U_2730] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2730,U_2732)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2730),c_Nat_OSuc(U_2732)) ) ),
inference(miniscope,[status(thm)],[f_871_2]) ).
fof(f_871_4,plain,
( ! [U_2733,U_2731] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2731),c_Nat_OSuc(U_2733))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2731,U_2733) )
& ! [U_2732,U_2730] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2730,U_2732)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2730),c_Nat_OSuc(U_2732)) ) ),
inference(definitional_conversion,[status(esa)],[f_871_3]) ).
cnf(f_871_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2730,U_2732)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2730),c_Nat_OSuc(U_2732)) ),
inference(clausify,[status(thm)],[f_871_4]) ).
cnf(f_871_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2731),c_Nat_OSuc(U_2733))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2731,U_2733) ),
inference(clausify,[status(thm)],[f_871_4]) ).
fof(f_872_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).
fof(f_872_2,plain,
! [U_2735,U_2734] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2734,c_Nat_OSuc(U_2735))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2734,U_2735) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
fof(f_872_3,plain,
! [U_2735,U_2734] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2734,c_Nat_OSuc(U_2735))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2734,U_2735) ),
inference(definitional_conversion,[status(esa)],[f_872_2]) ).
cnf(f_872_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2734,c_Nat_OSuc(U_2735))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2734,U_2735) ),
inference(clausify,[status(thm)],[f_872_3]) ).
fof(f_873_1,plain,
! [V_n,V_m] :
( V_m = c_Nat_OSuc(V_n)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__SucE]) ).
fof(f_873_2,plain,
! [U_2737,U_2736] :
( U_2736 = c_Nat_OSuc(U_2737)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2736,U_2737)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2736,c_Nat_OSuc(U_2737)) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
fof(f_873_3,plain,
! [U_2737,U_2736] :
( U_2736 = c_Nat_OSuc(U_2737)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2736,U_2737)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2736,c_Nat_OSuc(U_2737)) ),
inference(definitional_conversion,[status(esa)],[f_873_2]) ).
cnf(f_873_4,plain,
( U_2736 = c_Nat_OSuc(U_2737)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2736,U_2737)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2736,c_Nat_OSuc(U_2737)) ),
inference(clausify,[status(thm)],[f_873_3]) ).
fof(f_874_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leD]) ).
fof(f_874_2,plain,
! [U_2739,U_2738] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2738,U_2739)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2738),U_2739) ),
inference(variable_rename,[status(thm)],[f_874_1]) ).
fof(f_874_3,plain,
! [U_2739,U_2738] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2738,U_2739)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2738),U_2739) ),
inference(definitional_conversion,[status(esa)],[f_874_2]) ).
cnf(f_874_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2738,U_2739)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2738),U_2739) ),
inference(clausify,[status(thm)],[f_874_3]) ).
fof(f_875_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = 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_875_2,plain,
! [U_2740] : c_Nat_OSuc(U_2740) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2740,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_875_1]) ).
fof(f_875_3,plain,
! [U_2740] : c_Nat_OSuc(U_2740) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2740,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_875_2]) ).
cnf(f_875_4,plain,
c_Nat_OSuc(U_2740) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2740,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_875_3]) ).
fof(f_876_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = 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_876_2,plain,
! [U_2741] : c_Nat_OSuc(U_2741) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2741),
inference(variable_rename,[status(thm)],[f_876_1]) ).
fof(f_876_3,plain,
! [U_2741] : c_Nat_OSuc(U_2741) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2741),
inference(definitional_conversion,[status(esa)],[f_876_2]) ).
cnf(f_876_4,plain,
c_Nat_OSuc(U_2741) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2741),
inference(clausify,[status(thm)],[f_876_3]) ).
fof(f_877_1,plain,
! [V_m,V_n] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).
fof(f_877_2,plain,
! [U_2743,U_2742] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2743),U_2742) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2743,U_2742))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2742,U_2743) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
fof(f_877_3,plain,
! [U_2742,U_2743] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2743),U_2742) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2743,U_2742))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2742,U_2743) ),
inference(definitional_conversion,[status(esa)],[f_877_2]) ).
cnf(f_877_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2743),U_2742) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2743,U_2742))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2742,U_2743) ),
inference(clausify,[status(thm)],[f_877_3]) ).
fof(f_878_1,plain,
! [V_y,V_x] :
( V_x = V_y
| c_Nat_OSuc(V_x) != c_Nat_OSuc(V_y) ),
inference(fof_nnf,[status(thm)],[fact_Suc__inject]) ).
fof(f_878_2,plain,
! [U_2745,U_2744] :
( U_2744 = U_2745
| c_Nat_OSuc(U_2744) != c_Nat_OSuc(U_2745) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
fof(f_878_3,plain,
! [U_2744,U_2745] :
( U_2744 = U_2745
| c_Nat_OSuc(U_2744) != c_Nat_OSuc(U_2745) ),
inference(definitional_conversion,[status(esa)],[f_878_2]) ).
cnf(f_878_4,plain,
( U_2744 = U_2745
| c_Nat_OSuc(U_2744) != c_Nat_OSuc(U_2745) ),
inference(clausify,[status(thm)],[f_878_3]) ).
fof(f_879_1,plain,
! [V_nat_H_2,V_nat_2] :
( ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
| V_nat_2 != V_nat_H_2 )
& ( V_nat_2 = V_nat_H_2
| c_Nat_OSuc(V_nat_2) != c_Nat_OSuc(V_nat_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat_Oinject]) ).
fof(f_879_2,plain,
! [U_2747,U_2746] :
( ( c_Nat_OSuc(U_2746) = c_Nat_OSuc(U_2747)
| U_2746 != U_2747 )
& ( U_2746 = U_2747
| c_Nat_OSuc(U_2746) != c_Nat_OSuc(U_2747) ) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
fof(f_879_3,plain,
( ! [U_2751,U_2749] :
( c_Nat_OSuc(U_2749) = c_Nat_OSuc(U_2751)
| U_2749 != U_2751 )
& ! [U_2750,U_2748] :
( U_2748 = U_2750
| c_Nat_OSuc(U_2748) != c_Nat_OSuc(U_2750) ) ),
inference(miniscope,[status(thm)],[f_879_2]) ).
fof(f_879_4,plain,
( ! [U_2749,U_2751] :
( c_Nat_OSuc(U_2749) = c_Nat_OSuc(U_2751)
| U_2749 != U_2751 )
& ! [U_2750,U_2748] :
( U_2748 = U_2750
| c_Nat_OSuc(U_2748) != c_Nat_OSuc(U_2750) ) ),
inference(definitional_conversion,[status(esa)],[f_879_3]) ).
cnf(f_879_5,plain,
( U_2748 = U_2750
| c_Nat_OSuc(U_2748) != c_Nat_OSuc(U_2750) ),
inference(clausify,[status(thm)],[f_879_4]) ).
cnf(f_879_6,plain,
( c_Nat_OSuc(U_2749) = c_Nat_OSuc(U_2751)
| U_2749 != U_2751 ),
inference(clausify,[status(thm)],[f_879_4]) ).
fof(f_880_1,plain,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_880_2,plain,
! [U_2752] : c_Nat_OSuc(U_2752) != U_2752,
inference(variable_rename,[status(thm)],[f_880_1]) ).
fof(f_880_3,plain,
! [U_2752] : c_Nat_OSuc(U_2752) != U_2752,
inference(definitional_conversion,[status(esa)],[f_880_2]) ).
cnf(f_880_4,plain,
c_Nat_OSuc(U_2752) != U_2752,
inference(clausify,[status(thm)],[f_880_3]) ).
fof(f_881_1,plain,
! [V_n] : V_n != c_Nat_OSuc(V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_881_2,plain,
! [U_2753] : U_2753 != c_Nat_OSuc(U_2753),
inference(variable_rename,[status(thm)],[f_881_1]) ).
fof(f_881_3,plain,
! [U_2753] : U_2753 != c_Nat_OSuc(U_2753),
inference(definitional_conversion,[status(esa)],[f_881_2]) ).
cnf(f_881_4,plain,
U_2753 != c_Nat_OSuc(U_2753),
inference(clausify,[status(thm)],[f_881_3]) ).
fof(f_882_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).
fof(f_882_2,plain,
! [U_2756,U_2755,U_2754] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2754)),U_2755) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2754)),U_2756)
| U_2755 != U_2756 )
& ( U_2755 = U_2756
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2754)),U_2755) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2754)),U_2756) ) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
fof(f_882_3,plain,
( ! [U_2762,U_2760] :
( ! [U_2758] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2758)),U_2760) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2758)),U_2762)
| U_2760 != U_2762 )
& ! [U_2761,U_2759] :
( ! [U_2757] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2757)),U_2759) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2757)),U_2761)
| U_2759 = U_2761 ) ),
inference(miniscope,[status(thm)],[f_882_2]) ).
fof(f_882_4,plain,
( ! [U_2762,U_2758,U_2760] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2758)),U_2760) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2758)),U_2762)
| U_2760 != U_2762 )
& ! [U_2761,U_2759,U_2757] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2757)),U_2759) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2757)),U_2761)
| U_2759 = U_2761 ) ),
inference(definitional_conversion,[status(esa)],[f_882_3]) ).
cnf(f_882_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2757)),U_2759) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2757)),U_2761)
| U_2759 = U_2761 ),
inference(clausify,[status(thm)],[f_882_4]) ).
cnf(f_882_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2758)),U_2760) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2758)),U_2762)
| U_2760 != U_2762 ),
inference(clausify,[status(thm)],[f_882_4]) ).
fof(f_883_1,plain,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(f_883_2,plain,
! [U_2763] : c_Nat_OSuc(U_2763) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_883_1]) ).
fof(f_883_3,plain,
! [U_2763] : c_Nat_OSuc(U_2763) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_883_2]) ).
cnf(f_883_4,plain,
c_Nat_OSuc(U_2763) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_883_3]) ).
fof(f_884_1,plain,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
inference(fof_nnf,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(f_884_2,plain,
! [U_2764] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2764),
inference(variable_rename,[status(thm)],[f_884_1]) ).
fof(f_884_3,plain,
! [U_2764] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2764),
inference(definitional_conversion,[status(esa)],[f_884_2]) ).
cnf(f_884_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2764),
inference(clausify,[status(thm)],[f_884_3]) ).
fof(f_885_1,plain,
! [V_nat_H_1] : 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_885_2,plain,
! [U_2765] : c_Nat_OSuc(U_2765) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_885_1]) ).
fof(f_885_3,plain,
! [U_2765] : c_Nat_OSuc(U_2765) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_885_2]) ).
cnf(f_885_4,plain,
c_Nat_OSuc(U_2765) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_885_3]) ).
fof(f_886_1,plain,
! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_Suc__not__Zero]) ).
fof(f_886_2,plain,
! [U_2766] : c_Nat_OSuc(U_2766) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_886_1]) ).
fof(f_886_3,plain,
! [U_2766] : c_Nat_OSuc(U_2766) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_886_2]) ).
cnf(f_886_4,plain,
c_Nat_OSuc(U_2766) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_886_3]) ).
fof(f_887_1,plain,
! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H),
inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(f_887_2,plain,
! [U_2767] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2767),
inference(variable_rename,[status(thm)],[f_887_1]) ).
fof(f_887_3,plain,
! [U_2767] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2767),
inference(definitional_conversion,[status(esa)],[f_887_2]) ).
cnf(f_887_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2767),
inference(clausify,[status(thm)],[f_887_3]) ).
fof(f_888_1,plain,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
inference(fof_nnf,[status(thm)],[fact_Zero__not__Suc]) ).
fof(f_888_2,plain,
! [U_2768] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2768),
inference(variable_rename,[status(thm)],[f_888_1]) ).
fof(f_888_3,plain,
! [U_2768] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2768),
inference(definitional_conversion,[status(esa)],[f_888_2]) ).
cnf(f_888_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2768),
inference(clausify,[status(thm)],[f_888_3]) ).
fof(f_889_1,plain,
! [V_n_2,V_ma_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).
fof(f_889_2,plain,
! [U_2770,U_2769] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2769,U_2770)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2770,c_Nat_OSuc(U_2769)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2770,c_Nat_OSuc(U_2769))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2769,U_2770) ) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
fof(f_889_3,plain,
( ! [U_2774,U_2772] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2772,U_2774)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2774,c_Nat_OSuc(U_2772)) )
& ! [U_2773,U_2771] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2773,c_Nat_OSuc(U_2771))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2771,U_2773) ) ),
inference(miniscope,[status(thm)],[f_889_2]) ).
fof(f_889_4,plain,
( ! [U_2774,U_2772] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2772,U_2774)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2774,c_Nat_OSuc(U_2772)) )
& ! [U_2773,U_2771] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2773,c_Nat_OSuc(U_2771))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2771,U_2773) ) ),
inference(definitional_conversion,[status(esa)],[f_889_3]) ).
cnf(f_889_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2773,c_Nat_OSuc(U_2771))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2771,U_2773) ),
inference(clausify,[status(thm)],[f_889_4]) ).
cnf(f_889_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2772,U_2774)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2774,c_Nat_OSuc(U_2772)) ),
inference(clausify,[status(thm)],[f_889_4]) ).
fof(f_890_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ( V_ma_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).
fof(f_890_2,plain,
! [U_2776,U_2775] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,c_Nat_OSuc(U_2776))
| ( U_2775 != U_2776
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,U_2776) ) )
& ( U_2775 = U_2776
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,U_2776)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,c_Nat_OSuc(U_2776)) ) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
fof(f_890_3,plain,
( ! [U_2780,U_2778] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,c_Nat_OSuc(U_2780))
| ( U_2778 != U_2780
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,U_2780) ) )
& ! [U_2779,U_2777] :
( U_2777 = U_2779
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,U_2779)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,c_Nat_OSuc(U_2779)) ) ),
inference(miniscope,[status(thm)],[f_890_2]) ).
fof(f_890_4,plain,
( ! [U_2780,U_2778] :
( U_2778 != U_2780
| ~ sP275(U_2780,U_2778) )
& ! [U_2780,U_2778] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,U_2780)
| ~ sP275(U_2780,U_2778) )
& ! [U_2780,U_2778] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,c_Nat_OSuc(U_2780))
| sP275(U_2780,U_2778) )
& ! [U_2777,U_2779] :
( U_2777 = U_2779
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,U_2779)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,c_Nat_OSuc(U_2779)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275])],[f_890_3]) ).
cnf(f_890_5,plain,
( U_2777 = U_2779
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,U_2779)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,c_Nat_OSuc(U_2779)) ),
inference(clausify,[status(thm)],[f_890_4]) ).
cnf(f_890_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,c_Nat_OSuc(U_2780))
| sP275(U_2780,U_2778) ),
inference(clausify,[status(thm)],[f_890_4]) ).
cnf(f_890_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,U_2780)
| ~ sP275(U_2780,U_2778) ),
inference(clausify,[status(thm)],[f_890_4]) ).
cnf(f_890_8,plain,
( U_2778 != U_2780
| ~ sP275(U_2780,U_2778) ),
inference(clausify,[status(thm)],[f_890_4]) ).
fof(f_891_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).
fof(f_891_2,plain,
! [U_2782,U_2781] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2781),c_Nat_OSuc(U_2782))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2781,U_2782) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2781,U_2782)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2781),c_Nat_OSuc(U_2782)) ) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
fof(f_891_3,plain,
( ! [U_2786,U_2784] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2784),c_Nat_OSuc(U_2786))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2784,U_2786) )
& ! [U_2785,U_2783] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2783,U_2785)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2783),c_Nat_OSuc(U_2785)) ) ),
inference(miniscope,[status(thm)],[f_891_2]) ).
fof(f_891_4,plain,
( ! [U_2784,U_2786] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2784),c_Nat_OSuc(U_2786))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2784,U_2786) )
& ! [U_2783,U_2785] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2783,U_2785)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2783),c_Nat_OSuc(U_2785)) ) ),
inference(definitional_conversion,[status(esa)],[f_891_3]) ).
cnf(f_891_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2783,U_2785)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2783),c_Nat_OSuc(U_2785)) ),
inference(clausify,[status(thm)],[f_891_4]) ).
cnf(f_891_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2784),c_Nat_OSuc(U_2786))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2784,U_2786) ),
inference(clausify,[status(thm)],[f_891_4]) ).
fof(f_892_1,plain,
! [V_ma_2,V_n_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
| V_n_2 != V_ma_2 )
& ( V_n_2 = V_ma_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(f_892_2,plain,
! [U_2788,U_2787] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,c_Nat_OSuc(U_2788))
| U_2787 != U_2788 )
& ( U_2787 = U_2788
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,c_Nat_OSuc(U_2788)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,U_2788) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
fof(f_892_3,plain,
( ! [U_2787,U_2788] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,c_Nat_OSuc(U_2788))
| U_2787 != U_2788
| ~ sP276(U_2787,U_2788) )
& ! [U_2787,U_2788] :
( U_2787 = U_2788
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,c_Nat_OSuc(U_2788))
| ~ sP276(U_2787,U_2788) )
& ! [U_2787,U_2788] :
( sP276(U_2787,U_2788)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,U_2788) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_892_2]) ).
cnf(f_892_4,plain,
( sP276(U_2787,U_2788)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,U_2788) ),
inference(clausify,[status(thm)],[f_892_3]) ).
cnf(f_892_5,plain,
( U_2787 = U_2788
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,c_Nat_OSuc(U_2788))
| ~ sP276(U_2787,U_2788) ),
inference(clausify,[status(thm)],[f_892_3]) ).
cnf(f_892_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,c_Nat_OSuc(U_2788))
| U_2787 != U_2788
| ~ sP276(U_2787,U_2788) ),
inference(clausify,[status(thm)],[f_892_3]) ).
fof(f_893_1,plain,
! [V_m,V_n] :
( V_m = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).
fof(f_893_2,plain,
! [U_2790,U_2789] :
( U_2790 = U_2789
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2789,c_Nat_OSuc(U_2790))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2789,U_2790) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
fof(f_893_3,plain,
! [U_2789,U_2790] :
( U_2790 = U_2789
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2789,c_Nat_OSuc(U_2790))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2789,U_2790) ),
inference(definitional_conversion,[status(esa)],[f_893_2]) ).
cnf(f_893_4,plain,
( U_2790 = U_2789
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2789,c_Nat_OSuc(U_2790))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2789,U_2790) ),
inference(clausify,[status(thm)],[f_893_3]) ).
fof(f_894_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).
fof(f_894_2,plain,
! [U_2792,U_2791] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,c_Nat_OSuc(U_2792))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,U_2792) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
fof(f_894_3,plain,
! [U_2792,U_2791] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,c_Nat_OSuc(U_2792))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,U_2792) ),
inference(definitional_conversion,[status(esa)],[f_894_2]) ).
cnf(f_894_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,c_Nat_OSuc(U_2792))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,U_2792) ),
inference(clausify,[status(thm)],[f_894_3]) ).
fof(f_895_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
| c_Nat_OSuc(V_m) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).
fof(f_895_2,plain,
! [U_2794,U_2793] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2793),U_2794)
| c_Nat_OSuc(U_2793) = U_2794
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2793,U_2794) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
! [U_2793,U_2794] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2793),U_2794)
| c_Nat_OSuc(U_2793) = U_2794
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2793,U_2794) ),
inference(definitional_conversion,[status(esa)],[f_895_2]) ).
cnf(f_895_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2793),U_2794)
| c_Nat_OSuc(U_2793) = U_2794
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2793,U_2794) ),
inference(clausify,[status(thm)],[f_895_3]) ).
fof(f_896_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).
fof(f_896_2,plain,
! [U_2797,U_2796,U_2795] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2795),U_2797)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2796,U_2797)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2795,U_2796) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
fof(f_896_3,plain,
! [U_2796,U_2795,U_2797] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2795),U_2797)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2796,U_2797)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2795,U_2796) ),
inference(definitional_conversion,[status(esa)],[f_896_2]) ).
cnf(f_896_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2795),U_2797)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2796,U_2797)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2795,U_2796) ),
inference(clausify,[status(thm)],[f_896_3]) ).
fof(f_897_1,plain,
! [V_n,V_m] :
( V_m = V_n
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_less__SucE]) ).
fof(f_897_2,plain,
! [U_2799,U_2798] :
( U_2798 = U_2799
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2798,U_2799)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2798,c_Nat_OSuc(U_2799)) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
fof(f_897_3,plain,
! [U_2798,U_2799] :
( U_2798 = U_2799
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2798,U_2799)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2798,c_Nat_OSuc(U_2799)) ),
inference(definitional_conversion,[status(esa)],[f_897_2]) ).
cnf(f_897_4,plain,
( U_2798 = U_2799
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2798,U_2799)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2798,c_Nat_OSuc(U_2799)) ),
inference(clausify,[status(thm)],[f_897_3]) ).
fof(f_898_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessD]) ).
fof(f_898_2,plain,
! [U_2801,U_2800] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2800,U_2801)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2800),U_2801) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
fof(f_898_3,plain,
! [U_2801,U_2800] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2800,U_2801)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2800),U_2801) ),
inference(definitional_conversion,[status(esa)],[f_898_2]) ).
cnf(f_898_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2800,U_2801)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2800),U_2801) ),
inference(clausify,[status(thm)],[f_898_3]) ).
fof(f_899_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD]) ).
fof(f_899_2,plain,
! [U_2803,U_2802] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2802,U_2803)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2802),c_Nat_OSuc(U_2803)) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
! [U_2802,U_2803] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2802,U_2803)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2802),c_Nat_OSuc(U_2803)) ),
inference(definitional_conversion,[status(esa)],[f_899_2]) ).
cnf(f_899_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2802,U_2803)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2802),c_Nat_OSuc(U_2803)) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ( ! [B_j] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
| V_ma_2 != c_Nat_OSuc(B_j) )
& V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
& V_ma_2 = c_Nat_OSuc(B_j) )
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).
fof(f_900_2,plain,
! [U_2807,U_2806] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2806,c_Nat_OSuc(U_2807))
| ( ! [U_2805] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2805,U_2807)
| U_2806 != c_Nat_OSuc(U_2805) )
& U_2806 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_2804] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2804,U_2807)
& U_2806 = c_Nat_OSuc(U_2804) )
| U_2806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2806,c_Nat_OSuc(U_2807)) ) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
fof(f_900_3,plain,
( ! [U_2811,U_2809] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2809,c_Nat_OSuc(U_2811))
| ( ! [U_2805] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2805,U_2811)
| U_2809 != c_Nat_OSuc(U_2805) )
& U_2809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2810,U_2808] :
( ? [U_2804] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2804,U_2810)
& U_2808 = c_Nat_OSuc(U_2804) )
| U_2808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2808,c_Nat_OSuc(U_2810)) ) ),
inference(miniscope,[status(thm)],[f_900_2]) ).
fof(f_900_4,plain,
( ! [U_2811,U_2809] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2809,c_Nat_OSuc(U_2811))
| ( ! [U_2805] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2805,U_2811)
| U_2809 != c_Nat_OSuc(U_2805) )
& U_2809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2810,U_2808] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK59(U_2810,U_2808),U_2810)
& U_2808 = c_Nat_OSuc(sK59(U_2810,U_2808)) )
| U_2808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2808,c_Nat_OSuc(U_2810)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_2804,sK59(U_2810,U_2808))],[f_900_3]) ).
fof(f_900_5,plain,
( ! [U_2805,U_2809,U_2811] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2805,U_2811)
| U_2809 != c_Nat_OSuc(U_2805)
| ~ sP278(U_2805,U_2809,U_2811) )
& ! [U_2805,U_2809,U_2811] :
( U_2809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP278(U_2805,U_2809,U_2811) )
& ! [U_2808,U_2810] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK59(U_2810,U_2808),U_2810)
| ~ sP277(U_2808,U_2810) )
& ! [U_2808,U_2810] :
( U_2808 = c_Nat_OSuc(sK59(U_2810,U_2808))
| ~ sP277(U_2808,U_2810) )
& ! [U_2805,U_2809,U_2811] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2809,c_Nat_OSuc(U_2811))
| sP278(U_2805,U_2809,U_2811) )
& ! [U_2808,U_2810] :
( sP277(U_2808,U_2810)
| U_2808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2808,c_Nat_OSuc(U_2810)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277,sP278])],[f_900_4]) ).
cnf(f_900_6,plain,
( sP277(U_2808,U_2810)
| U_2808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2808,c_Nat_OSuc(U_2810)) ),
inference(clausify,[status(thm)],[f_900_5]) ).
cnf(f_900_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2809,c_Nat_OSuc(U_2811))
| sP278(U_2805,U_2809,U_2811) ),
inference(clausify,[status(thm)],[f_900_5]) ).
cnf(f_900_8,plain,
( U_2808 = c_Nat_OSuc(sK59(U_2810,U_2808))
| ~ sP277(U_2808,U_2810) ),
inference(clausify,[status(thm)],[f_900_5]) ).
cnf(f_900_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK59(U_2810,U_2808),U_2810)
| ~ sP277(U_2808,U_2810) ),
inference(clausify,[status(thm)],[f_900_5]) ).
cnf(f_900_10,plain,
( U_2809 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP278(U_2805,U_2809,U_2811) ),
inference(clausify,[status(thm)],[f_900_5]) ).
cnf(f_900_11,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2805,U_2811)
| U_2809 != c_Nat_OSuc(U_2805)
| ~ sP278(U_2805,U_2809,U_2811) ),
inference(clausify,[status(thm)],[f_900_5]) ).
fof(f_901_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).
fof(f_901_2,plain,
! [U_2812] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2812,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2812,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
fof(f_901_3,plain,
( ! [U_2814] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2814,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2814 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2813] :
( U_2813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2813,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_901_2]) ).
fof(f_901_4,plain,
( ! [U_2814] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2814,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2814 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2813] :
( U_2813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2813,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa)],[f_901_3]) ).
cnf(f_901_5,plain,
( U_2813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2813,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_901_4]) ).
cnf(f_901_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2814,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2814 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_901_4]) ).
fof(f_902_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| ! [B_m] : V_n_2 != c_Nat_OSuc(B_m) )
& ( ? [B_m] : V_n_2 = c_Nat_OSuc(B_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).
fof(f_902_2,plain,
! [U_2817] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2817)
| ! [U_2816] : U_2817 != c_Nat_OSuc(U_2816) )
& ( ? [U_2815] : U_2817 = c_Nat_OSuc(U_2815)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2817) ) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
fof(f_902_3,plain,
( ! [U_2819] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2819)
| ! [U_2816] : U_2819 != c_Nat_OSuc(U_2816) )
& ! [U_2818] :
( ? [U_2815] : U_2818 = c_Nat_OSuc(U_2815)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2818) ) ),
inference(miniscope,[status(thm)],[f_902_2]) ).
fof(f_902_4,plain,
( ! [U_2819] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2819)
| ! [U_2816] : U_2819 != c_Nat_OSuc(U_2816) )
& ! [U_2818] :
( U_2818 = c_Nat_OSuc(sK60(U_2818))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2818) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_2815,sK60(U_2818))],[f_902_3]) ).
fof(f_902_5,plain,
( ! [U_2819,U_2816] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2819)
| U_2819 != c_Nat_OSuc(U_2816) )
& ! [U_2818] :
( U_2818 = c_Nat_OSuc(sK60(U_2818))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2818) ) ),
inference(definitional_conversion,[status(esa)],[f_902_4]) ).
cnf(f_902_6,plain,
( U_2818 = c_Nat_OSuc(sK60(U_2818))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2818) ),
inference(clausify,[status(thm)],[f_902_5]) ).
cnf(f_902_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2819)
| U_2819 != c_Nat_OSuc(U_2816) ),
inference(clausify,[status(thm)],[f_902_5]) ).
fof(f_903_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1]) ).
fof(f_903_2,plain,
! [U_2822,U_2821,U_2820] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2820)),U_2821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2820)),U_2822))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2821,U_2822) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2821,U_2822)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2820)),U_2821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2820)),U_2822)) ) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
fof(f_903_3,plain,
( ! [U_2828,U_2826] :
( ! [U_2824] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2824)),U_2826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2824)),U_2828))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2826,U_2828) )
& ! [U_2827,U_2825] :
( ! [U_2823] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2823)),U_2825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2823)),U_2827))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2825,U_2827) ) ),
inference(miniscope,[status(thm)],[f_903_2]) ).
fof(f_903_4,plain,
( ! [U_2828,U_2824,U_2826] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2824)),U_2826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2824)),U_2828))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2826,U_2828) )
& ! [U_2823,U_2825,U_2827] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2823)),U_2825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2823)),U_2827))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2825,U_2827) ) ),
inference(definitional_conversion,[status(esa)],[f_903_3]) ).
cnf(f_903_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2823)),U_2825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2823)),U_2827))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2825,U_2827) ),
inference(clausify,[status(thm)],[f_903_4]) ).
cnf(f_903_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2824)),U_2826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2824)),U_2828))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2826,U_2828) ),
inference(clausify,[status(thm)],[f_903_4]) ).
fof(f_904_1,plain,
! [V_n_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff]) ).
fof(f_904_2,plain,
! [U_2830,U_2829] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2829),U_2830) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2830 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2829 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_2830 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2829 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2829),U_2830) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
fof(f_904_3,plain,
( ! [U_2834,U_2832] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2832),U_2834) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2834 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2832 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_2833,U_2831] :
( ( U_2833 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2831 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2831),U_2833) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_904_2]) ).
fof(f_904_4,plain,
( ! [U_2831,U_2833] :
( U_2833 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP279(U_2831,U_2833) )
& ! [U_2831,U_2833] :
( U_2831 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP279(U_2831,U_2833) )
& ! [U_2834,U_2832] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2832),U_2834) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2834 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2832 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_2831,U_2833] :
( sP279(U_2831,U_2833)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2831),U_2833) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279])],[f_904_3]) ).
cnf(f_904_5,plain,
( sP279(U_2831,U_2833)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2831),U_2833) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_904_4]) ).
cnf(f_904_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2832),U_2834) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2834 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2832 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_904_4]) ).
cnf(f_904_7,plain,
( U_2831 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP279(U_2831,U_2833) ),
inference(clausify,[status(thm)],[f_904_4]) ).
cnf(f_904_8,plain,
( U_2833 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP279(U_2831,U_2833) ),
inference(clausify,[status(thm)],[f_904_4]) ).
fof(f_905_1,plain,
! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)),
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(f_905_2,plain,
! [U_2839,U_2838,U_2837,U_2836,U_2835] : hAPP(hAPP(c_Power_Opower_Opower(U_2835,U_2836,U_2837),U_2838),c_Nat_OSuc(U_2839)) = hAPP(hAPP(U_2837,U_2838),hAPP(hAPP(c_Power_Opower_Opower(U_2835,U_2836,U_2837),U_2838),U_2839)),
inference(variable_rename,[status(thm)],[f_905_1]) ).
fof(f_905_3,plain,
! [U_2835,U_2836,U_2838,U_2837,U_2839] : hAPP(hAPP(c_Power_Opower_Opower(U_2835,U_2836,U_2837),U_2838),c_Nat_OSuc(U_2839)) = hAPP(hAPP(U_2837,U_2838),hAPP(hAPP(c_Power_Opower_Opower(U_2835,U_2836,U_2837),U_2838),U_2839)),
inference(definitional_conversion,[status(esa)],[f_905_2]) ).
cnf(f_905_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_2835,U_2836,U_2837),U_2838),c_Nat_OSuc(U_2839)) = hAPP(hAPP(U_2837,U_2838),hAPP(hAPP(c_Power_Opower_Opower(U_2835,U_2836,U_2837),U_2838),U_2839)),
inference(clausify,[status(thm)],[f_905_3]) ).
fof(f_906_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),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_906_2,plain,
! [U_2842,U_2841,U_2840] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2840),hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),U_2841),U_2842)),U_2841) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),U_2841),c_Nat_OSuc(U_2842))
| ~ class_Rings_Ocomm__semiring__1(U_2840) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
fof(f_906_3,plain,
! [U_2840,U_2841,U_2842] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2840),hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),U_2841),U_2842)),U_2841) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),U_2841),c_Nat_OSuc(U_2842))
| ~ class_Rings_Ocomm__semiring__1(U_2840) ),
inference(definitional_conversion,[status(esa)],[f_906_2]) ).
cnf(f_906_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2840),hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),U_2841),U_2842)),U_2841) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2840),U_2841),c_Nat_OSuc(U_2842))
| ~ class_Rings_Ocomm__semiring__1(U_2840) ),
inference(clausify,[status(thm)],[f_906_3]) ).
fof(f_907_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),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_907_2,plain,
! [U_2845,U_2844,U_2843] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2843),U_2844),hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),U_2845)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),c_Nat_OSuc(U_2845))
| ~ class_Rings_Ocomm__semiring__1(U_2843) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
fof(f_907_3,plain,
! [U_2843,U_2844,U_2845] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2843),U_2844),hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),U_2845)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),c_Nat_OSuc(U_2845))
| ~ class_Rings_Ocomm__semiring__1(U_2843) ),
inference(definitional_conversion,[status(esa)],[f_907_2]) ).
cnf(f_907_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2843),U_2844),hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),U_2845)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2843),U_2844),c_Nat_OSuc(U_2845))
| ~ class_Rings_Ocomm__semiring__1(U_2843) ),
inference(clausify,[status(thm)],[f_907_3]) ).
fof(f_908_1,plain,
! [V_q,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),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_908_2,plain,
! [U_2848,U_2847,U_2846] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2847),c_Nat_OSuc(U_2848)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2846),U_2847),hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2847),U_2848))
| ~ class_Rings_Ocomm__semiring__1(U_2846) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
fof(f_908_3,plain,
! [U_2846,U_2847,U_2848] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2847),c_Nat_OSuc(U_2848)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2846),U_2847),hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2847),U_2848))
| ~ class_Rings_Ocomm__semiring__1(U_2846) ),
inference(definitional_conversion,[status(esa)],[f_908_2]) ).
cnf(f_908_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2847),c_Nat_OSuc(U_2848)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2846),U_2847),hAPP(hAPP(c_Power_Opower__class_Opower(U_2846),U_2847),U_2848))
| ~ class_Rings_Ocomm__semiring__1(U_2846) ),
inference(clausify,[status(thm)],[f_908_3]) ).
fof(f_909_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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_909_2,plain,
! [U_2851,U_2850,U_2849] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2849),U_2850),c_Nat_OSuc(U_2851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2849),U_2850),hAPP(hAPP(c_Power_Opower__class_Opower(U_2849),U_2850),U_2851))
| ~ class_Power_Opower(U_2849) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
fof(f_909_3,plain,
! [U_2849,U_2850,U_2851] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2849),U_2850),c_Nat_OSuc(U_2851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2849),U_2850),hAPP(hAPP(c_Power_Opower__class_Opower(U_2849),U_2850),U_2851))
| ~ class_Power_Opower(U_2849) ),
inference(definitional_conversion,[status(esa)],[f_909_2]) ).
cnf(f_909_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2849),U_2850),c_Nat_OSuc(U_2851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2849),U_2850),hAPP(hAPP(c_Power_Opower__class_Opower(U_2849),U_2850),U_2851))
| ~ class_Power_Opower(U_2849) ),
inference(clausify,[status(thm)],[f_909_3]) ).
fof(f_910_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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_910_2,plain,
! [U_2854,U_2853,U_2852] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2852),U_2853),c_Nat_OSuc(U_2854)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2852),hAPP(hAPP(c_Power_Opower__class_Opower(U_2852),U_2853),U_2854)),U_2853)
| ~ class_Groups_Omonoid__mult(U_2852) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
fof(f_910_3,plain,
! [U_2852,U_2853,U_2854] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2852),U_2853),c_Nat_OSuc(U_2854)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2852),hAPP(hAPP(c_Power_Opower__class_Opower(U_2852),U_2853),U_2854)),U_2853)
| ~ class_Groups_Omonoid__mult(U_2852) ),
inference(definitional_conversion,[status(esa)],[f_910_2]) ).
cnf(f_910_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2852),U_2853),c_Nat_OSuc(U_2854)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2852),hAPP(hAPP(c_Power_Opower__class_Opower(U_2852),U_2853),U_2854)),U_2853)
| ~ class_Groups_Omonoid__mult(U_2852) ),
inference(clausify,[status(thm)],[f_910_3]) ).
fof(f_911_1,plain,
! [V_n,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),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_911_2,plain,
! [U_2856,U_2855] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2855),c_Groups_Ozero__class_Ozero(U_2855)),c_Nat_OSuc(U_2856)) = c_Groups_Ozero__class_Ozero(U_2855)
| ~ class_Rings_Osemiring__0(U_2855)
| ~ class_Power_Opower(U_2855) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
fof(f_911_3,plain,
! [U_2855,U_2856] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2855),c_Groups_Ozero__class_Ozero(U_2855)),c_Nat_OSuc(U_2856)) = c_Groups_Ozero__class_Ozero(U_2855)
| ~ class_Rings_Osemiring__0(U_2855)
| ~ class_Power_Opower(U_2855) ),
inference(definitional_conversion,[status(esa)],[f_911_2]) ).
cnf(f_911_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2855),c_Groups_Ozero__class_Ozero(U_2855)),c_Nat_OSuc(U_2856)) = c_Groups_Ozero__class_Ozero(U_2855)
| ~ class_Rings_Osemiring__0(U_2855)
| ~ class_Power_Opower(U_2855) ),
inference(clausify,[status(thm)],[f_911_3]) ).
fof(f_912_1,plain,
! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_power__Suc__0]) ).
fof(f_912_2,plain,
! [U_2857] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2857) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_912_1]) ).
fof(f_912_3,plain,
! [U_2857] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2857) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_912_2]) ).
cnf(f_912_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2857) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_912_3]) ).
fof(f_913_1,plain,
! [V_ma_2,V_x_2] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( V_x_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2) != 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_913_2,plain,
! [U_2859,U_2858] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2859) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_2858 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2859 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_2858 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2859 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2859) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
fof(f_913_3,plain,
( ! [U_2863,U_2861] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2861),U_2863) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_2861 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2863 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2862,U_2860] :
( U_2860 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2862 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2860),U_2862) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_913_2]) ).
fof(f_913_4,plain,
( ! [U_2863,U_2861] :
( U_2861 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP280(U_2863,U_2861) )
& ! [U_2863,U_2861] :
( U_2863 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP280(U_2863,U_2861) )
& ! [U_2863,U_2861] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2861),U_2863) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP280(U_2863,U_2861) )
& ! [U_2862,U_2860] :
( U_2860 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2862 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2860),U_2862) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_913_3]) ).
cnf(f_913_5,plain,
( U_2860 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2862 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2860),U_2862) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_913_4]) ).
cnf(f_913_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2861),U_2863) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP280(U_2863,U_2861) ),
inference(clausify,[status(thm)],[f_913_4]) ).
cnf(f_913_7,plain,
( U_2863 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP280(U_2863,U_2861) ),
inference(clausify,[status(thm)],[f_913_4]) ).
cnf(f_913_8,plain,
( U_2861 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP280(U_2863,U_2861) ),
inference(clausify,[status(thm)],[f_913_4]) ).
fof(f_914_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base]) ).
fof(f_914_2,plain,
! [U_2867,U_2866,U_2865,U_2864] :
( c_Orderings_Oord__class_Oless__eq(U_2864,U_2865,U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(U_2864,c_Groups_Ozero__class_Ozero(U_2864),U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(U_2864,hAPP(hAPP(c_Power_Opower__class_Opower(U_2864),U_2865),c_Nat_OSuc(U_2866)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2864),U_2867),c_Nat_OSuc(U_2866)))
| ~ class_Rings_Olinordered__semidom(U_2864) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
fof(f_914_3,plain,
! [U_2864,U_2867,U_2866,U_2865] :
( c_Orderings_Oord__class_Oless__eq(U_2864,U_2865,U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(U_2864,c_Groups_Ozero__class_Ozero(U_2864),U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(U_2864,hAPP(hAPP(c_Power_Opower__class_Opower(U_2864),U_2865),c_Nat_OSuc(U_2866)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2864),U_2867),c_Nat_OSuc(U_2866)))
| ~ class_Rings_Olinordered__semidom(U_2864) ),
inference(definitional_conversion,[status(esa)],[f_914_2]) ).
cnf(f_914_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2864,U_2865,U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(U_2864,c_Groups_Ozero__class_Ozero(U_2864),U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(U_2864,hAPP(hAPP(c_Power_Opower__class_Opower(U_2864),U_2865),c_Nat_OSuc(U_2866)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2864),U_2867),c_Nat_OSuc(U_2866)))
| ~ class_Rings_Olinordered__semidom(U_2864) ),
inference(clausify,[status(thm)],[f_914_3]) ).
fof(f_915_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ 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),c_Nat_OSuc(V_n)) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__base]) ).
fof(f_915_2,plain,
! [U_2871,U_2870,U_2869,U_2868] :
( U_2869 = U_2871
| ~ c_Orderings_Oord__class_Oless__eq(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2871)
| ~ c_Orderings_Oord__class_Oless__eq(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2869)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2869),c_Nat_OSuc(U_2870)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),c_Nat_OSuc(U_2870))
| ~ class_Rings_Olinordered__semidom(U_2868) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
fof(f_915_3,plain,
! [U_2870,U_2868,U_2869,U_2871] :
( U_2869 = U_2871
| ~ c_Orderings_Oord__class_Oless__eq(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2871)
| ~ c_Orderings_Oord__class_Oless__eq(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2869)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2869),c_Nat_OSuc(U_2870)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),c_Nat_OSuc(U_2870))
| ~ class_Rings_Olinordered__semidom(U_2868) ),
inference(definitional_conversion,[status(esa)],[f_915_2]) ).
cnf(f_915_4,plain,
( U_2869 = U_2871
| ~ c_Orderings_Oord__class_Oless__eq(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2871)
| ~ c_Orderings_Oord__class_Oless__eq(U_2868,c_Groups_Ozero__class_Ozero(U_2868),U_2869)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2869),c_Nat_OSuc(U_2870)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2868),U_2871),c_Nat_OSuc(U_2870))
| ~ class_Rings_Olinordered__semidom(U_2868) ),
inference(clausify,[status(thm)],[f_915_3]) ).
fof(f_916_1,plain,
! [V_n,V_a,T_a] :
( 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),c_Nat_OSuc(V_n)))
| ~ 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_916_2,plain,
! [U_2874,U_2873,U_2872] :
( c_Orderings_Oord__class_Oless(U_2872,c_Groups_Oone__class_Oone(U_2872),hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2873),c_Nat_OSuc(U_2874)))
| ~ c_Orderings_Oord__class_Oless(U_2872,c_Groups_Oone__class_Oone(U_2872),U_2873)
| ~ class_Rings_Olinordered__semidom(U_2872) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
fof(f_916_3,plain,
! [U_2873,U_2872,U_2874] :
( c_Orderings_Oord__class_Oless(U_2872,c_Groups_Oone__class_Oone(U_2872),hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2873),c_Nat_OSuc(U_2874)))
| ~ c_Orderings_Oord__class_Oless(U_2872,c_Groups_Oone__class_Oone(U_2872),U_2873)
| ~ class_Rings_Olinordered__semidom(U_2872) ),
inference(definitional_conversion,[status(esa)],[f_916_2]) ).
cnf(f_916_4,plain,
( c_Orderings_Oord__class_Oless(U_2872,c_Groups_Oone__class_Oone(U_2872),hAPP(hAPP(c_Power_Opower__class_Opower(U_2872),U_2873),c_Nat_OSuc(U_2874)))
| ~ c_Orderings_Oord__class_Oless(U_2872,c_Groups_Oone__class_Oone(U_2872),U_2873)
| ~ class_Rings_Olinordered__semidom(U_2872) ),
inference(clausify,[status(thm)],[f_916_3]) ).
fof(f_917_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
& V_x_2 != V_y_2 ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__disj]) ).
fof(f_917_2,plain,
! [U_2877,U_2876,U_2875] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2876),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2877),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( U_2876 != c_Groups_Ouminus__class_Ouminus(U_2875,U_2877)
& U_2876 != U_2877 ) )
& ( U_2876 = c_Groups_Ouminus__class_Ouminus(U_2875,U_2877)
| U_2876 = U_2877
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2876),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2877),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(U_2875) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
fof(f_917_3,plain,
( ! [U_2876,U_2877,U_2875] :
( U_2876 != c_Groups_Ouminus__class_Ouminus(U_2875,U_2877)
| ~ sP281(U_2876,U_2877,U_2875) )
& ! [U_2876,U_2877,U_2875] :
( U_2876 != U_2877
| ~ sP281(U_2876,U_2877,U_2875) )
& ! [U_2876,U_2877,U_2875] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2876),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2877),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| sP281(U_2876,U_2877,U_2875)
| ~ sP282(U_2876,U_2877,U_2875) )
& ! [U_2876,U_2877,U_2875] :
( U_2876 = c_Groups_Ouminus__class_Ouminus(U_2875,U_2877)
| U_2876 = U_2877
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2876),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2877),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ sP282(U_2876,U_2877,U_2875) )
& ! [U_2876,U_2877,U_2875] :
( sP282(U_2876,U_2877,U_2875)
| ~ class_Rings_Oidom(U_2875) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281,sP282])],[f_917_2]) ).
cnf(f_917_4,plain,
( sP282(U_2876,U_2877,U_2875)
| ~ class_Rings_Oidom(U_2875) ),
inference(clausify,[status(thm)],[f_917_3]) ).
cnf(f_917_5,plain,
( U_2876 = c_Groups_Ouminus__class_Ouminus(U_2875,U_2877)
| U_2876 = U_2877
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2876),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2877),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ sP282(U_2876,U_2877,U_2875) ),
inference(clausify,[status(thm)],[f_917_3]) ).
cnf(f_917_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2876),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2875),U_2877),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| sP281(U_2876,U_2877,U_2875)
| ~ sP282(U_2876,U_2877,U_2875) ),
inference(clausify,[status(thm)],[f_917_3]) ).
cnf(f_917_7,plain,
( U_2876 != U_2877
| ~ sP281(U_2876,U_2877,U_2875) ),
inference(clausify,[status(thm)],[f_917_3]) ).
cnf(f_917_8,plain,
( U_2876 != c_Groups_Ouminus__class_Ouminus(U_2875,U_2877)
| ~ sP281(U_2876,U_2877,U_2875) ),
inference(clausify,[status(thm)],[f_917_3]) ).
fof(f_918_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_one__less__mult]) ).
fof(f_918_2,plain,
! [U_2879,U_2878] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2878))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2879)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2878) ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
fof(f_918_3,plain,
! [U_2879,U_2878] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2878))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2879)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2878) ),
inference(definitional_conversion,[status(esa)],[f_918_2]) ).
cnf(f_918_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2879),U_2878))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2879)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2878) ),
inference(clausify,[status(thm)],[f_918_3]) ).
fof(f_919_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_919_2,plain,
! [U_2881,U_2880] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2881))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2881)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2880) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
fof(f_919_3,plain,
! [U_2880,U_2881] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2881))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2881)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2880) ),
inference(definitional_conversion,[status(esa)],[f_919_2]) ).
cnf(f_919_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2880,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2880),U_2881))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2881)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2880) ),
inference(clausify,[status(thm)],[f_919_3]) ).
fof(f_920_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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_920_2,plain,
! [U_2883,U_2882] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2882,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2883),U_2882))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2883)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2882) ),
inference(variable_rename,[status(thm)],[f_920_1]) ).
fof(f_920_3,plain,
! [U_2882,U_2883] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2882,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2883),U_2882))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2883)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2882) ),
inference(definitional_conversion,[status(esa)],[f_920_2]) ).
cnf(f_920_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2882,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2883),U_2882))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2883)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2882) ),
inference(clausify,[status(thm)],[f_920_3]) ).
fof(f_921_1,plain,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)
| ~ 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_921_2,plain,
! [U_2885,U_2884] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2884,c_Nat_OSuc(U_2885)),U_2884)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2884) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
fof(f_921_3,plain,
! [U_2884,U_2885] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2884,c_Nat_OSuc(U_2885)),U_2884)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2884) ),
inference(definitional_conversion,[status(esa)],[f_921_2]) ).
cnf(f_921_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2884,c_Nat_OSuc(U_2885)),U_2884)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2884) ),
inference(clausify,[status(thm)],[f_921_3]) ).
fof(f_922_1,plain,
! [V_n] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n
| ~ 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_922_2,plain,
! [U_2886] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2886,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2886
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2886) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
fof(f_922_3,plain,
! [U_2886] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2886,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2886
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2886) ),
inference(definitional_conversion,[status(esa)],[f_922_2]) ).
cnf(f_922_4,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2886,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2886
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2886) ),
inference(clausify,[status(thm)],[f_922_3]) ).
fof(f_923_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ma_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ma_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).
fof(f_923_2,plain,
! [U_2888,U_2887] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2887),U_2888))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2888)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2887) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2888)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2887) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2887),U_2888)) ) ),
inference(variable_rename,[status(thm)],[f_923_1]) ).
fof(f_923_3,plain,
( ! [U_2892,U_2890] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),U_2892))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2890) )
& ! [U_2891,U_2889] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2891)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2889) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)) ) ),
inference(miniscope,[status(thm)],[f_923_2]) ).
fof(f_923_4,plain,
( ! [U_2891,U_2889] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2891)
| ~ sP283(U_2891,U_2889) )
& ! [U_2891,U_2889] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2889)
| ~ sP283(U_2891,U_2889) )
& ! [U_2892,U_2890] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),U_2892))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2890) )
& ! [U_2891,U_2889] :
( sP283(U_2891,U_2889)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_923_3]) ).
cnf(f_923_5,plain,
( sP283(U_2891,U_2889)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2891)) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),U_2892))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2890) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2889)
| ~ sP283(U_2891,U_2889) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2891)
| ~ sP283(U_2891,U_2889) ),
inference(clausify,[status(thm)],[f_923_4]) ).
fof(f_924_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).
fof(f_924_2,plain,
! [U_2893] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2893))),
inference(variable_rename,[status(thm)],[f_924_1]) ).
fof(f_924_3,plain,
! [U_2893] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2893))),
inference(definitional_conversion,[status(esa)],[f_924_2]) ).
cnf(f_924_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2893))),
inference(clausify,[status(thm)],[f_924_3]) ).
fof(f_925_1,plain,
! [V_m,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))
| ~ 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_925_2,plain,
! [U_2896,U_2895,U_2894] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2896,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2895,U_2894))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2896,U_2894),c_Nat_OSuc(U_2895))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2894,U_2895) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
fof(f_925_3,plain,
! [U_2894,U_2896,U_2895] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2896,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2895,U_2894))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2896,U_2894),c_Nat_OSuc(U_2895))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2894,U_2895) ),
inference(definitional_conversion,[status(esa)],[f_925_2]) ).
cnf(f_925_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2896,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2895,U_2894))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2896,U_2894),c_Nat_OSuc(U_2895))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2894,U_2895) ),
inference(clausify,[status(thm)],[f_925_3]) ).
fof(f_926_1,plain,
! [V_m,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))
| ~ 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_926_2,plain,
! [U_2899,U_2898,U_2897] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2898,U_2897)),U_2899) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2898),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2897,U_2899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2897,U_2898) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
fof(f_926_3,plain,
! [U_2897,U_2898,U_2899] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2898,U_2897)),U_2899) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2898),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2897,U_2899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2897,U_2898) ),
inference(definitional_conversion,[status(esa)],[f_926_2]) ).
cnf(f_926_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2898,U_2897)),U_2899) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2898),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2897,U_2899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2897,U_2898) ),
inference(clausify,[status(thm)],[f_926_3]) ).
fof(f_927_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__one]) ).
fof(f_927_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_927_1]) ).
cnf(f_927_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_927_2]) ).
fof(f_928_1,plain,
! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(f_928_2,plain,
! [U_2900] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2900)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2900),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_928_1]) ).
fof(f_928_3,plain,
! [U_2900] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2900)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2900),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_928_2]) ).
cnf(f_928_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2900)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2900),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_928_3]) ).
fof(f_929_1,plain,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_929_2,plain,
! [U_2902,U_2901] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2901),U_2902))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2901) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
fof(f_929_3,plain,
! [U_2901,U_2902] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2901),U_2902))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2901) ),
inference(definitional_conversion,[status(esa)],[f_929_2]) ).
cnf(f_929_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2901),U_2902))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2901) ),
inference(clausify,[status(thm)],[f_929_3]) ).
fof(f_930_1,plain,
! [V_n,V_r,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self]) ).
fof(f_930_2,plain,
! [U_2905,U_2904,U_2903] :
( c_Orderings_Oord__class_Oless__eq(U_2903,hAPP(hAPP(c_Power_Opower__class_Opower(U_2903),U_2904),c_Nat_OSuc(U_2905)),U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(U_2903,U_2904,c_Groups_Oone__class_Oone(U_2903))
| ~ c_Orderings_Oord__class_Oless__eq(U_2903,c_Groups_Ozero__class_Ozero(U_2903),U_2904)
| ~ class_Rings_Olinordered__semidom(U_2903) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
fof(f_930_3,plain,
! [U_2903,U_2904,U_2905] :
( c_Orderings_Oord__class_Oless__eq(U_2903,hAPP(hAPP(c_Power_Opower__class_Opower(U_2903),U_2904),c_Nat_OSuc(U_2905)),U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(U_2903,U_2904,c_Groups_Oone__class_Oone(U_2903))
| ~ c_Orderings_Oord__class_Oless__eq(U_2903,c_Groups_Ozero__class_Ozero(U_2903),U_2904)
| ~ class_Rings_Olinordered__semidom(U_2903) ),
inference(definitional_conversion,[status(esa)],[f_930_2]) ).
cnf(f_930_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2903,hAPP(hAPP(c_Power_Opower__class_Opower(U_2903),U_2904),c_Nat_OSuc(U_2905)),U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(U_2903,U_2904,c_Groups_Oone__class_Oone(U_2903))
| ~ c_Orderings_Oord__class_Oless__eq(U_2903,c_Groups_Ozero__class_Ozero(U_2903),U_2904)
| ~ class_Rings_Olinordered__semidom(U_2903) ),
inference(clausify,[status(thm)],[f_930_3]) ).
fof(f_931_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ 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_931_2,plain,
! [U_2908,U_2907,U_2906] :
( c_Orderings_Oord__class_Oless(U_2906,hAPP(hAPP(c_Power_Opower__class_Opower(U_2906),U_2907),c_Nat_OSuc(U_2908)),c_Groups_Oone__class_Oone(U_2906))
| ~ c_Orderings_Oord__class_Oless(U_2906,U_2907,c_Groups_Oone__class_Oone(U_2906))
| ~ c_Orderings_Oord__class_Oless(U_2906,c_Groups_Ozero__class_Ozero(U_2906),U_2907)
| ~ class_Rings_Olinordered__semidom(U_2906) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
fof(f_931_3,plain,
! [U_2906,U_2907,U_2908] :
( c_Orderings_Oord__class_Oless(U_2906,hAPP(hAPP(c_Power_Opower__class_Opower(U_2906),U_2907),c_Nat_OSuc(U_2908)),c_Groups_Oone__class_Oone(U_2906))
| ~ c_Orderings_Oord__class_Oless(U_2906,U_2907,c_Groups_Oone__class_Oone(U_2906))
| ~ c_Orderings_Oord__class_Oless(U_2906,c_Groups_Ozero__class_Ozero(U_2906),U_2907)
| ~ class_Rings_Olinordered__semidom(U_2906) ),
inference(definitional_conversion,[status(esa)],[f_931_2]) ).
cnf(f_931_4,plain,
( c_Orderings_Oord__class_Oless(U_2906,hAPP(hAPP(c_Power_Opower__class_Opower(U_2906),U_2907),c_Nat_OSuc(U_2908)),c_Groups_Oone__class_Oone(U_2906))
| ~ c_Orderings_Oord__class_Oless(U_2906,U_2907,c_Groups_Oone__class_Oone(U_2906))
| ~ c_Orderings_Oord__class_Oless(U_2906,c_Groups_Ozero__class_Ozero(U_2906),U_2907)
| ~ class_Rings_Olinordered__semidom(U_2906) ),
inference(clausify,[status(thm)],[f_931_3]) ).
fof(f_932_1,plain,
! [V_y,V_n,V_p,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_lemma__realpow__diff]) ).
fof(f_932_2,plain,
! [U_2912,U_2911,U_2910,U_2909] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2909),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2911),U_2910)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2909),hAPP(hAPP(c_Power_Opower__class_Opower(U_2909),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2911,U_2910))),U_2912)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2910,U_2911)
| ~ class_Groups_Omonoid__mult(U_2909) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
fof(f_932_3,plain,
! [U_2910,U_2909,U_2911,U_2912] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2909),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2911),U_2910)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2909),hAPP(hAPP(c_Power_Opower__class_Opower(U_2909),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2911,U_2910))),U_2912)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2910,U_2911)
| ~ class_Groups_Omonoid__mult(U_2909) ),
inference(definitional_conversion,[status(esa)],[f_932_2]) ).
cnf(f_932_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2909),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2911),U_2910)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2909),hAPP(hAPP(c_Power_Opower__class_Opower(U_2909),U_2912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2911,U_2910))),U_2912)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2910,U_2911)
| ~ class_Groups_Omonoid__mult(U_2909) ),
inference(clausify,[status(thm)],[f_932_3]) ).
fof(f_933_1,plain,
! [V_n] :
( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ 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_933_2,plain,
! [U_2913] :
( U_2913 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2913,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2913) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
fof(f_933_3,plain,
! [U_2913] :
( U_2913 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2913,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2913) ),
inference(definitional_conversion,[status(esa)],[f_933_2]) ).
cnf(f_933_4,plain,
( U_2913 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2913,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2913) ),
inference(clausify,[status(thm)],[f_933_3]) ).
fof(f_934_1,plain,
! [V_n] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n
| ~ 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_934_2,plain,
! [U_2914] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2914,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2914
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2914) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
fof(f_934_3,plain,
! [U_2914] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2914,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2914
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2914) ),
inference(definitional_conversion,[status(esa)],[f_934_2]) ).
cnf(f_934_4,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2914,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2914
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2914) ),
inference(clausify,[status(thm)],[f_934_3]) ).
fof(f_935_1,plain,
! [V_n,V_m] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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) )
& ( 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_935_2,plain,
! [U_2916,U_2915] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2915,U_2916) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2915,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2916))
| U_2915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2915,U_2916) = U_2916
| U_2915 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
fof(f_935_3,plain,
( ! [U_2920,U_2918] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2918,U_2920) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2918,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2920))
| U_2918 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2919,U_2917] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2917,U_2919) = U_2919
| U_2917 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_935_2]) ).
fof(f_935_4,plain,
( ! [U_2920,U_2918] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2918,U_2920) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2918,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2920))
| U_2918 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2919,U_2917] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2917,U_2919) = U_2919
| U_2917 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_935_3]) ).
cnf(f_935_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2917,U_2919) = U_2919
| U_2917 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_935_4]) ).
cnf(f_935_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2918,U_2920) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2918,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2920))
| U_2918 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_935_4]) ).
fof(f_936_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff]) ).
fof(f_936_2,plain,
! [U_2926,U_2925] :
( ( ( c_SEQ_OBseq(U_2925,U_2926)
| ! [U_2924] :
? [U_2923] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,U_2923)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2924))) )
& ( ? [U_2922] :
! [U_2921] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,U_2921)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2922)))
| ~ c_SEQ_OBseq(U_2925,U_2926) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2925) ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
fof(f_936_3,plain,
! [U_2926,U_2925] :
( ( ( c_SEQ_OBseq(U_2925,U_2926)
| ! [U_2924] :
? [U_2923] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,U_2923)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2924))) )
& ( ! [U_2921] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,U_2921)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK61(U_2926,U_2925))))
| ~ c_SEQ_OBseq(U_2925,U_2926) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2925) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_2922,sK61(U_2926,U_2925))],[f_936_2]) ).
fof(f_936_4,plain,
! [U_2926,U_2925] :
( ( ( c_SEQ_OBseq(U_2925,U_2926)
| ! [U_2924] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,sK62(U_2926,U_2925,U_2924))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2924))) )
& ( ! [U_2921] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,U_2921)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK61(U_2926,U_2925))))
| ~ c_SEQ_OBseq(U_2925,U_2926) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2925) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_2923,sK62(U_2926,U_2925,U_2924))],[f_936_3]) ).
fof(f_936_5,plain,
( ! [U_2921,U_2924,U_2925,U_2926] :
( c_SEQ_OBseq(U_2925,U_2926)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,sK62(U_2926,U_2925,U_2924))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2924)))
| ~ sP284(U_2921,U_2924,U_2925,U_2926) )
& ! [U_2921,U_2924,U_2925,U_2926] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,U_2921)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK61(U_2926,U_2925))))
| ~ c_SEQ_OBseq(U_2925,U_2926)
| ~ sP284(U_2921,U_2924,U_2925,U_2926) )
& ! [U_2921,U_2924,U_2925,U_2926] :
( sP284(U_2921,U_2924,U_2925,U_2926)
| ~ class_RealVector_Oreal__normed__vector(U_2925) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_936_4]) ).
cnf(f_936_6,plain,
( sP284(U_2921,U_2924,U_2925,U_2926)
| ~ class_RealVector_Oreal__normed__vector(U_2925) ),
inference(clausify,[status(thm)],[f_936_5]) ).
cnf(f_936_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,U_2921)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK61(U_2926,U_2925))))
| ~ c_SEQ_OBseq(U_2925,U_2926)
| ~ sP284(U_2921,U_2924,U_2925,U_2926) ),
inference(clausify,[status(thm)],[f_936_5]) ).
cnf(f_936_8,plain,
( c_SEQ_OBseq(U_2925,U_2926)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2925,hAPP(U_2926,sK62(U_2926,U_2925,U_2924))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2924)))
| ~ sP284(U_2921,U_2924,U_2925,U_2926) ),
inference(clausify,[status(thm)],[f_936_5]) ).
fof(f_937_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff1a]) ).
fof(f_937_2,plain,
! [U_2932,U_2931] :
( ( ( c_SEQ_OBseq(U_2931,U_2932)
| ! [U_2930] :
? [U_2929] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,U_2929)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2930))) )
& ( ? [U_2928] :
! [U_2927] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,U_2927)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2928)))
| ~ c_SEQ_OBseq(U_2931,U_2932) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2931) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
! [U_2932,U_2931] :
( ( ( c_SEQ_OBseq(U_2931,U_2932)
| ! [U_2930] :
? [U_2929] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,U_2929)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2930))) )
& ( ! [U_2927] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,U_2927)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK63(U_2932,U_2931))))
| ~ c_SEQ_OBseq(U_2931,U_2932) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2931) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_2928,sK63(U_2932,U_2931))],[f_937_2]) ).
fof(f_937_4,plain,
! [U_2932,U_2931] :
( ( ( c_SEQ_OBseq(U_2931,U_2932)
| ! [U_2930] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,sK64(U_2932,U_2931,U_2930))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2930))) )
& ( ! [U_2927] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,U_2927)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK63(U_2932,U_2931))))
| ~ c_SEQ_OBseq(U_2931,U_2932) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2931) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_2929,sK64(U_2932,U_2931,U_2930))],[f_937_3]) ).
fof(f_937_5,plain,
( ! [U_2930,U_2927,U_2931,U_2932] :
( c_SEQ_OBseq(U_2931,U_2932)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,sK64(U_2932,U_2931,U_2930))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2930)))
| ~ sP285(U_2930,U_2927,U_2931,U_2932) )
& ! [U_2930,U_2927,U_2931,U_2932] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,U_2927)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK63(U_2932,U_2931))))
| ~ c_SEQ_OBseq(U_2931,U_2932)
| ~ sP285(U_2930,U_2927,U_2931,U_2932) )
& ! [U_2930,U_2927,U_2931,U_2932] :
( sP285(U_2930,U_2927,U_2931,U_2932)
| ~ class_RealVector_Oreal__normed__vector(U_2931) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285])],[f_937_4]) ).
cnf(f_937_6,plain,
( sP285(U_2930,U_2927,U_2931,U_2932)
| ~ class_RealVector_Oreal__normed__vector(U_2931) ),
inference(clausify,[status(thm)],[f_937_5]) ).
cnf(f_937_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,U_2927)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK63(U_2932,U_2931))))
| ~ c_SEQ_OBseq(U_2931,U_2932)
| ~ sP285(U_2930,U_2927,U_2931,U_2932) ),
inference(clausify,[status(thm)],[f_937_5]) ).
cnf(f_937_8,plain,
( c_SEQ_OBseq(U_2931,U_2932)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2931,hAPP(U_2932,sK64(U_2932,U_2931,U_2930))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2930)))
| ~ sP285(U_2930,U_2927,U_2931,U_2932) ),
inference(clausify,[status(thm)],[f_937_5]) ).
fof(f_938_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__diff]) ).
fof(f_938_2,plain,
! [U_2935,U_2934,U_2933] :
( c_Groups_Ominus__class_Ominus(U_2933,hAPP(hAPP(c_Power_Opower__class_Opower(U_2933),U_2934),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2933),U_2935),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),c_Groups_Ominus__class_Ominus(U_2933,U_2934,U_2935)),c_Groups_Oplus__class_Oplus(U_2933,U_2934,U_2935))
| ~ class_Rings_Ocomm__ring__1(U_2933) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
fof(f_938_3,plain,
! [U_2933,U_2934,U_2935] :
( c_Groups_Ominus__class_Ominus(U_2933,hAPP(hAPP(c_Power_Opower__class_Opower(U_2933),U_2934),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2933),U_2935),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),c_Groups_Ominus__class_Ominus(U_2933,U_2934,U_2935)),c_Groups_Oplus__class_Oplus(U_2933,U_2934,U_2935))
| ~ class_Rings_Ocomm__ring__1(U_2933) ),
inference(definitional_conversion,[status(esa)],[f_938_2]) ).
cnf(f_938_4,plain,
( c_Groups_Ominus__class_Ominus(U_2933,hAPP(hAPP(c_Power_Opower__class_Opower(U_2933),U_2934),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2933),U_2935),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),c_Groups_Ominus__class_Ominus(U_2933,U_2934,U_2935)),c_Groups_Oplus__class_Oplus(U_2933,U_2934,U_2935))
| ~ class_Rings_Ocomm__ring__1(U_2933) ),
inference(clausify,[status(thm)],[f_938_3]) ).
fof(f_939_1,plain,
! [V_x,V_y] :
( ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y),V_x) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) ),
inference(fof_nnf,[status(thm)],[fact_reals__Archimedean4]) ).
fof(f_939_2,plain,
! [U_2938,U_2937] :
( ? [U_2936] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2936))),U_2937))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2936)),U_2937),U_2938) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2938)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2937) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
fof(f_939_3,plain,
! [U_2938,U_2937] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK65(U_2938,U_2937)))),U_2937))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK65(U_2938,U_2937))),U_2937),U_2938) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2938)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2937) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_2936,sK65(U_2938,U_2937))],[f_939_2]) ).
fof(f_939_4,plain,
( ! [U_2937,U_2938] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK65(U_2938,U_2937)))),U_2937))
| ~ sP286(U_2937,U_2938) )
& ! [U_2937,U_2938] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK65(U_2938,U_2937))),U_2937),U_2938)
| ~ sP286(U_2937,U_2938) )
& ! [U_2937,U_2938] :
( sP286(U_2937,U_2938)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2938)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2937) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_939_3]) ).
cnf(f_939_5,plain,
( sP286(U_2937,U_2938)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2938)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2937) ),
inference(clausify,[status(thm)],[f_939_4]) ).
cnf(f_939_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK65(U_2938,U_2937))),U_2937),U_2938)
| ~ sP286(U_2937,U_2938) ),
inference(clausify,[status(thm)],[f_939_4]) ).
cnf(f_939_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK65(U_2938,U_2937)))),U_2937))
| ~ sP286(U_2937,U_2938) ),
inference(clausify,[status(thm)],[f_939_4]) ).
fof(f_940_1,plain,
! [V_k,V_m] :
( 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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
| ~ 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_940_2,plain,
! [U_2940,U_2939] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2940),U_2939),U_2940) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2940),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2939,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2939) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
fof(f_940_3,plain,
! [U_2939,U_2940] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2940),U_2939),U_2940) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2940),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2939,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2939) ),
inference(definitional_conversion,[status(esa)],[f_940_2]) ).
cnf(f_940_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2940),U_2939),U_2940) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2940),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2939,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2940)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2939) ),
inference(clausify,[status(thm)],[f_940_3]) ).
fof(f_941_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ 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_941_2,plain,
! [U_2942,U_2941] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2941,U_2942))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2942)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2941) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
fof(f_941_3,plain,
! [U_2942,U_2941] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2941,U_2942))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2942)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2941) ),
inference(definitional_conversion,[status(esa)],[f_941_2]) ).
cnf(f_941_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2941,U_2942))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2942)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2941) ),
inference(clausify,[status(thm)],[f_941_3]) ).
fof(f_942_1,plain,
! [V_a,T_a] :
( 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_942_2,plain,
! [U_2944,U_2943] :
( c_Divides_Odiv__class_Odiv(U_2943,U_2944,U_2944) = c_Groups_Oone__class_Oone(U_2943)
| U_2944 = c_Groups_Ozero__class_Ozero(U_2943)
| ~ class_Divides_Osemiring__div(U_2943) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
fof(f_942_3,plain,
! [U_2943,U_2944] :
( c_Divides_Odiv__class_Odiv(U_2943,U_2944,U_2944) = c_Groups_Oone__class_Oone(U_2943)
| U_2944 = c_Groups_Ozero__class_Ozero(U_2943)
| ~ class_Divides_Osemiring__div(U_2943) ),
inference(definitional_conversion,[status(esa)],[f_942_2]) ).
cnf(f_942_4,plain,
( c_Divides_Odiv__class_Odiv(U_2943,U_2944,U_2944) = c_Groups_Oone__class_Oone(U_2943)
| U_2944 = c_Groups_Ozero__class_Ozero(U_2943)
| ~ class_Divides_Osemiring__div(U_2943) ),
inference(clausify,[status(thm)],[f_942_3]) ).
fof(f_943_1,plain,
! [V_a] :
( 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_943_2,plain,
! [U_2945] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2945,U_2945) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
fof(f_943_3,plain,
! [U_2945] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2945,U_2945) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_943_2]) ).
cnf(f_943_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2945,U_2945) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2945 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_943_3]) ).
fof(f_944_1,plain,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus__zminus]) ).
fof(f_944_2,plain,
! [U_2947,U_2946] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2946),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2947)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2946,U_2947),
inference(variable_rename,[status(thm)],[f_944_1]) ).
fof(f_944_3,plain,
! [U_2947,U_2946] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2946),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2947)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2946,U_2947),
inference(definitional_conversion,[status(esa)],[f_944_2]) ).
cnf(f_944_4,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2946),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2947)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2946,U_2947),
inference(clausify,[status(thm)],[f_944_3]) ).
fof(f_945_1,plain,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2]) ).
fof(f_945_2,plain,
! [U_2949,U_2948] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2948,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2949)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2948),U_2949),
inference(variable_rename,[status(thm)],[f_945_1]) ).
fof(f_945_3,plain,
! [U_2948,U_2949] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2948,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2949)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2948),U_2949),
inference(definitional_conversion,[status(esa)],[f_945_2]) ).
cnf(f_945_4,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2948,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2949)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2948),U_2949),
inference(clausify,[status(thm)],[f_945_3]) ).
fof(f_946_1,plain,
! [V_a,T_a] :
( 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_946_2,plain,
! [U_2951,U_2950] :
( c_Divides_Odiv__class_Odiv(U_2950,U_2951,c_Groups_Oone__class_Oone(U_2950)) = U_2951
| ~ class_Divides_Osemiring__div(U_2950) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
fof(f_946_3,plain,
! [U_2950,U_2951] :
( c_Divides_Odiv__class_Odiv(U_2950,U_2951,c_Groups_Oone__class_Oone(U_2950)) = U_2951
| ~ class_Divides_Osemiring__div(U_2950) ),
inference(definitional_conversion,[status(esa)],[f_946_2]) ).
cnf(f_946_4,plain,
( c_Divides_Odiv__class_Odiv(U_2950,U_2951,c_Groups_Oone__class_Oone(U_2950)) = U_2951
| ~ class_Divides_Osemiring__div(U_2950) ),
inference(clausify,[status(thm)],[f_946_3]) ).
fof(f_947_1,plain,
! [V_a_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ 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_947_2,plain,
! [U_2953,U_2952] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2953,U_2952),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2953,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2953,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2953,U_2952),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2952) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
fof(f_947_3,plain,
( ! [U_2953,U_2952] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2953,U_2952),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2953,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP287(U_2953,U_2952) )
& ! [U_2953,U_2952] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2953,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2953,U_2952),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP287(U_2953,U_2952) )
& ! [U_2953,U_2952] :
( sP287(U_2953,U_2952)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2952) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287])],[f_947_2]) ).
cnf(f_947_4,plain,
( sP287(U_2953,U_2952)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2952) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2953,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2953,U_2952),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP287(U_2953,U_2952) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2953,U_2952),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2953,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP287(U_2953,U_2952) ),
inference(clausify,[status(thm)],[f_947_3]) ).
fof(f_948_1,plain,
! [V_a_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ 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_948_2,plain,
! [U_2955,U_2954] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2955,U_2954),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2955) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2955,U_2954),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2954,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
fof(f_948_3,plain,
( ! [U_2954,U_2955] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2955,U_2954),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2955)
| ~ sP288(U_2954,U_2955) )
& ! [U_2954,U_2955] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2955,U_2954),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP288(U_2954,U_2955) )
& ! [U_2954,U_2955] :
( sP288(U_2954,U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2954,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_948_2]) ).
cnf(f_948_4,plain,
( sP288(U_2954,U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2954,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_948_3]) ).
cnf(f_948_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2955,U_2954),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP288(U_2954,U_2955) ),
inference(clausify,[status(thm)],[f_948_3]) ).
cnf(f_948_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2955,U_2954),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2955)
| ~ sP288(U_2954,U_2955) ),
inference(clausify,[status(thm)],[f_948_3]) ).
fof(f_949_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
| ~ 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_949_2,plain,
! [U_2957,U_2956] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2956,U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2957)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2956,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
fof(f_949_3,plain,
! [U_2957,U_2956] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2956,U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2957)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2956,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(definitional_conversion,[status(esa)],[f_949_2]) ).
cnf(f_949_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2956,U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2957)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2956,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_949_3]) ).
fof(f_950_1,plain,
! [V_b,V_a,V_c,T_a] :
( 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_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_950_2,plain,
! [U_2961,U_2960,U_2959,U_2958] :
( c_Divides_Odiv__class_Odiv(U_2958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2958),U_2959),U_2960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2958),U_2959),U_2961)) = c_Divides_Odiv__class_Odiv(U_2958,U_2960,U_2961)
| U_2959 = c_Groups_Ozero__class_Ozero(U_2958)
| ~ class_Divides_Osemiring__div(U_2958) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
fof(f_950_3,plain,
! [U_2958,U_2959,U_2960,U_2961] :
( c_Divides_Odiv__class_Odiv(U_2958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2958),U_2959),U_2960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2958),U_2959),U_2961)) = c_Divides_Odiv__class_Odiv(U_2958,U_2960,U_2961)
| U_2959 = c_Groups_Ozero__class_Ozero(U_2958)
| ~ class_Divides_Osemiring__div(U_2958) ),
inference(definitional_conversion,[status(esa)],[f_950_2]) ).
cnf(f_950_4,plain,
( c_Divides_Odiv__class_Odiv(U_2958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2958),U_2959),U_2960),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2958),U_2959),U_2961)) = c_Divides_Odiv__class_Odiv(U_2958,U_2960,U_2961)
| U_2959 = c_Groups_Ozero__class_Ozero(U_2958)
| ~ class_Divides_Osemiring__div(U_2958) ),
inference(clausify,[status(thm)],[f_950_3]) ).
fof(f_951_1,plain,
! [V_b,V_a,V_c,T_a] :
( 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)) = 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_951_2,plain,
! [U_2965,U_2964,U_2963,U_2962] :
( c_Divides_Odiv__class_Odiv(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2964),U_2963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2965),U_2963)) = c_Divides_Odiv__class_Odiv(U_2962,U_2964,U_2965)
| U_2963 = c_Groups_Ozero__class_Ozero(U_2962)
| ~ class_Divides_Osemiring__div(U_2962) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
fof(f_951_3,plain,
! [U_2962,U_2963,U_2964,U_2965] :
( c_Divides_Odiv__class_Odiv(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2964),U_2963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2965),U_2963)) = c_Divides_Odiv__class_Odiv(U_2962,U_2964,U_2965)
| U_2963 = c_Groups_Ozero__class_Ozero(U_2962)
| ~ class_Divides_Osemiring__div(U_2962) ),
inference(definitional_conversion,[status(esa)],[f_951_2]) ).
cnf(f_951_4,plain,
( c_Divides_Odiv__class_Odiv(U_2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2964),U_2963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2962),U_2965),U_2963)) = c_Divides_Odiv__class_Odiv(U_2962,U_2964,U_2965)
| U_2963 = c_Groups_Ozero__class_Ozero(U_2962)
| ~ class_Divides_Osemiring__div(U_2962) ),
inference(clausify,[status(thm)],[f_951_3]) ).
fof(f_952_1,plain,
! [V_a,V_b,T_a] :
( 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_952_2,plain,
! [U_2968,U_2967,U_2966] :
( c_Divides_Odiv__class_Odiv(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),U_2967) = U_2968
| U_2967 = c_Groups_Ozero__class_Ozero(U_2966)
| ~ class_Divides_Osemiring__div(U_2966) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
fof(f_952_3,plain,
! [U_2967,U_2966,U_2968] :
( c_Divides_Odiv__class_Odiv(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),U_2967) = U_2968
| U_2967 = c_Groups_Ozero__class_Ozero(U_2966)
| ~ class_Divides_Osemiring__div(U_2966) ),
inference(definitional_conversion,[status(esa)],[f_952_2]) ).
cnf(f_952_4,plain,
( c_Divides_Odiv__class_Odiv(U_2966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2966),U_2967),U_2968),U_2967) = U_2968
| U_2967 = c_Groups_Ozero__class_Ozero(U_2966)
| ~ class_Divides_Osemiring__div(U_2966) ),
inference(clausify,[status(thm)],[f_952_3]) ).
fof(f_953_1,plain,
! [V_a,V_b,T_a] :
( 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_953_2,plain,
! [U_2971,U_2970,U_2969] :
( c_Divides_Odiv__class_Odiv(U_2969,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2969),U_2971),U_2970),U_2970) = U_2971
| U_2970 = c_Groups_Ozero__class_Ozero(U_2969)
| ~ class_Divides_Osemiring__div(U_2969) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
fof(f_953_3,plain,
! [U_2970,U_2969,U_2971] :
( c_Divides_Odiv__class_Odiv(U_2969,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2969),U_2971),U_2970),U_2970) = U_2971
| U_2970 = c_Groups_Ozero__class_Ozero(U_2969)
| ~ class_Divides_Osemiring__div(U_2969) ),
inference(definitional_conversion,[status(esa)],[f_953_2]) ).
cnf(f_953_4,plain,
( c_Divides_Odiv__class_Odiv(U_2969,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2969),U_2971),U_2970),U_2970) = U_2971
| U_2970 = c_Groups_Ozero__class_Ozero(U_2969)
| ~ class_Divides_Osemiring__div(U_2969) ),
inference(clausify,[status(thm)],[f_953_3]) ).
fof(f_954_1,plain,
! [V_b,V_a,V_c,T_a] :
( ( ( 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_Divides_Odiv__class_Odiv(T_a,V_a,V_b)
| V_c = c_Groups_Ozero__class_Ozero(T_a) )
& ( 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_954_2,plain,
! [U_2975,U_2974,U_2973,U_2972] :
( ( ( c_Divides_Odiv__class_Odiv(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)) = c_Divides_Odiv__class_Odiv(U_2972,U_2974,U_2975)
| U_2973 = c_Groups_Ozero__class_Ozero(U_2972) )
& ( c_Divides_Odiv__class_Odiv(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)) = c_Groups_Ozero__class_Ozero(U_2972)
| U_2973 != c_Groups_Ozero__class_Ozero(U_2972) ) )
| ~ class_Divides_Osemiring__div(U_2972) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
fof(f_954_3,plain,
( ! [U_2973,U_2972,U_2974,U_2975] :
( c_Divides_Odiv__class_Odiv(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)) = c_Divides_Odiv__class_Odiv(U_2972,U_2974,U_2975)
| U_2973 = c_Groups_Ozero__class_Ozero(U_2972)
| ~ sP289(U_2973,U_2972,U_2974,U_2975) )
& ! [U_2973,U_2972,U_2974,U_2975] :
( c_Divides_Odiv__class_Odiv(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)) = c_Groups_Ozero__class_Ozero(U_2972)
| U_2973 != c_Groups_Ozero__class_Ozero(U_2972)
| ~ sP289(U_2973,U_2972,U_2974,U_2975) )
& ! [U_2973,U_2972,U_2974,U_2975] :
( sP289(U_2973,U_2972,U_2974,U_2975)
| ~ class_Divides_Osemiring__div(U_2972) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289])],[f_954_2]) ).
cnf(f_954_4,plain,
( sP289(U_2973,U_2972,U_2974,U_2975)
| ~ class_Divides_Osemiring__div(U_2972) ),
inference(clausify,[status(thm)],[f_954_3]) ).
cnf(f_954_5,plain,
( c_Divides_Odiv__class_Odiv(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)) = c_Groups_Ozero__class_Ozero(U_2972)
| U_2973 != c_Groups_Ozero__class_Ozero(U_2972)
| ~ sP289(U_2973,U_2972,U_2974,U_2975) ),
inference(clausify,[status(thm)],[f_954_3]) ).
cnf(f_954_6,plain,
( c_Divides_Odiv__class_Odiv(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)) = c_Divides_Odiv__class_Odiv(U_2972,U_2974,U_2975)
| U_2973 = c_Groups_Ozero__class_Ozero(U_2972)
| ~ sP289(U_2973,U_2972,U_2974,U_2975) ),
inference(clausify,[status(thm)],[f_954_3]) ).
fof(f_955_1,plain,
! [V_b] : 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_955_2,plain,
! [U_2976] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2976) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_955_1]) ).
fof(f_955_3,plain,
! [U_2976] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2976) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_955_2]) ).
cnf(f_955_4,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2976) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_955_3]) ).
fof(f_956_1,plain,
! [V_a,T_a] :
( 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_956_2,plain,
! [U_2978,U_2977] :
( c_Divides_Odiv__class_Odiv(U_2977,U_2978,c_Groups_Ozero__class_Ozero(U_2977)) = c_Groups_Ozero__class_Ozero(U_2977)
| ~ class_Divides_Osemiring__div(U_2977) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
fof(f_956_3,plain,
! [U_2977,U_2978] :
( c_Divides_Odiv__class_Odiv(U_2977,U_2978,c_Groups_Ozero__class_Ozero(U_2977)) = c_Groups_Ozero__class_Ozero(U_2977)
| ~ class_Divides_Osemiring__div(U_2977) ),
inference(definitional_conversion,[status(esa)],[f_956_2]) ).
cnf(f_956_4,plain,
( c_Divides_Odiv__class_Odiv(U_2977,U_2978,c_Groups_Ozero__class_Ozero(U_2977)) = c_Groups_Ozero__class_Ozero(U_2977)
| ~ class_Divides_Osemiring__div(U_2977) ),
inference(clausify,[status(thm)],[f_956_3]) ).
fof(f_957_1,plain,
! [V_a,T_a] :
( 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_957_2,plain,
! [U_2980,U_2979] :
( c_Divides_Odiv__class_Odiv(U_2979,c_Groups_Ozero__class_Ozero(U_2979),U_2980) = c_Groups_Ozero__class_Ozero(U_2979)
| ~ class_Divides_Osemiring__div(U_2979) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
! [U_2979,U_2980] :
( c_Divides_Odiv__class_Odiv(U_2979,c_Groups_Ozero__class_Ozero(U_2979),U_2980) = c_Groups_Ozero__class_Ozero(U_2979)
| ~ class_Divides_Osemiring__div(U_2979) ),
inference(definitional_conversion,[status(esa)],[f_957_2]) ).
cnf(f_957_4,plain,
( c_Divides_Odiv__class_Odiv(U_2979,c_Groups_Ozero__class_Ozero(U_2979),U_2980) = c_Groups_Ozero__class_Ozero(U_2979)
| ~ class_Divides_Osemiring__div(U_2979) ),
inference(clausify,[status(thm)],[f_957_3]) ).
fof(f_958_1,plain,
! [V_k_2,V_i_2] :
( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
| ~ 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) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
& 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)
| 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_958_2,plain,
! [U_2982,U_2981] :
( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2981,U_2982) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2982,U_2981)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2981,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2981,U_2982)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2981) )
& U_2982 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2982,U_2981)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2981,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2981,U_2982)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2981) )
| U_2982 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2981,U_2982) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
fof(f_958_3,plain,
( ! [U_2986,U_2984] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2984,U_2986) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2986,U_2984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2984,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2984,U_2986)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2984) )
& U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2985,U_2983] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2985,U_2983)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2983,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2983,U_2985)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2983) )
| U_2985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2983,U_2985) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_958_2]) ).
fof(f_958_4,plain,
( ! [U_2984,U_2986] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2986,U_2984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2984,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP292(U_2984,U_2986) )
& ! [U_2984,U_2986] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2984,U_2986)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2984)
| ~ sP292(U_2984,U_2986) )
& ! [U_2984,U_2986] :
( U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP292(U_2984,U_2986) )
& ! [U_2983,U_2985] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2985,U_2983)
| ~ sP291(U_2983,U_2985) )
& ! [U_2983,U_2985] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2983,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP291(U_2983,U_2985) )
& ! [U_2983,U_2985] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2983,U_2985)
| ~ sP290(U_2983,U_2985) )
& ! [U_2983,U_2985] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2983)
| ~ sP290(U_2983,U_2985) )
& ! [U_2984,U_2986] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2984,U_2986) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP292(U_2984,U_2986) )
& ! [U_2983,U_2985] :
( sP291(U_2983,U_2985)
| sP290(U_2983,U_2985)
| U_2985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2983,U_2985) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290,sP291,sP292])],[f_958_3]) ).
cnf(f_958_5,plain,
( sP291(U_2983,U_2985)
| sP290(U_2983,U_2985)
| U_2985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2983,U_2985) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_6,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2984,U_2986) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP292(U_2984,U_2986) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2983)
| ~ sP290(U_2983,U_2985) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_8,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2983,U_2985)
| ~ sP290(U_2983,U_2985) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2983,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP291(U_2983,U_2985) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_10,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2985,U_2983)
| ~ sP291(U_2983,U_2985) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_11,plain,
( U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP292(U_2984,U_2986) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_12,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2984,U_2986)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2984)
| ~ sP292(U_2984,U_2986) ),
inference(clausify,[status(thm)],[f_958_4]) ).
cnf(f_958_13,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2986,U_2984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2984,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP292(U_2984,U_2986) ),
inference(clausify,[status(thm)],[f_958_4]) ).
fof(f_959_1,plain,
! [V_a_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)) ) )
| ~ 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_959_2,plain,
! [U_2988,U_2987] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2988,U_2987))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2988) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2988)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2988,U_2987)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2987) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
fof(f_959_3,plain,
( ! [U_2988,U_2987] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2988,U_2987))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2988)
| ~ sP293(U_2988,U_2987) )
& ! [U_2988,U_2987] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2988)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2988,U_2987))
| ~ sP293(U_2988,U_2987) )
& ! [U_2988,U_2987] :
( sP293(U_2988,U_2987)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2987) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_959_2]) ).
cnf(f_959_4,plain,
( sP293(U_2988,U_2987)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2987) ),
inference(clausify,[status(thm)],[f_959_3]) ).
cnf(f_959_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2988)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2988,U_2987))
| ~ sP293(U_2988,U_2987) ),
inference(clausify,[status(thm)],[f_959_3]) ).
cnf(f_959_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2988,U_2987))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2988)
| ~ sP293(U_2988,U_2987) ),
inference(clausify,[status(thm)],[f_959_3]) ).
fof(f_960_1,plain,
! [V_i_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)) ) )
| ~ 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_960_2,plain,
! [U_2990,U_2989] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2990,U_2989))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2989,U_2990) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2989,U_2990)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2990,U_2989)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2989) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
fof(f_960_3,plain,
( ! [U_2989,U_2990] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2990,U_2989))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2989,U_2990)
| ~ sP294(U_2989,U_2990) )
& ! [U_2989,U_2990] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2989,U_2990)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2990,U_2989))
| ~ sP294(U_2989,U_2990) )
& ! [U_2989,U_2990] :
( sP294(U_2989,U_2990)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2989) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_960_2]) ).
cnf(f_960_4,plain,
( sP294(U_2989,U_2990)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2989) ),
inference(clausify,[status(thm)],[f_960_3]) ).
cnf(f_960_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2989,U_2990)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2990,U_2989))
| ~ sP294(U_2989,U_2990) ),
inference(clausify,[status(thm)],[f_960_3]) ).
cnf(f_960_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2990,U_2989))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2989,U_2990)
| ~ sP294(U_2989,U_2990) ),
inference(clausify,[status(thm)],[f_960_3]) ).
fof(f_961_1,plain,
! [V_b_2,V_a_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_a_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_a_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)) ) )
| ~ 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_961_2,plain,
! [U_2992,U_2991] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2991,U_2992))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2992,U_2991) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2992,U_2991) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2991,U_2992)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2991) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
fof(f_961_3,plain,
( ! [U_2991,U_2992] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992)
| ~ sP295(U_2991,U_2992) )
& ! [U_2991,U_2992] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2992,U_2991)
| ~ sP295(U_2991,U_2992) )
& ! [U_2991,U_2992] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2991,U_2992))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2992,U_2991)
| ~ sP296(U_2991,U_2992) )
& ! [U_2991,U_2992] :
( sP295(U_2991,U_2992)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2991,U_2992))
| ~ sP296(U_2991,U_2992) )
& ! [U_2991,U_2992] :
( sP296(U_2991,U_2992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2991) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295,sP296])],[f_961_2]) ).
cnf(f_961_4,plain,
( sP296(U_2991,U_2992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2991) ),
inference(clausify,[status(thm)],[f_961_3]) ).
cnf(f_961_5,plain,
( sP295(U_2991,U_2992)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2991,U_2992))
| ~ sP296(U_2991,U_2992) ),
inference(clausify,[status(thm)],[f_961_3]) ).
cnf(f_961_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2991,U_2992))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2992,U_2991)
| ~ sP296(U_2991,U_2992) ),
inference(clausify,[status(thm)],[f_961_3]) ).
cnf(f_961_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2992,U_2991)
| ~ sP295(U_2991,U_2992) ),
inference(clausify,[status(thm)],[f_961_3]) ).
cnf(f_961_8,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2992)
| ~ sP295(U_2991,U_2992) ),
inference(clausify,[status(thm)],[f_961_3]) ).
fof(f_962_1,plain,
! [V_b,V_b_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ 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_962_2,plain,
! [U_2995,U_2994,U_2993] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2993,U_2995),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2993,U_2994))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2994,U_2995)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2994)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2993) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
fof(f_962_3,plain,
! [U_2995,U_2993,U_2994] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2993,U_2995),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2993,U_2994))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2994,U_2995)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2994)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2993) ),
inference(definitional_conversion,[status(esa)],[f_962_2]) ).
cnf(f_962_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2993,U_2995),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2993,U_2994))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2994,U_2995)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2994)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2993) ),
inference(clausify,[status(thm)],[f_962_3]) ).
fof(f_963_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ 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_963_2,plain,
! [U_2997,U_2996] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2996,U_2997),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2997,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2996) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
fof(f_963_3,plain,
! [U_2997,U_2996] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2996,U_2997),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2997,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2996) ),
inference(definitional_conversion,[status(esa)],[f_963_2]) ).
cnf(f_963_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2996,U_2997),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2997,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2996) ),
inference(clausify,[status(thm)],[f_963_3]) ).
fof(f_964_1,plain,
! [V_b,V_a] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
| ~ 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_964_2,plain,
! [U_2999,U_2998] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2998,U_2999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2998,U_2999)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2998) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
fof(f_964_3,plain,
! [U_2999,U_2998] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2998,U_2999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2998,U_2999)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2998) ),
inference(definitional_conversion,[status(esa)],[f_964_2]) ).
cnf(f_964_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2998,U_2999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2998,U_2999)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2998) ),
inference(clausify,[status(thm)],[f_964_3]) ).
fof(f_965_1,plain,
! [V_a_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_2,V_b_2)) ) )
| ~ 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_965_2,plain,
! [U_3001,U_3000] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3001,U_3000))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3001,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3001,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3001,U_3000)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3000,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
fof(f_965_3,plain,
( ! [U_3001,U_3000] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3001,U_3000))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3001,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP297(U_3001,U_3000) )
& ! [U_3001,U_3000] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3001,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3001,U_3000))
| ~ sP297(U_3001,U_3000) )
& ! [U_3001,U_3000] :
( sP297(U_3001,U_3000)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3000,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP297])],[f_965_2]) ).
cnf(f_965_4,plain,
( sP297(U_3001,U_3000)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3000,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_965_3]) ).
cnf(f_965_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3001,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3001,U_3000))
| ~ sP297(U_3001,U_3000) ),
inference(clausify,[status(thm)],[f_965_3]) ).
cnf(f_965_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3001,U_3000))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3001,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP297(U_3001,U_3000) ),
inference(clausify,[status(thm)],[f_965_3]) ).
fof(f_966_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
| ~ 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_966_2,plain,
! [U_3003,U_3002] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3002,U_3003),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3002,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
fof(f_966_3,plain,
! [U_3003,U_3002] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3002,U_3003),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3002,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(definitional_conversion,[status(esa)],[f_966_2]) ).
cnf(f_966_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3002,U_3003),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3003)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3002,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_966_3]) ).
fof(f_967_1,plain,
! [V_b,V_b_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ 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_967_2,plain,
! [U_3006,U_3005,U_3004] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3004,U_3005),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3004,U_3006))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3005,U_3006)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3005)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3004,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
fof(f_967_3,plain,
! [U_3006,U_3004,U_3005] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3004,U_3005),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3004,U_3006))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3005,U_3006)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3005)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3004,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(definitional_conversion,[status(esa)],[f_967_2]) ).
cnf(f_967_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3004,U_3005),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3004,U_3006))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3005,U_3006)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3005)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3004,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_967_3]) ).
fof(f_968_1,plain,
! [V_b,V_a] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
| ~ 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_968_2,plain,
! [U_3008,U_3007] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3007,U_3008) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3008,U_3007)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3007,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
fof(f_968_3,plain,
! [U_3008,U_3007] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3007,U_3008) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3008,U_3007)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3007,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(definitional_conversion,[status(esa)],[f_968_2]) ).
cnf(f_968_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3007,U_3008) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3008,U_3007)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3007,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_968_3]) ).
fof(f_969_1,plain,
! [V_b,V_a_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono1]) ).
fof(f_969_2,plain,
! [U_3011,U_3010,U_3009] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3009,U_3011),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3010,U_3011))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3009,U_3010) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
fof(f_969_3,plain,
! [U_3011,U_3010,U_3009] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3009,U_3011),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3010,U_3011))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3009,U_3010) ),
inference(definitional_conversion,[status(esa)],[f_969_2]) ).
cnf(f_969_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3009,U_3011),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3010,U_3011))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3009,U_3010) ),
inference(clausify,[status(thm)],[f_969_3]) ).
fof(f_970_1,plain,
! [V_b,V_a_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ 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_970_2,plain,
! [U_3014,U_3013,U_3012] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3013,U_3014),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3012,U_3014))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3014,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,U_3013) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
fof(f_970_3,plain,
! [U_3014,U_3012,U_3013] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3013,U_3014),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3012,U_3014))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3014,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,U_3013) ),
inference(definitional_conversion,[status(esa)],[f_970_2]) ).
cnf(f_970_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3013,U_3014),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3012,U_3014))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3014,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3012,U_3013) ),
inference(clausify,[status(thm)],[f_970_3]) ).
fof(f_971_1,plain,
! [V_k,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
| ~ 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_971_2,plain,
! [U_3016,U_3015] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3015,U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_3016)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
fof(f_971_3,plain,
! [U_3015,U_3016] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3015,U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_3016)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ),
inference(definitional_conversion,[status(esa)],[f_971_2]) ).
cnf(f_971_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3015,U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_3016)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ),
inference(clausify,[status(thm)],[f_971_3]) ).
fof(f_972_1,plain,
! [V_b,V_a,V_c] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)
| ~ 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_972_2,plain,
! [U_3019,U_3018,U_3017] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3019),U_3017)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3018,U_3019),U_3017)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3017) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
fof(f_972_3,plain,
! [U_3018,U_3017,U_3019] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3019),U_3017)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3018,U_3019),U_3017)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3017) ),
inference(definitional_conversion,[status(esa)],[f_972_2]) ).
cnf(f_972_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3018,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3019),U_3017)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3018,U_3019),U_3017)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3017) ),
inference(clausify,[status(thm)],[f_972_3]) ).
fof(f_973_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,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_Groups_Oplus__class_Oplus(T_a,V_c,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_973_2,plain,
! [U_3023,U_3022,U_3021,U_3020] :
( c_Divides_Odiv__class_Odiv(U_3020,c_Groups_Oplus__class_Oplus(U_3020,U_3022,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3020),U_3023),U_3021)),U_3021) = c_Groups_Oplus__class_Oplus(U_3020,U_3023,c_Divides_Odiv__class_Odiv(U_3020,U_3022,U_3021))
| U_3021 = c_Groups_Ozero__class_Ozero(U_3020)
| ~ class_Divides_Osemiring__div(U_3020) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
fof(f_973_3,plain,
! [U_3020,U_3021,U_3022,U_3023] :
( c_Divides_Odiv__class_Odiv(U_3020,c_Groups_Oplus__class_Oplus(U_3020,U_3022,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3020),U_3023),U_3021)),U_3021) = c_Groups_Oplus__class_Oplus(U_3020,U_3023,c_Divides_Odiv__class_Odiv(U_3020,U_3022,U_3021))
| U_3021 = c_Groups_Ozero__class_Ozero(U_3020)
| ~ class_Divides_Osemiring__div(U_3020) ),
inference(definitional_conversion,[status(esa)],[f_973_2]) ).
cnf(f_973_4,plain,
( c_Divides_Odiv__class_Odiv(U_3020,c_Groups_Oplus__class_Oplus(U_3020,U_3022,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3020),U_3023),U_3021)),U_3021) = c_Groups_Oplus__class_Oplus(U_3020,U_3023,c_Divides_Odiv__class_Odiv(U_3020,U_3022,U_3021))
| U_3021 = c_Groups_Ozero__class_Ozero(U_3020)
| ~ class_Divides_Osemiring__div(U_3020) ),
inference(clausify,[status(thm)],[f_973_3]) ).
fof(f_974_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,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_Groups_Oplus__class_Oplus(T_a,V_c,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_974_2,plain,
! [U_3027,U_3026,U_3025,U_3024] :
( c_Divides_Odiv__class_Odiv(U_3024,c_Groups_Oplus__class_Oplus(U_3024,U_3026,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3024),U_3025),U_3027)),U_3025) = c_Groups_Oplus__class_Oplus(U_3024,U_3027,c_Divides_Odiv__class_Odiv(U_3024,U_3026,U_3025))
| U_3025 = c_Groups_Ozero__class_Ozero(U_3024)
| ~ class_Divides_Osemiring__div(U_3024) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
fof(f_974_3,plain,
! [U_3025,U_3024,U_3026,U_3027] :
( c_Divides_Odiv__class_Odiv(U_3024,c_Groups_Oplus__class_Oplus(U_3024,U_3026,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3024),U_3025),U_3027)),U_3025) = c_Groups_Oplus__class_Oplus(U_3024,U_3027,c_Divides_Odiv__class_Odiv(U_3024,U_3026,U_3025))
| U_3025 = c_Groups_Ozero__class_Ozero(U_3024)
| ~ class_Divides_Osemiring__div(U_3024) ),
inference(definitional_conversion,[status(esa)],[f_974_2]) ).
cnf(f_974_4,plain,
( c_Divides_Odiv__class_Odiv(U_3024,c_Groups_Oplus__class_Oplus(U_3024,U_3026,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3024),U_3025),U_3027)),U_3025) = c_Groups_Oplus__class_Oplus(U_3024,U_3027,c_Divides_Odiv__class_Odiv(U_3024,U_3026,U_3025))
| U_3025 = c_Groups_Ozero__class_Ozero(U_3024)
| ~ class_Divides_Osemiring__div(U_3024) ),
inference(clausify,[status(thm)],[f_974_3]) ).
fof(f_975_1,plain,
! [V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,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_975_2,plain,
! [U_3030,U_3029,U_3028] :
( c_Divides_Odiv__class_Odiv(U_3028,c_Groups_Oplus__class_Oplus(U_3028,U_3029,U_3030),U_3029) = c_Groups_Oplus__class_Oplus(U_3028,c_Divides_Odiv__class_Odiv(U_3028,U_3030,U_3029),c_Groups_Oone__class_Oone(U_3028))
| U_3029 = c_Groups_Ozero__class_Ozero(U_3028)
| ~ class_Divides_Osemiring__div(U_3028) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
fof(f_975_3,plain,
! [U_3028,U_3029,U_3030] :
( c_Divides_Odiv__class_Odiv(U_3028,c_Groups_Oplus__class_Oplus(U_3028,U_3029,U_3030),U_3029) = c_Groups_Oplus__class_Oplus(U_3028,c_Divides_Odiv__class_Odiv(U_3028,U_3030,U_3029),c_Groups_Oone__class_Oone(U_3028))
| U_3029 = c_Groups_Ozero__class_Ozero(U_3028)
| ~ class_Divides_Osemiring__div(U_3028) ),
inference(definitional_conversion,[status(esa)],[f_975_2]) ).
cnf(f_975_4,plain,
( c_Divides_Odiv__class_Odiv(U_3028,c_Groups_Oplus__class_Oplus(U_3028,U_3029,U_3030),U_3029) = c_Groups_Oplus__class_Oplus(U_3028,c_Divides_Odiv__class_Odiv(U_3028,U_3030,U_3029),c_Groups_Oone__class_Oone(U_3028))
| U_3029 = c_Groups_Ozero__class_Ozero(U_3028)
| ~ class_Divides_Osemiring__div(U_3028) ),
inference(clausify,[status(thm)],[f_975_3]) ).
fof(f_976_1,plain,
! [V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,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_976_2,plain,
! [U_3033,U_3032,U_3031] :
( c_Divides_Odiv__class_Odiv(U_3031,c_Groups_Oplus__class_Oplus(U_3031,U_3033,U_3032),U_3032) = c_Groups_Oplus__class_Oplus(U_3031,c_Divides_Odiv__class_Odiv(U_3031,U_3033,U_3032),c_Groups_Oone__class_Oone(U_3031))
| U_3032 = c_Groups_Ozero__class_Ozero(U_3031)
| ~ class_Divides_Osemiring__div(U_3031) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
fof(f_976_3,plain,
! [U_3031,U_3032,U_3033] :
( c_Divides_Odiv__class_Odiv(U_3031,c_Groups_Oplus__class_Oplus(U_3031,U_3033,U_3032),U_3032) = c_Groups_Oplus__class_Oplus(U_3031,c_Divides_Odiv__class_Odiv(U_3031,U_3033,U_3032),c_Groups_Oone__class_Oone(U_3031))
| U_3032 = c_Groups_Ozero__class_Ozero(U_3031)
| ~ class_Divides_Osemiring__div(U_3031) ),
inference(definitional_conversion,[status(esa)],[f_976_2]) ).
cnf(f_976_4,plain,
( c_Divides_Odiv__class_Odiv(U_3031,c_Groups_Oplus__class_Oplus(U_3031,U_3033,U_3032),U_3032) = c_Groups_Oplus__class_Oplus(U_3031,c_Divides_Odiv__class_Odiv(U_3031,U_3033,U_3032),c_Groups_Oone__class_Oone(U_3031))
| U_3032 = c_Groups_Ozero__class_Ozero(U_3031)
| ~ class_Divides_Osemiring__div(U_3031) ),
inference(clausify,[status(thm)],[f_976_3]) ).
fof(f_977_1,plain,
! [V_k_2,V_n_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2)))
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& ? [B_j] :
( V_n_2 = 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)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) ) )
& 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_n_2 = 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)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) ) )
& 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_n_2 != 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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) ) )
| ~ 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_n_2 != 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)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) ) )
| ~ 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,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).
fof(f_977_2,plain,
! [U_3044,U_3043,U_3042] :
( ( hBOOL(hAPP(U_3042,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3043,U_3044)))
| ( ? [U_3041] :
( ~ hBOOL(hAPP(U_3042,U_3041))
& ? [U_3040] :
( U_3043 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3041),U_3040)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3040,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3044,U_3040) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3044,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ? [U_3039] :
( ~ hBOOL(hAPP(U_3042,U_3039))
& ? [U_3038] :
( U_3043 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3039),U_3038)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3038,U_3044)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3038) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3044) )
| ( ~ hBOOL(hAPP(U_3042,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3044 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_3037] :
( hBOOL(hAPP(U_3042,U_3037))
| ! [U_3036] :
( U_3043 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3044,U_3036) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3044,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3035] :
( hBOOL(hAPP(U_3042,U_3035))
| ! [U_3034] :
( U_3043 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3044),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3044) )
& ( hBOOL(hAPP(U_3042,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3044 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3042,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3043,U_3044))) ) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
fof(f_977_3,plain,
( ! [U_3050,U_3048,U_3046] :
( hBOOL(hAPP(U_3046,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3048,U_3050)))
| ( ? [U_3041] :
( ~ hBOOL(hAPP(U_3046,U_3041))
& ? [U_3040] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),U_3041),U_3040)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3040,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,U_3040) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ? [U_3039] :
( ~ hBOOL(hAPP(U_3046,U_3039))
& ? [U_3038] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),U_3039),U_3038)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3038,U_3050)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3038) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3050) )
| ( ~ hBOOL(hAPP(U_3046,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3049,U_3047,U_3045] :
( ( ( ! [U_3037] :
( hBOOL(hAPP(U_3045,U_3037))
| ! [U_3036] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,U_3036) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3035] :
( hBOOL(hAPP(U_3045,U_3035))
| ! [U_3034] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3049)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3049) )
& ( hBOOL(hAPP(U_3045,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3045,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3047,U_3049))) ) ),
inference(miniscope,[status(thm)],[f_977_2]) ).
fof(f_977_4,plain,
( ! [U_3050,U_3048,U_3046] :
( hBOOL(hAPP(U_3046,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3048,U_3050)))
| ( ? [U_3041] :
( ~ hBOOL(hAPP(U_3046,U_3041))
& ? [U_3040] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),U_3041),U_3040)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3040,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,U_3040) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3046,sK66(U_3050,U_3048,U_3046)))
& ? [U_3038] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK66(U_3050,U_3048,U_3046)),U_3038)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3038,U_3050)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3038) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3050) )
| ( ~ hBOOL(hAPP(U_3046,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3049,U_3047,U_3045] :
( ( ( ! [U_3037] :
( hBOOL(hAPP(U_3045,U_3037))
| ! [U_3036] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,U_3036) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3035] :
( hBOOL(hAPP(U_3045,U_3035))
| ! [U_3034] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3049)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3049) )
& ( hBOOL(hAPP(U_3045,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3045,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3047,U_3049))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3039,sK66(U_3050,U_3048,U_3046))],[f_977_3]) ).
fof(f_977_5,plain,
( ! [U_3050,U_3048,U_3046] :
( hBOOL(hAPP(U_3046,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3048,U_3050)))
| ( ? [U_3041] :
( ~ hBOOL(hAPP(U_3046,U_3041))
& ? [U_3040] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),U_3041),U_3040)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3040,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,U_3040) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3046,sK66(U_3050,U_3048,U_3046)))
& U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK66(U_3050,U_3048,U_3046)),sK67(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK67(U_3050,U_3048,U_3046),U_3050)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK67(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3050) )
| ( ~ hBOOL(hAPP(U_3046,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3049,U_3047,U_3045] :
( ( ( ! [U_3037] :
( hBOOL(hAPP(U_3045,U_3037))
| ! [U_3036] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,U_3036) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3035] :
( hBOOL(hAPP(U_3045,U_3035))
| ! [U_3034] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3049)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3049) )
& ( hBOOL(hAPP(U_3045,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3045,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3047,U_3049))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3038,sK67(U_3050,U_3048,U_3046))],[f_977_4]) ).
fof(f_977_6,plain,
( ! [U_3050,U_3048,U_3046] :
( hBOOL(hAPP(U_3046,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3048,U_3050)))
| ( ~ hBOOL(hAPP(U_3046,sK68(U_3050,U_3048,U_3046)))
& ? [U_3040] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK68(U_3050,U_3048,U_3046)),U_3040)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3040,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,U_3040) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3046,sK66(U_3050,U_3048,U_3046)))
& U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK66(U_3050,U_3048,U_3046)),sK67(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK67(U_3050,U_3048,U_3046),U_3050)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK67(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3050) )
| ( ~ hBOOL(hAPP(U_3046,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3049,U_3047,U_3045] :
( ( ( ! [U_3037] :
( hBOOL(hAPP(U_3045,U_3037))
| ! [U_3036] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,U_3036) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3035] :
( hBOOL(hAPP(U_3045,U_3035))
| ! [U_3034] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3049)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3049) )
& ( hBOOL(hAPP(U_3045,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3045,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3047,U_3049))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3041,sK68(U_3050,U_3048,U_3046))],[f_977_5]) ).
fof(f_977_7,plain,
( ! [U_3050,U_3048,U_3046] :
( hBOOL(hAPP(U_3046,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3048,U_3050)))
| ( ~ hBOOL(hAPP(U_3046,sK68(U_3050,U_3048,U_3046)))
& U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK68(U_3050,U_3048,U_3046)),sK69(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK69(U_3050,U_3048,U_3046),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,sK69(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3046,sK66(U_3050,U_3048,U_3046)))
& U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK66(U_3050,U_3048,U_3046)),sK67(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK67(U_3050,U_3048,U_3046),U_3050)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK67(U_3050,U_3048,U_3046))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3050) )
| ( ~ hBOOL(hAPP(U_3046,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3049,U_3047,U_3045] :
( ( ( ! [U_3037] :
( hBOOL(hAPP(U_3045,U_3037))
| ! [U_3036] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,U_3036) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3035] :
( hBOOL(hAPP(U_3045,U_3035))
| ! [U_3034] :
( U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3049)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3049) )
& ( hBOOL(hAPP(U_3045,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3045,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3047,U_3049))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3040,sK69(U_3050,U_3048,U_3046))],[f_977_6]) ).
fof(f_977_8,plain,
( ! [U_3050,U_3046,U_3048] :
( ~ hBOOL(hAPP(U_3046,sK68(U_3050,U_3048,U_3046)))
| ~ sP301(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK68(U_3050,U_3048,U_3046)),sK69(U_3050,U_3048,U_3046))
| ~ sP301(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK69(U_3050,U_3048,U_3046),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP301(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,sK69(U_3050,U_3048,U_3046))
| ~ sP301(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP301(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( ~ hBOOL(hAPP(U_3046,sK66(U_3050,U_3048,U_3046)))
| ~ sP300(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK66(U_3050,U_3048,U_3046)),sK67(U_3050,U_3048,U_3046))
| ~ sP300(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK67(U_3050,U_3048,U_3046),U_3050)
| ~ sP300(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK67(U_3050,U_3048,U_3046))
| ~ sP300(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046,U_3048] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3050)
| ~ sP300(U_3050,U_3046,U_3048) )
& ! [U_3050,U_3046] :
( ~ hBOOL(hAPP(U_3046,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP299(U_3050,U_3046) )
& ! [U_3050,U_3046] :
( U_3050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP299(U_3050,U_3046) )
& ! [U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047] :
( hBOOL(hAPP(U_3045,U_3037))
| U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,U_3036)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047) )
& ! [U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047] :
( hBOOL(hAPP(U_3045,U_3035))
| U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3049)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3049)
| ~ sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047) )
& ! [U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047] :
( hBOOL(hAPP(U_3045,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047) )
& ! [U_3050,U_3046,U_3048] :
( hBOOL(hAPP(U_3046,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3048,U_3050)))
| sP301(U_3050,U_3046,U_3048)
| sP300(U_3050,U_3046,U_3048)
| sP299(U_3050,U_3046) )
& ! [U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047] :
( sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047)
| ~ hBOOL(hAPP(U_3045,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3047,U_3049))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298,sP299,sP300,sP301])],[f_977_7]) ).
cnf(f_977_9,plain,
( sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047)
| ~ hBOOL(hAPP(U_3045,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3047,U_3049))) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_10,plain,
( hBOOL(hAPP(U_3046,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3048,U_3050)))
| sP301(U_3050,U_3046,U_3048)
| sP300(U_3050,U_3046,U_3048)
| sP299(U_3050,U_3046) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_11,plain,
( hBOOL(hAPP(U_3045,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_12,plain,
( hBOOL(hAPP(U_3045,U_3035))
| U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3035),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3034,U_3049)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3034)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3049)
| ~ sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_13,plain,
( hBOOL(hAPP(U_3045,U_3037))
| U_3047 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3049),U_3037),U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,U_3036)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3049,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP298(U_3036,U_3035,U_3034,U_3037,U_3049,U_3045,U_3047) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_14,plain,
( U_3050 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP299(U_3050,U_3046) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_15,plain,
( ~ hBOOL(hAPP(U_3046,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP299(U_3050,U_3046) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_16,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3050)
| ~ sP300(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_17,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK67(U_3050,U_3048,U_3046))
| ~ sP300(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_18,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK67(U_3050,U_3048,U_3046),U_3050)
| ~ sP300(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_19,plain,
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK66(U_3050,U_3048,U_3046)),sK67(U_3050,U_3048,U_3046))
| ~ sP300(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_20,plain,
( ~ hBOOL(hAPP(U_3046,sK66(U_3050,U_3048,U_3046)))
| ~ sP300(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_21,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP301(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_22,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3050,sK69(U_3050,U_3048,U_3046))
| ~ sP301(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_23,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK69(U_3050,U_3048,U_3046),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ sP301(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_24,plain,
( U_3048 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3050),sK68(U_3050,U_3048,U_3046)),sK69(U_3050,U_3048,U_3046))
| ~ sP301(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
cnf(f_977_25,plain,
( ~ hBOOL(hAPP(U_3046,sK68(U_3050,U_3048,U_3046)))
| ~ sP301(U_3050,U_3046,U_3048) ),
inference(clausify,[status(thm)],[f_977_8]) ).
fof(f_978_1,plain,
! [V_r_1,V_y,V_b_1,V_a_1] :
( 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)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) )
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) )
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) )
| V_a_1 != 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_978_2,plain,
! [U_3054,U_3053,U_3052,U_3051] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3051,U_3052) = U_3053
| U_3052 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3054,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3052,U_3054) )
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3052) )
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3054,U_3052)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3054) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3052) )
| U_3051 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3052),U_3053),U_3054) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
fof(f_978_3,plain,
( ! [U_3052,U_3054] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3054,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3052,U_3054)
| ~ sP303(U_3052,U_3054) )
& ! [U_3052,U_3054] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3052)
| ~ sP303(U_3052,U_3054) )
& ! [U_3052,U_3054] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3054,U_3052)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3054)
| ~ sP302(U_3052,U_3054) )
& ! [U_3052,U_3054] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3052)
| ~ sP302(U_3052,U_3054) )
& ! [U_3052,U_3054,U_3051,U_3053] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3051,U_3052) = U_3053
| U_3052 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP303(U_3052,U_3054)
| sP302(U_3052,U_3054)
| U_3051 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3052),U_3053),U_3054) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302,sP303])],[f_978_2]) ).
cnf(f_978_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3051,U_3052) = U_3053
| U_3052 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| sP303(U_3052,U_3054)
| sP302(U_3052,U_3054)
| U_3051 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3052),U_3053),U_3054) ),
inference(clausify,[status(thm)],[f_978_3]) ).
cnf(f_978_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3052)
| ~ sP302(U_3052,U_3054) ),
inference(clausify,[status(thm)],[f_978_3]) ).
cnf(f_978_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3054,U_3052)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3054)
| ~ sP302(U_3052,U_3054) ),
inference(clausify,[status(thm)],[f_978_3]) ).
cnf(f_978_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3052)
| ~ sP303(U_3052,U_3054) ),
inference(clausify,[status(thm)],[f_978_3]) ).
cnf(f_978_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3054,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3052,U_3054)
| ~ sP303(U_3052,U_3054) ),
inference(clausify,[status(thm)],[f_978_3]) ).
fof(f_979_1,plain,
! [V_k,V_l] :
( ( c_SMT_Oz3div(V_k,V_l) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l)))
| 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) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l)
| ~ 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_979_2,plain,
! [U_3056,U_3055] :
( ( c_SMT_Oz3div(U_3056,U_3055) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3056,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_3055)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3055) )
& ( c_SMT_Oz3div(U_3056,U_3055) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3056,U_3055)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3055) ) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
fof(f_979_3,plain,
( ! [U_3060,U_3058] :
( c_SMT_Oz3div(U_3060,U_3058) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3060,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_3058)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3058) )
& ! [U_3059,U_3057] :
( c_SMT_Oz3div(U_3059,U_3057) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3059,U_3057)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3057) ) ),
inference(miniscope,[status(thm)],[f_979_2]) ).
fof(f_979_4,plain,
( ! [U_3058,U_3060] :
( c_SMT_Oz3div(U_3060,U_3058) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3060,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_3058)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3058) )
& ! [U_3057,U_3059] :
( c_SMT_Oz3div(U_3059,U_3057) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3059,U_3057)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3057) ) ),
inference(definitional_conversion,[status(esa)],[f_979_3]) ).
cnf(f_979_5,plain,
( c_SMT_Oz3div(U_3059,U_3057) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3059,U_3057)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3057) ),
inference(clausify,[status(thm)],[f_979_4]) ).
cnf(f_979_6,plain,
( c_SMT_Oz3div(U_3060,U_3058) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3060,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_3058)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3058) ),
inference(clausify,[status(thm)],[f_979_4]) ).
fof(f_980_1,plain,
! [V_r] :
( ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) ),
inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6a]) ).
fof(f_980_2,plain,
! [U_3062] :
( ? [U_3061] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3062,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3061)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3061),U_3062) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3062) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
fof(f_980_3,plain,
! [U_3062] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3062,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK70(U_3062))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK70(U_3062)),U_3062) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3062) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_3061,sK70(U_3062))],[f_980_2]) ).
fof(f_980_4,plain,
( ! [U_3062] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3062,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK70(U_3062))))
| ~ sP304(U_3062) )
& ! [U_3062] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK70(U_3062)),U_3062)
| ~ sP304(U_3062) )
& ! [U_3062] :
( sP304(U_3062)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3062) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP304])],[f_980_3]) ).
cnf(f_980_5,plain,
( sP304(U_3062)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3062) ),
inference(clausify,[status(thm)],[f_980_4]) ).
cnf(f_980_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK70(U_3062)),U_3062)
| ~ sP304(U_3062) ),
inference(clausify,[status(thm)],[f_980_4]) ).
cnf(f_980_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3062,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK70(U_3062))))
| ~ sP304(U_3062) ),
inference(clausify,[status(thm)],[f_980_4]) ).
fof(f_981_1,plain,
! [V_m] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
inference(fof_nnf,[status(thm)],[fact_div__1]) ).
fof(f_981_2,plain,
! [U_3063] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3063,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3063,
inference(variable_rename,[status(thm)],[f_981_1]) ).
fof(f_981_3,plain,
! [U_3063] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3063,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3063,
inference(definitional_conversion,[status(esa)],[f_981_2]) ).
cnf(f_981_4,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3063,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3063,
inference(clausify,[status(thm)],[f_981_3]) ).
fof(f_982_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,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_982_2,plain,
! [U_3065,U_3064] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3064,U_3065),U_3064),
inference(variable_rename,[status(thm)],[f_982_1]) ).
fof(f_982_3,plain,
! [U_3064,U_3065] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3064,U_3065),U_3064),
inference(definitional_conversion,[status(esa)],[f_982_2]) ).
cnf(f_982_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3064,U_3065),U_3064),
inference(clausify,[status(thm)],[f_982_3]) ).
fof(f_983_1,plain,
! [V_k,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__le__mono]) ).
fof(f_983_2,plain,
! [U_3068,U_3067,U_3066] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3066,U_3068),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3067,U_3068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3066,U_3067) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
fof(f_983_3,plain,
! [U_3067,U_3068,U_3066] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3066,U_3068),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3067,U_3068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3066,U_3067) ),
inference(definitional_conversion,[status(esa)],[f_983_2]) ).
cnf(f_983_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3066,U_3068),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3067,U_3068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3066,U_3067) ),
inference(clausify,[status(thm)],[f_983_3]) ).
fof(f_984_1,plain,
! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,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_984_2,plain,
! [U_3071,U_3070,U_3069] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3069,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3070),U_3071)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3069,U_3070),U_3071),
inference(variable_rename,[status(thm)],[f_984_1]) ).
fof(f_984_3,plain,
! [U_3071,U_3070,U_3069] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3069,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3070),U_3071)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3069,U_3070),U_3071),
inference(definitional_conversion,[status(esa)],[f_984_2]) ).
cnf(f_984_4,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3069,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3070),U_3071)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3069,U_3070),U_3071),
inference(clausify,[status(thm)],[f_984_3]) ).
fof(f_985_1,plain,
! [V_n,V_m] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__less]) ).
fof(f_985_2,plain,
! [U_3073,U_3072] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3072,U_3073) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3072,U_3073) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
fof(f_985_3,plain,
! [U_3073,U_3072] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3072,U_3073) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3072,U_3073) ),
inference(definitional_conversion,[status(esa)],[f_985_2]) ).
cnf(f_985_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3072,U_3073) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3072,U_3073) ),
inference(clausify,[status(thm)],[f_985_3]) ).
fof(f_986_1,plain,
! [V_n,V_m,V_k] :
( ( 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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)
| V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( 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_986_2,plain,
! [U_3076,U_3075,U_3074] :
( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3074),U_3075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3074),U_3076)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3075,U_3076)
| U_3074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3074),U_3075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3074),U_3076)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3074 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
fof(f_986_3,plain,
( ! [U_3082,U_3080,U_3078] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3078),U_3080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3078),U_3082)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3080,U_3082)
| U_3078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_3081,U_3079,U_3077] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3077),U_3079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3077),U_3081)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_986_2]) ).
fof(f_986_4,plain,
( ! [U_3082,U_3080,U_3078] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3078),U_3080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3078),U_3082)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3080,U_3082)
| U_3078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_3081,U_3077,U_3079] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3077),U_3079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3077),U_3081)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_986_3]) ).
cnf(f_986_5,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3077),U_3079),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3077),U_3081)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_986_4]) ).
cnf(f_986_6,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3078),U_3080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3078),U_3082)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3080,U_3082)
| U_3078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_986_4]) ).
fof(f_987_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__div__mult__right]) ).
fof(f_987_2,plain,
! [U_3086,U_3085,U_3084,U_3083] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),U_3084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_3083)),U_3085),U_3086)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),U_3084,U_3085),U_3086)
| ~ class_Fields_Ofield(U_3083) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
fof(f_987_3,plain,
! [U_3084,U_3083,U_3085,U_3086] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),U_3084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_3083)),U_3085),U_3086)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),U_3084,U_3085),U_3086)
| ~ class_Fields_Ofield(U_3083) ),
inference(definitional_conversion,[status(esa)],[f_987_2]) ).
cnf(f_987_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),U_3084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_3083)),U_3085),U_3086)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3083),U_3084,U_3085),U_3086)
| ~ class_Fields_Ofield(U_3083) ),
inference(clausify,[status(thm)],[f_987_3]) ).
fof(f_988_1,plain,
! [V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__div__minus__left]) ).
fof(f_988_2,plain,
! [U_3089,U_3088,U_3087] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3087),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3087),U_3088),U_3089) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3087),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3087),U_3088,U_3089))
| ~ class_Fields_Ofield(U_3087) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
fof(f_988_3,plain,
! [U_3087,U_3088,U_3089] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3087),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3087),U_3088),U_3089) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3087),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3087),U_3088,U_3089))
| ~ class_Fields_Ofield(U_3087) ),
inference(definitional_conversion,[status(esa)],[f_988_2]) ).
cnf(f_988_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3087),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3087),U_3088),U_3089) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3087),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3087),U_3088,U_3089))
| ~ class_Fields_Ofield(U_3087) ),
inference(clausify,[status(thm)],[f_988_3]) ).
fof(f_989_1,plain,
! [V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__div__minus__right]) ).
fof(f_989_2,plain,
! [U_3092,U_3091,U_3090] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3090),U_3092)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3090),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,U_3092))
| ~ class_Fields_Ofield(U_3090) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
fof(f_989_3,plain,
! [U_3090,U_3091,U_3092] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3090),U_3092)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3090),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,U_3092))
| ~ class_Fields_Ofield(U_3090) ),
inference(definitional_conversion,[status(esa)],[f_989_2]) ).
cnf(f_989_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3090),U_3092)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3090),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,U_3092))
| ~ class_Fields_Ofield(U_3090) ),
inference(clausify,[status(thm)],[f_989_3]) ).
fof(f_990_1,plain,
! [V_k,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ 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_990_2,plain,
! [U_3095,U_3094,U_3093] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3095,U_3094),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3095,U_3093))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3093,U_3094)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3093) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
fof(f_990_3,plain,
! [U_3095,U_3094,U_3093] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3095,U_3094),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3095,U_3093))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3093,U_3094)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3093) ),
inference(definitional_conversion,[status(esa)],[f_990_2]) ).
cnf(f_990_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3095,U_3094),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3095,U_3093))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3093,U_3094)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3093) ),
inference(clausify,[status(thm)],[f_990_3]) ).
fof(f_991_1,plain,
! [V_n,V_m,V_k] :
( 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_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)
| ~ 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_991_2,plain,
! [U_3098,U_3097,U_3096] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3096),U_3097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3096),U_3098)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3097,U_3098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3096) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
fof(f_991_3,plain,
! [U_3097,U_3096,U_3098] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3096),U_3097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3096),U_3098)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3097,U_3098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3096) ),
inference(definitional_conversion,[status(esa)],[f_991_2]) ).
cnf(f_991_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3096),U_3097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3096),U_3098)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3097,U_3098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3096) ),
inference(clausify,[status(thm)],[f_991_3]) ).
fof(f_992_1,plain,
! [V_m,V_n] :
( 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
| ~ 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_992_2,plain,
! [U_3100,U_3099] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),U_3099),U_3099) = U_3100
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3099) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
fof(f_992_3,plain,
! [U_3100,U_3099] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),U_3099),U_3099) = U_3100
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3099) ),
inference(definitional_conversion,[status(esa)],[f_992_2]) ).
cnf(f_992_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3100),U_3099),U_3099) = U_3100
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3099) ),
inference(clausify,[status(thm)],[f_992_3]) ).
fof(f_993_1,plain,
! [V_m,V_n] :
( 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
| ~ 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_993_2,plain,
! [U_3102,U_3101] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3101),U_3102),U_3101) = U_3102
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3101) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
fof(f_993_3,plain,
! [U_3101,U_3102] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3101),U_3102),U_3101) = U_3102
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3101) ),
inference(definitional_conversion,[status(esa)],[f_993_2]) ).
cnf(f_993_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3101),U_3102),U_3101) = U_3102
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3101) ),
inference(clausify,[status(thm)],[f_993_3]) ).
fof(f_994_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ 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_994_2,plain,
! [U_3104,U_3103] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3104,U_3103),U_3104)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3104)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3103) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
fof(f_994_3,plain,
! [U_3104,U_3103] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3104,U_3103),U_3104)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3104)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3103) ),
inference(definitional_conversion,[status(esa)],[f_994_2]) ).
cnf(f_994_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3104,U_3103),U_3104)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3104)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3103) ),
inference(clausify,[status(thm)],[f_994_3]) ).
fof(f_995_1,plain,
! [V_m,V_n] :
( ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
& ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) )
| ~ 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_995_2,plain,
! [U_3106,U_3105] :
( ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3106,U_3105) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3106,U_3105),U_3105))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3106,U_3105) )
& ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3106,U_3105) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3106,U_3105) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3105) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
fof(f_995_3,plain,
( ! [U_3105,U_3106] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3106,U_3105) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3106,U_3105),U_3105))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3106,U_3105)
| ~ sP305(U_3105,U_3106) )
& ! [U_3105,U_3106] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3106,U_3105) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3106,U_3105)
| ~ sP305(U_3105,U_3106) )
& ! [U_3105,U_3106] :
( sP305(U_3105,U_3106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP305])],[f_995_2]) ).
cnf(f_995_4,plain,
( sP305(U_3105,U_3106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3105) ),
inference(clausify,[status(thm)],[f_995_3]) ).
cnf(f_995_5,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3106,U_3105) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3106,U_3105)
| ~ sP305(U_3105,U_3106) ),
inference(clausify,[status(thm)],[f_995_3]) ).
cnf(f_995_6,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3106,U_3105) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3106,U_3105),U_3105))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3106,U_3105)
| ~ sP305(U_3105,U_3106) ),
inference(clausify,[status(thm)],[f_995_3]) ).
fof(f_996_1,plain,
! [V_m,V_n] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ 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_996_2,plain,
! [U_3108,U_3107] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3108,U_3107) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3108,U_3107),U_3107))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3108,U_3107)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3107) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
fof(f_996_3,plain,
! [U_3107,U_3108] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3108,U_3107) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3108,U_3107),U_3107))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3108,U_3107)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3107) ),
inference(definitional_conversion,[status(esa)],[f_996_2]) ).
cnf(f_996_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3108,U_3107) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3108,U_3107),U_3107))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3108,U_3107)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3107) ),
inference(clausify,[status(thm)],[f_996_3]) ).
fof(f_997_1,plain,
! [V_k_2,V_n_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& V_n_2 = 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)
& 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_n_2 != 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)
| ~ 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,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div]) ).
fof(f_997_2,plain,
! [U_3115,U_3114,U_3113] :
( ( hBOOL(hAPP(U_3113,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3114,U_3115)))
| ( ? [U_3112,U_3111] :
( ~ hBOOL(hAPP(U_3113,U_3112))
& U_3114 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),U_3112),U_3111)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3111,U_3115) )
& U_3115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3113,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_3110,U_3109] :
( hBOOL(hAPP(U_3113,U_3110))
| U_3114 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3115),U_3110),U_3109)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3109,U_3115) )
| U_3115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3113,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3113,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3114,U_3115))) ) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
fof(f_997_3,plain,
( ! [U_3121,U_3119,U_3117] :
( hBOOL(hAPP(U_3117,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3119,U_3121)))
| ( ? [U_3112,U_3111] :
( ~ hBOOL(hAPP(U_3117,U_3112))
& U_3119 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3121),U_3112),U_3111)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3111,U_3121) )
& U_3121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3120,U_3118,U_3116] :
( ( ( ! [U_3110,U_3109] :
( hBOOL(hAPP(U_3116,U_3110))
| U_3118 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3120),U_3110),U_3109)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3109,U_3120) )
| U_3120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3116,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3118,U_3120))) ) ),
inference(miniscope,[status(thm)],[f_997_2]) ).
fof(f_997_4,plain,
( ! [U_3121,U_3119,U_3117] :
( hBOOL(hAPP(U_3117,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3119,U_3121)))
| ( ? [U_3111] :
( ~ hBOOL(hAPP(U_3117,sK71(U_3121,U_3119,U_3117)))
& U_3119 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3121),sK71(U_3121,U_3119,U_3117)),U_3111)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3111,U_3121) )
& U_3121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3120,U_3118,U_3116] :
( ( ( ! [U_3110,U_3109] :
( hBOOL(hAPP(U_3116,U_3110))
| U_3118 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3120),U_3110),U_3109)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3109,U_3120) )
| U_3120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3116,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3118,U_3120))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_3112,sK71(U_3121,U_3119,U_3117))],[f_997_3]) ).
fof(f_997_5,plain,
( ! [U_3121,U_3119,U_3117] :
( hBOOL(hAPP(U_3117,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3119,U_3121)))
| ( ~ hBOOL(hAPP(U_3117,sK71(U_3121,U_3119,U_3117)))
& U_3119 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3121),sK71(U_3121,U_3119,U_3117)),sK72(U_3121,U_3119,U_3117))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK72(U_3121,U_3119,U_3117),U_3121)
& U_3121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3120,U_3118,U_3116] :
( ( ( ! [U_3110,U_3109] :
( hBOOL(hAPP(U_3116,U_3110))
| U_3118 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3120),U_3110),U_3109)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3109,U_3120) )
| U_3120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3116,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3118,U_3120))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3111,sK72(U_3121,U_3119,U_3117))],[f_997_4]) ).
fof(f_997_6,plain,
( ! [U_3117,U_3119,U_3121] :
( ~ hBOOL(hAPP(U_3117,sK71(U_3121,U_3119,U_3117)))
| ~ sP308(U_3117,U_3119,U_3121) )
& ! [U_3117,U_3119,U_3121] :
( U_3119 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3121),sK71(U_3121,U_3119,U_3117)),sK72(U_3121,U_3119,U_3117))
| ~ sP308(U_3117,U_3119,U_3121) )
& ! [U_3117,U_3119,U_3121] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK72(U_3121,U_3119,U_3117),U_3121)
| ~ sP308(U_3117,U_3119,U_3121) )
& ! [U_3117,U_3119,U_3121] :
( U_3121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP308(U_3117,U_3119,U_3121) )
& ! [U_3117,U_3121] :
( ~ hBOOL(hAPP(U_3117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP307(U_3117,U_3121) )
& ! [U_3117,U_3121] :
( U_3121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP307(U_3117,U_3121) )
& ! [U_3110,U_3109,U_3116,U_3120,U_3118] :
( hBOOL(hAPP(U_3116,U_3110))
| U_3118 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3120),U_3110),U_3109)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3109,U_3120)
| U_3120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP306(U_3110,U_3109,U_3116,U_3120,U_3118) )
& ! [U_3110,U_3109,U_3116,U_3120,U_3118] :
( hBOOL(hAPP(U_3116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP306(U_3110,U_3109,U_3116,U_3120,U_3118) )
& ! [U_3117,U_3119,U_3121] :
( hBOOL(hAPP(U_3117,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3119,U_3121)))
| sP308(U_3117,U_3119,U_3121)
| sP307(U_3117,U_3121) )
& ! [U_3110,U_3109,U_3116,U_3120,U_3118] :
( sP306(U_3110,U_3109,U_3116,U_3120,U_3118)
| ~ hBOOL(hAPP(U_3116,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3118,U_3120))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306,sP307,sP308])],[f_997_5]) ).
cnf(f_997_7,plain,
( sP306(U_3110,U_3109,U_3116,U_3120,U_3118)
| ~ hBOOL(hAPP(U_3116,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3118,U_3120))) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_8,plain,
( hBOOL(hAPP(U_3117,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3119,U_3121)))
| sP308(U_3117,U_3119,U_3121)
| sP307(U_3117,U_3121) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_9,plain,
( hBOOL(hAPP(U_3116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3120 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP306(U_3110,U_3109,U_3116,U_3120,U_3118) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_10,plain,
( hBOOL(hAPP(U_3116,U_3110))
| U_3118 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3120),U_3110),U_3109)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3109,U_3120)
| U_3120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP306(U_3110,U_3109,U_3116,U_3120,U_3118) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_11,plain,
( U_3121 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP307(U_3117,U_3121) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_12,plain,
( ~ hBOOL(hAPP(U_3117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP307(U_3117,U_3121) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_13,plain,
( U_3121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP308(U_3117,U_3119,U_3121) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_14,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK72(U_3121,U_3119,U_3117),U_3121)
| ~ sP308(U_3117,U_3119,U_3121) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_15,plain,
( U_3119 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3121),sK71(U_3121,U_3119,U_3117)),sK72(U_3121,U_3119,U_3117))
| ~ sP308(U_3117,U_3119,U_3121) ),
inference(clausify,[status(thm)],[f_997_6]) ).
cnf(f_997_16,plain,
( ~ hBOOL(hAPP(U_3117,sK71(U_3121,U_3119,U_3117)))
| ~ sP308(U_3117,U_3119,U_3121) ),
inference(clausify,[status(thm)],[f_997_6]) ).
fof(f_998_1,plain,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add]) ).
fof(f_998_2,plain,
! [U_3122] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3122))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3122) ),
inference(variable_rename,[status(thm)],[f_998_1]) ).
fof(f_998_3,plain,
! [U_3122] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3122))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3122) ),
inference(definitional_conversion,[status(esa)],[f_998_2]) ).
cnf(f_998_4,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3122))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3122) ),
inference(clausify,[status(thm)],[f_998_3]) ).
fof(f_999_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]) ).
fof(f_999_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_999_1]) ).
cnf(f_999_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_999_2]) ).
fof(f_1000_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]) ).
fof(f_1000_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1000_1]) ).
cnf(f_1000_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]) ).
fof(f_1001_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1001_1]) ).
cnf(f_1001_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]) ).
fof(f_1002_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1002_1]) ).
cnf(f_1002_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1002_2]) ).
fof(f_1003_1,plain,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra]) ).
fof(f_1003_2,plain,
! [U_3124,U_3123] :
( class_Lattices_Oboolean__algebra(tc_fun(U_3124,U_3123))
| ~ class_Lattices_Oboolean__algebra(U_3123) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
fof(f_1003_3,plain,
! [U_3123,U_3124] :
( class_Lattices_Oboolean__algebra(tc_fun(U_3124,U_3123))
| ~ class_Lattices_Oboolean__algebra(U_3123) ),
inference(definitional_conversion,[status(esa)],[f_1003_2]) ).
cnf(f_1003_4,plain,
( class_Lattices_Oboolean__algebra(tc_fun(U_3124,U_3123))
| ~ class_Lattices_Oboolean__algebra(U_3123) ),
inference(clausify,[status(thm)],[f_1003_3]) ).
fof(f_1004_1,plain,
! [T_2,T_1] :
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder]) ).
fof(f_1004_2,plain,
! [U_3126,U_3125] :
( class_Orderings_Opreorder(tc_fun(U_3126,U_3125))
| ~ class_Orderings_Opreorder(U_3125) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
fof(f_1004_3,plain,
! [U_3125,U_3126] :
( class_Orderings_Opreorder(tc_fun(U_3126,U_3125))
| ~ class_Orderings_Opreorder(U_3125) ),
inference(definitional_conversion,[status(esa)],[f_1004_2]) ).
cnf(f_1004_4,plain,
( class_Orderings_Opreorder(tc_fun(U_3126,U_3125))
| ~ class_Orderings_Opreorder(U_3125) ),
inference(clausify,[status(thm)],[f_1004_3]) ).
fof(f_1005_1,plain,
! [T_2,T_1] :
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder]) ).
fof(f_1005_2,plain,
! [U_3128,U_3127] :
( class_Orderings_Oorder(tc_fun(U_3128,U_3127))
| ~ class_Orderings_Oorder(U_3127) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
fof(f_1005_3,plain,
! [U_3127,U_3128] :
( class_Orderings_Oorder(tc_fun(U_3128,U_3127))
| ~ class_Orderings_Oorder(U_3127) ),
inference(definitional_conversion,[status(esa)],[f_1005_2]) ).
cnf(f_1005_4,plain,
( class_Orderings_Oorder(tc_fun(U_3128,U_3127))
| ~ class_Orderings_Oorder(U_3127) ),
inference(clausify,[status(thm)],[f_1005_3]) ).
fof(f_1006_1,plain,
! [T_2,T_1] :
( class_Orderings_Oord(tc_fun(T_2,T_1))
| ~ class_Orderings_Oord(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord]) ).
fof(f_1006_2,plain,
! [U_3130,U_3129] :
( class_Orderings_Oord(tc_fun(U_3130,U_3129))
| ~ class_Orderings_Oord(U_3129) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
fof(f_1006_3,plain,
! [U_3129,U_3130] :
( class_Orderings_Oord(tc_fun(U_3130,U_3129))
| ~ class_Orderings_Oord(U_3129) ),
inference(definitional_conversion,[status(esa)],[f_1006_2]) ).
cnf(f_1006_4,plain,
( class_Orderings_Oord(tc_fun(U_3130,U_3129))
| ~ class_Orderings_Oord(U_3129) ),
inference(clausify,[status(thm)],[f_1006_3]) ).
fof(f_1007_1,plain,
! [T_2,T_1] :
( class_Groups_Ouminus(tc_fun(T_2,T_1))
| ~ class_Groups_Ouminus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus]) ).
fof(f_1007_2,plain,
! [U_3132,U_3131] :
( class_Groups_Ouminus(tc_fun(U_3132,U_3131))
| ~ class_Groups_Ouminus(U_3131) ),
inference(variable_rename,[status(thm)],[f_1007_1]) ).
fof(f_1007_3,plain,
! [U_3131,U_3132] :
( class_Groups_Ouminus(tc_fun(U_3132,U_3131))
| ~ class_Groups_Ouminus(U_3131) ),
inference(definitional_conversion,[status(esa)],[f_1007_2]) ).
cnf(f_1007_4,plain,
( class_Groups_Ouminus(tc_fun(U_3132,U_3131))
| ~ class_Groups_Ouminus(U_3131) ),
inference(clausify,[status(thm)],[f_1007_3]) ).
fof(f_1008_1,plain,
! [T_2,T_1] :
( class_Groups_Ominus(tc_fun(T_2,T_1))
| ~ class_Groups_Ominus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus]) ).
fof(f_1008_2,plain,
! [U_3134,U_3133] :
( class_Groups_Ominus(tc_fun(U_3134,U_3133))
| ~ class_Groups_Ominus(U_3133) ),
inference(variable_rename,[status(thm)],[f_1008_1]) ).
fof(f_1008_3,plain,
! [U_3133,U_3134] :
( class_Groups_Ominus(tc_fun(U_3134,U_3133))
| ~ class_Groups_Ominus(U_3133) ),
inference(definitional_conversion,[status(esa)],[f_1008_2]) ).
cnf(f_1008_4,plain,
( class_Groups_Ominus(tc_fun(U_3134,U_3133))
| ~ class_Groups_Ominus(U_3133) ),
inference(clausify,[status(thm)],[f_1008_3]) ).
fof(f_1009_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1009_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1009_1]) ).
cnf(f_1009_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1009_2]) ).
fof(f_1010_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(f_1010_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1010_1]) ).
cnf(f_1010_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1010_2]) ).
fof(f_1011_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(f_1011_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1011_1]) ).
cnf(f_1011_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1011_2]) ).
fof(f_1012_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1012_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1012_1]) ).
cnf(f_1012_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1012_2]) ).
fof(f_1013_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).
fof(f_1013_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1013_1]) ).
cnf(f_1013_3,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1013_2]) ).
fof(f_1014_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).
fof(f_1014_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1014_1]) ).
cnf(f_1014_3,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1014_2]) ).
fof(f_1015_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1015_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1015_1]) ).
cnf(f_1015_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1015_2]) ).
fof(f_1016_1,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]) ).
fof(f_1016_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1016_1]) ).
cnf(f_1016_3,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1016_2]) ).
fof(f_1017_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).
fof(f_1017_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1017_1]) ).
cnf(f_1017_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1017_2]) ).
fof(f_1018_1,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).
fof(f_1018_2,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1018_1]) ).
cnf(f_1018_3,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1018_2]) ).
fof(f_1019_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1019_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1019_1]) ).
cnf(f_1019_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1019_2]) ).
fof(f_1020_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]) ).
fof(f_1020_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1020_1]) ).
cnf(f_1020_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1020_2]) ).
fof(f_1021_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).
fof(f_1021_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1021_1]) ).
cnf(f_1021_3,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1021_2]) ).
fof(f_1022_1,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).
fof(f_1022_2,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1022_1]) ).
cnf(f_1022_3,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1022_2]) ).
fof(f_1023_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).
fof(f_1023_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1023_1]) ).
cnf(f_1023_3,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1023_2]) ).
fof(f_1024_1,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).
fof(f_1024_2,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1024_1]) ).
cnf(f_1024_3,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1024_2]) ).
fof(f_1025_1,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).
fof(f_1025_2,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1025_1]) ).
cnf(f_1025_3,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1025_2]) ).
fof(f_1026_1,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).
fof(f_1026_2,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1026_1]) ).
cnf(f_1026_3,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1026_2]) ).
fof(f_1027_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).
fof(f_1027_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1027_1]) ).
cnf(f_1027_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1027_2]) ).
fof(f_1028_1,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).
fof(f_1028_2,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1028_1]) ).
cnf(f_1028_3,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1028_2]) ).
fof(f_1029_1,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).
fof(f_1029_2,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1029_1]) ).
cnf(f_1029_3,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1029_2]) ).
fof(f_1030_1,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).
fof(f_1030_2,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1030_1]) ).
cnf(f_1030_3,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1030_2]) ).
fof(f_1031_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).
fof(f_1031_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1031_1]) ).
cnf(f_1031_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1031_2]) ).
fof(f_1032_1,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).
fof(f_1032_2,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1032_1]) ).
cnf(f_1032_3,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1032_2]) ).
fof(f_1033_1,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).
fof(f_1033_2,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1033_1]) ).
cnf(f_1033_3,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1033_2]) ).
fof(f_1034_1,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).
fof(f_1034_2,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1034_1]) ).
cnf(f_1034_3,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1034_2]) ).
fof(f_1035_1,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).
fof(f_1035_2,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1035_1]) ).
cnf(f_1035_3,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1035_2]) ).
fof(f_1036_1,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).
fof(f_1036_2,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1036_1]) ).
cnf(f_1036_3,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1036_2]) ).
fof(f_1037_1,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).
fof(f_1037_2,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1037_1]) ).
cnf(f_1037_3,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1037_2]) ).
fof(f_1038_1,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).
fof(f_1038_2,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1038_1]) ).
cnf(f_1038_3,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1038_2]) ).
fof(f_1039_1,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).
fof(f_1039_2,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1039_1]) ).
cnf(f_1039_3,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1039_2]) ).
fof(f_1040_1,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]) ).
fof(f_1040_2,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1040_1]) ).
cnf(f_1040_3,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1040_2]) ).
fof(f_1041_1,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).
fof(f_1041_2,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1041_1]) ).
cnf(f_1041_3,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1041_2]) ).
fof(f_1042_1,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).
fof(f_1042_2,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1042_1]) ).
cnf(f_1042_3,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1042_2]) ).
fof(f_1043_1,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).
fof(f_1043_2,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1043_1]) ).
cnf(f_1043_3,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1043_2]) ).
fof(f_1044_1,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).
fof(f_1044_2,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1044_1]) ).
cnf(f_1044_3,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1044_2]) ).
fof(f_1045_1,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).
fof(f_1045_2,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1045_1]) ).
cnf(f_1045_3,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1045_2]) ).
fof(f_1046_1,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).
fof(f_1046_2,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1046_1]) ).
cnf(f_1046_3,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1046_2]) ).
fof(f_1047_1,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
fof(f_1047_2,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1047_1]) ).
cnf(f_1047_3,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1047_2]) ).
fof(f_1048_1,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).
fof(f_1048_2,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1048_1]) ).
cnf(f_1048_3,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1048_2]) ).
fof(f_1049_1,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).
fof(f_1049_2,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1049_1]) ).
cnf(f_1049_3,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1049_2]) ).
fof(f_1050_1,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).
fof(f_1050_2,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1050_1]) ).
cnf(f_1050_3,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1050_2]) ).
fof(f_1051_1,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).
fof(f_1051_2,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1051_1]) ).
cnf(f_1051_3,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1051_2]) ).
fof(f_1052_1,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).
fof(f_1052_2,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1052_1]) ).
cnf(f_1052_3,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1052_2]) ).
fof(f_1053_1,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).
fof(f_1053_2,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1053_1]) ).
cnf(f_1053_3,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1053_2]) ).
fof(f_1054_1,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).
fof(f_1054_2,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1054_1]) ).
cnf(f_1054_3,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1054_2]) ).
fof(f_1055_1,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).
fof(f_1055_2,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1055_1]) ).
cnf(f_1055_3,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1055_2]) ).
fof(f_1056_1,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).
fof(f_1056_2,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1056_1]) ).
cnf(f_1056_3,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1056_2]) ).
fof(f_1057_1,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).
fof(f_1057_2,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1057_1]) ).
cnf(f_1057_3,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1057_2]) ).
fof(f_1058_1,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).
fof(f_1058_2,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1058_1]) ).
cnf(f_1058_3,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1058_2]) ).
fof(f_1059_1,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).
fof(f_1059_2,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1059_1]) ).
cnf(f_1059_3,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1059_2]) ).
fof(f_1060_1,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).
fof(f_1060_2,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1060_1]) ).
cnf(f_1060_3,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1060_2]) ).
fof(f_1061_1,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).
fof(f_1061_2,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1061_1]) ).
cnf(f_1061_3,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1061_2]) ).
fof(f_1062_1,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).
fof(f_1062_2,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1062_1]) ).
cnf(f_1062_3,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1062_2]) ).
fof(f_1063_1,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).
fof(f_1063_2,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1063_1]) ).
cnf(f_1063_3,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1063_2]) ).
fof(f_1064_1,plain,
class_Power_Opower(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).
fof(f_1064_2,plain,
class_Power_Opower(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1064_1]) ).
cnf(f_1064_3,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1064_2]) ).
fof(f_1065_1,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).
fof(f_1065_2,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1065_1]) ).
cnf(f_1065_3,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1065_2]) ).
fof(f_1066_1,plain,
class_Rings_Oring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).
fof(f_1066_2,plain,
class_Rings_Oring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1066_1]) ).
cnf(f_1066_3,plain,
class_Rings_Oring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1066_2]) ).
fof(f_1067_1,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).
fof(f_1067_2,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1067_1]) ).
cnf(f_1067_3,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1067_2]) ).
fof(f_1068_1,plain,
class_Groups_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).
fof(f_1068_2,plain,
class_Groups_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1068_1]) ).
cnf(f_1068_3,plain,
class_Groups_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1068_2]) ).
fof(f_1069_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1069_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1069_1]) ).
cnf(f_1069_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1069_2]) ).
fof(f_1070_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(f_1070_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1070_1]) ).
cnf(f_1070_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1070_2]) ).
fof(f_1071_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(f_1071_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1071_1]) ).
cnf(f_1071_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1071_2]) ).
fof(f_1072_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1072_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1072_1]) ).
cnf(f_1072_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1072_2]) ).
fof(f_1073_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).
fof(f_1073_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1073_1]) ).
cnf(f_1073_3,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1073_2]) ).
fof(f_1074_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1074_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1074_1]) ).
cnf(f_1074_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1074_2]) ).
fof(f_1075_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).
fof(f_1075_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1075_1]) ).
cnf(f_1075_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1075_2]) ).
fof(f_1076_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1076_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1076_1]) ).
cnf(f_1076_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1076_2]) ).
fof(f_1077_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).
fof(f_1077_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1077_1]) ).
cnf(f_1077_3,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1077_2]) ).
fof(f_1078_1,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).
fof(f_1078_2,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1078_1]) ).
cnf(f_1078_3,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1078_2]) ).
fof(f_1079_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
fof(f_1079_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1079_1]) ).
cnf(f_1079_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1079_2]) ).
fof(f_1080_1,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).
fof(f_1080_2,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1080_1]) ).
cnf(f_1080_3,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1080_2]) ).
fof(f_1081_1,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
fof(f_1081_2,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1081_1]) ).
cnf(f_1081_3,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1081_2]) ).
fof(f_1082_1,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).
fof(f_1082_2,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1082_1]) ).
cnf(f_1082_3,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1082_2]) ).
fof(f_1083_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).
fof(f_1083_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1083_1]) ).
cnf(f_1083_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1083_2]) ).
fof(f_1084_1,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).
fof(f_1084_2,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1084_1]) ).
cnf(f_1084_3,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1084_2]) ).
fof(f_1085_1,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).
fof(f_1085_2,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1085_1]) ).
cnf(f_1085_3,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1085_2]) ).
fof(f_1086_1,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).
fof(f_1086_2,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1086_1]) ).
cnf(f_1086_3,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1086_2]) ).
fof(f_1087_1,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).
fof(f_1087_2,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1087_1]) ).
cnf(f_1087_3,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1087_2]) ).
fof(f_1088_1,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
fof(f_1088_2,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1088_1]) ).
cnf(f_1088_3,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1088_2]) ).
fof(f_1089_1,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]) ).
fof(f_1089_2,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1089_1]) ).
cnf(f_1089_3,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1089_2]) ).
fof(f_1090_1,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).
fof(f_1090_2,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1090_1]) ).
cnf(f_1090_3,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1090_2]) ).
fof(f_1091_1,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).
fof(f_1091_2,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1091_1]) ).
cnf(f_1091_3,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1091_2]) ).
fof(f_1092_1,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).
fof(f_1092_2,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1092_1]) ).
cnf(f_1092_3,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1092_2]) ).
fof(f_1093_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(f_1093_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1093_1]) ).
cnf(f_1093_3,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1093_2]) ).
fof(f_1094_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(f_1094_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1094_1]) ).
cnf(f_1094_3,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1094_2]) ).
fof(f_1095_1,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).
fof(f_1095_2,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1095_1]) ).
cnf(f_1095_3,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1095_2]) ).
fof(f_1096_1,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).
fof(f_1096_2,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1096_1]) ).
cnf(f_1096_3,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1096_2]) ).
fof(f_1097_1,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).
fof(f_1097_2,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1097_1]) ).
cnf(f_1097_3,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1097_2]) ).
fof(f_1098_1,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).
fof(f_1098_2,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1098_1]) ).
cnf(f_1098_3,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1098_2]) ).
fof(f_1099_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
fof(f_1099_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1099_1]) ).
cnf(f_1099_3,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1099_2]) ).
fof(f_1100_1,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).
fof(f_1100_2,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1100_1]) ).
cnf(f_1100_3,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1100_2]) ).
fof(f_1101_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
fof(f_1101_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1101_1]) ).
cnf(f_1101_3,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1101_2]) ).
fof(f_1102_1,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).
fof(f_1102_2,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1102_1]) ).
cnf(f_1102_3,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1102_2]) ).
fof(f_1103_1,plain,
class_Power_Opower(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).
fof(f_1103_2,plain,
class_Power_Opower(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1103_1]) ).
cnf(f_1103_3,plain,
class_Power_Opower(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1103_2]) ).
fof(f_1104_1,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).
fof(f_1104_2,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1104_1]) ).
cnf(f_1104_3,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1104_2]) ).
fof(f_1105_1,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).
fof(f_1105_2,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1105_1]) ).
cnf(f_1105_3,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1105_2]) ).
fof(f_1106_1,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
fof(f_1106_2,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1106_1]) ).
cnf(f_1106_3,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1106_2]) ).
fof(f_1107_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
fof(f_1107_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1107_1]) ).
cnf(f_1107_3,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1107_2]) ).
fof(f_1108_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
fof(f_1108_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1108_1]) ).
cnf(f_1108_3,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1108_2]) ).
fof(f_1109_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
fof(f_1109_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1109_1]) ).
cnf(f_1109_3,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1109_2]) ).
fof(f_1110_1,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).
fof(f_1110_2,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1110_1]) ).
cnf(f_1110_3,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1110_2]) ).
fof(f_1111_1,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).
fof(f_1111_2,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1111_1]) ).
cnf(f_1111_3,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1111_2]) ).
fof(f_1112_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1112_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1112_1]) ).
cnf(f_1112_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1112_2]) ).
fof(f_1113_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(f_1113_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1113_1]) ).
cnf(f_1113_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1113_2]) ).
fof(f_1114_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(f_1114_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1114_1]) ).
cnf(f_1114_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1114_2]) ).
fof(f_1115_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1115_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1115_1]) ).
cnf(f_1115_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1115_2]) ).
fof(f_1116_1,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
fof(f_1116_2,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1116_1]) ).
cnf(f_1116_3,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1116_2]) ).
fof(f_1117_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]) ).
fof(f_1117_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1117_1]) ).
cnf(f_1117_3,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1117_2]) ).
fof(f_1118_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]) ).
fof(f_1118_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1118_1]) ).
cnf(f_1118_3,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1118_2]) ).
fof(f_1119_1,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).
fof(f_1119_2,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1119_1]) ).
cnf(f_1119_3,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1119_2]) ).
fof(f_1120_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]) ).
fof(f_1120_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1120_1]) ).
cnf(f_1120_3,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1120_2]) ).
fof(f_1121_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1121_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1121_1]) ).
cnf(f_1121_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1121_2]) ).
fof(f_1122_1,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
fof(f_1122_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1122_1]) ).
cnf(f_1122_3,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1122_2]) ).
fof(f_1123_1,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
fof(f_1123_2,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1123_1]) ).
cnf(f_1123_3,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1123_2]) ).
fof(f_1124_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
fof(f_1124_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1124_1]) ).
cnf(f_1124_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1124_2]) ).
fof(f_1125_1,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
fof(f_1125_2,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1125_1]) ).
cnf(f_1125_3,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1125_2]) ).
fof(f_1126_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1126_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1126_1]) ).
cnf(f_1126_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1126_2]) ).
fof(f_1127_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]) ).
fof(f_1127_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1127_1]) ).
cnf(f_1127_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1127_2]) ).
fof(f_1128_1,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).
fof(f_1128_2,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1128_1]) ).
cnf(f_1128_3,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1128_2]) ).
fof(f_1129_1,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
fof(f_1129_2,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1129_1]) ).
cnf(f_1129_3,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1129_2]) ).
fof(f_1130_1,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
fof(f_1130_2,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1130_1]) ).
cnf(f_1130_3,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1130_2]) ).
fof(f_1131_1,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]) ).
fof(f_1131_2,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1131_1]) ).
cnf(f_1131_3,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1131_2]) ).
fof(f_1132_1,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).
fof(f_1132_2,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1132_1]) ).
cnf(f_1132_3,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1132_2]) ).
fof(f_1133_1,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]) ).
fof(f_1133_2,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1133_1]) ).
cnf(f_1133_3,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1133_2]) ).
fof(f_1134_1,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).
fof(f_1134_2,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1134_1]) ).
cnf(f_1134_3,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1134_2]) ).
fof(f_1135_1,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
fof(f_1135_2,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1135_1]) ).
cnf(f_1135_3,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1135_2]) ).
fof(f_1136_1,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]) ).
fof(f_1136_2,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1136_1]) ).
cnf(f_1136_3,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1136_2]) ).
fof(f_1137_1,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
fof(f_1137_2,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1137_1]) ).
cnf(f_1137_3,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1137_2]) ).
fof(f_1138_1,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).
fof(f_1138_2,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1138_1]) ).
cnf(f_1138_3,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1138_2]) ).
fof(f_1139_1,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).
fof(f_1139_2,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1139_1]) ).
cnf(f_1139_3,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1139_2]) ).
fof(f_1140_1,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).
fof(f_1140_2,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1140_1]) ).
cnf(f_1140_3,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1140_2]) ).
fof(f_1141_1,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
fof(f_1141_2,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1141_1]) ).
cnf(f_1141_3,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1141_2]) ).
fof(f_1142_1,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).
fof(f_1142_2,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1142_1]) ).
cnf(f_1142_3,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1142_2]) ).
fof(f_1143_1,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]) ).
fof(f_1143_2,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1143_1]) ).
cnf(f_1143_3,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1143_2]) ).
fof(f_1144_1,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).
fof(f_1144_2,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1144_1]) ).
cnf(f_1144_3,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1144_2]) ).
fof(f_1145_1,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
fof(f_1145_2,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1145_1]) ).
cnf(f_1145_3,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1145_2]) ).
fof(f_1146_1,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).
fof(f_1146_2,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1146_1]) ).
cnf(f_1146_3,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1146_2]) ).
fof(f_1147_1,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
fof(f_1147_2,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1147_1]) ).
cnf(f_1147_3,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1147_2]) ).
fof(f_1148_1,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(f_1148_2,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1148_1]) ).
cnf(f_1148_3,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1148_2]) ).
fof(f_1149_1,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]) ).
fof(f_1149_2,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1149_1]) ).
cnf(f_1149_3,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1149_2]) ).
fof(f_1150_1,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).
fof(f_1150_2,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1150_1]) ).
cnf(f_1150_3,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1150_2]) ).
fof(f_1151_1,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).
fof(f_1151_2,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1151_1]) ).
cnf(f_1151_3,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1151_2]) ).
fof(f_1152_1,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).
fof(f_1152_2,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1152_1]) ).
cnf(f_1152_3,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1152_2]) ).
fof(f_1153_1,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
fof(f_1153_2,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1153_1]) ).
cnf(f_1153_3,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1153_2]) ).
fof(f_1154_1,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(f_1154_2,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1154_1]) ).
cnf(f_1154_3,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1154_2]) ).
fof(f_1155_1,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(f_1155_2,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1155_1]) ).
cnf(f_1155_3,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1155_2]) ).
fof(f_1156_1,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
fof(f_1156_2,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1156_1]) ).
cnf(f_1156_3,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1156_2]) ).
fof(f_1157_1,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).
fof(f_1157_2,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1157_1]) ).
cnf(f_1157_3,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1157_2]) ).
fof(f_1158_1,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
fof(f_1158_2,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1158_1]) ).
cnf(f_1158_3,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1158_2]) ).
fof(f_1159_1,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).
fof(f_1159_2,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1159_1]) ).
cnf(f_1159_3,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1159_2]) ).
fof(f_1160_1,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(f_1160_2,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1160_1]) ).
cnf(f_1160_3,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1160_2]) ).
fof(f_1161_1,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).
fof(f_1161_2,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1161_1]) ).
cnf(f_1161_3,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1161_2]) ).
fof(f_1162_1,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]) ).
fof(f_1162_2,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1162_1]) ).
cnf(f_1162_3,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1162_2]) ).
fof(f_1163_1,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(f_1163_2,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1163_1]) ).
cnf(f_1163_3,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1163_2]) ).
fof(f_1164_1,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]) ).
fof(f_1164_2,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1164_1]) ).
cnf(f_1164_3,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1164_2]) ).
fof(f_1165_1,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).
fof(f_1165_2,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1165_1]) ).
cnf(f_1165_3,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1165_2]) ).
fof(f_1166_1,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).
fof(f_1166_2,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1166_1]) ).
cnf(f_1166_3,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1166_2]) ).
fof(f_1167_1,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]) ).
fof(f_1167_2,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1167_1]) ).
cnf(f_1167_3,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1167_2]) ).
fof(f_1168_1,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]) ).
fof(f_1168_2,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1168_1]) ).
cnf(f_1168_3,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1168_2]) ).
fof(f_1169_1,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]) ).
fof(f_1169_2,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1169_1]) ).
cnf(f_1169_3,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1169_2]) ).
fof(f_1170_1,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).
fof(f_1170_2,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1170_1]) ).
cnf(f_1170_3,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1170_2]) ).
fof(f_1171_1,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]) ).
fof(f_1171_2,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1171_1]) ).
cnf(f_1171_3,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1171_2]) ).
fof(f_1172_1,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]) ).
fof(f_1172_2,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1172_1]) ).
cnf(f_1172_3,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1172_2]) ).
fof(f_1173_1,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).
fof(f_1173_2,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1173_1]) ).
cnf(f_1173_3,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1173_2]) ).
fof(f_1174_1,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).
fof(f_1174_2,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1174_1]) ).
cnf(f_1174_3,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1174_2]) ).
fof(f_1175_1,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).
fof(f_1175_2,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1175_1]) ).
cnf(f_1175_3,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1175_2]) ).
fof(f_1176_1,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]) ).
fof(f_1176_2,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1176_1]) ).
cnf(f_1176_3,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1176_2]) ).
fof(f_1177_1,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).
fof(f_1177_2,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1177_1]) ).
cnf(f_1177_3,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1177_2]) ).
fof(f_1178_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1178_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1178_1]) ).
cnf(f_1178_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1178_2]) ).
fof(f_1179_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
fof(f_1179_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1179_1]) ).
cnf(f_1179_3,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1179_2]) ).
fof(f_1180_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).
fof(f_1180_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1180_1]) ).
cnf(f_1180_3,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1180_2]) ).
fof(f_1181_1,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(f_1181_2,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1181_1]) ).
cnf(f_1181_3,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1181_2]) ).
fof(f_1182_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1182_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1182_1]) ).
cnf(f_1182_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1182_2]) ).
fof(f_1183_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]) ).
fof(f_1183_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1183_1]) ).
cnf(f_1183_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1183_2]) ).
fof(f_1184_1,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(f_1184_2,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1184_1]) ).
cnf(f_1184_3,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1184_2]) ).
fof(f_1185_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]) ).
fof(f_1185_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1185_1]) ).
cnf(f_1185_3,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1185_2]) ).
fof(f_1186_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).
fof(f_1186_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1186_1]) ).
cnf(f_1186_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1186_2]) ).
fof(f_1187_1,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).
fof(f_1187_2,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1187_1]) ).
cnf(f_1187_3,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1187_2]) ).
fof(f_1188_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).
fof(f_1188_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1188_1]) ).
cnf(f_1188_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1188_2]) ).
fof(f_1189_1,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).
fof(f_1189_2,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1189_1]) ).
cnf(f_1189_3,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1189_2]) ).
fof(f_1190_1,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
fof(f_1190_2,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1190_1]) ).
cnf(f_1190_3,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1190_2]) ).
fof(f_1191_1,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
fof(f_1191_2,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1191_1]) ).
cnf(f_1191_3,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1191_2]) ).
fof(f_1192_1,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(f_1192_2,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1192_1]) ).
cnf(f_1192_3,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1192_2]) ).
fof(f_1193_1,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(f_1193_2,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1193_1]) ).
cnf(f_1193_3,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1193_2]) ).
fof(f_1194_1,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).
fof(f_1194_2,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1194_1]) ).
cnf(f_1194_3,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1194_2]) ).
fof(f_1195_1,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
fof(f_1195_2,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1195_1]) ).
cnf(f_1195_3,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1195_2]) ).
fof(f_1196_1,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
fof(f_1196_2,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1196_1]) ).
cnf(f_1196_3,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1196_2]) ).
fof(f_1197_1,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
fof(f_1197_2,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1197_1]) ).
cnf(f_1197_3,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1197_2]) ).
fof(f_1198_1,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
fof(f_1198_2,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1198_1]) ).
cnf(f_1198_3,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1198_2]) ).
fof(f_1199_1,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).
fof(f_1199_2,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1199_1]) ).
cnf(f_1199_3,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1199_2]) ).
fof(f_1200_1,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).
fof(f_1200_2,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1200_1]) ).
cnf(f_1200_3,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1200_2]) ).
fof(f_1201_1,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
fof(f_1201_2,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1201_1]) ).
cnf(f_1201_3,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1201_2]) ).
fof(f_1202_1,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
fof(f_1202_2,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1202_1]) ).
cnf(f_1202_3,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1202_2]) ).
fof(f_1203_1,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]) ).
fof(f_1203_2,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1203_1]) ).
cnf(f_1203_3,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1203_2]) ).
fof(f_1204_1,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
fof(f_1204_2,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1204_1]) ).
cnf(f_1204_3,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1204_2]) ).
fof(f_1205_1,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).
fof(f_1205_2,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1205_1]) ).
cnf(f_1205_3,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1205_2]) ).
fof(f_1206_1,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]) ).
fof(f_1206_2,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1206_1]) ).
cnf(f_1206_3,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1206_2]) ).
fof(f_1207_1,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).
fof(f_1207_2,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1207_1]) ).
cnf(f_1207_3,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1207_2]) ).
fof(f_1208_1,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]) ).
fof(f_1208_2,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1208_1]) ).
cnf(f_1208_3,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1208_2]) ).
fof(f_1209_1,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
fof(f_1209_2,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1209_1]) ).
cnf(f_1209_3,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1209_2]) ).
fof(f_1210_1,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
fof(f_1210_2,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1210_1]) ).
cnf(f_1210_3,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1210_2]) ).
fof(f_1211_1,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
fof(f_1211_2,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1211_1]) ).
cnf(f_1211_3,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1211_2]) ).
fof(f_1212_1,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).
fof(f_1212_2,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1212_1]) ).
cnf(f_1212_3,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1212_2]) ).
fof(f_1213_1,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
fof(f_1213_2,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1213_1]) ).
cnf(f_1213_3,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1213_2]) ).
fof(f_1214_1,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).
fof(f_1214_2,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1214_1]) ).
cnf(f_1214_3,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1214_2]) ).
fof(f_1215_1,plain,
! [T_1] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1215_2,plain,
! [U_3135] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3135))
| ~ class_Rings_Oidom(U_3135) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
fof(f_1215_3,plain,
! [U_3135] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3135))
| ~ class_Rings_Oidom(U_3135) ),
inference(definitional_conversion,[status(esa)],[f_1215_2]) ).
cnf(f_1215_4,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3135))
| ~ class_Rings_Oidom(U_3135) ),
inference(clausify,[status(thm)],[f_1215_3]) ).
fof(f_1216_1,plain,
! [T_1] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(f_1216_2,plain,
! [U_3136] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3136))
| ~ class_Rings_Olinordered__idom(U_3136) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
fof(f_1216_3,plain,
! [U_3136] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3136))
| ~ class_Rings_Olinordered__idom(U_3136) ),
inference(definitional_conversion,[status(esa)],[f_1216_2]) ).
cnf(f_1216_4,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3136))
| ~ class_Rings_Olinordered__idom(U_3136) ),
inference(clausify,[status(thm)],[f_1216_3]) ).
fof(f_1217_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(f_1217_2,plain,
! [U_3137] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3137))
| ~ class_Rings_Olinordered__idom(U_3137) ),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
fof(f_1217_3,plain,
! [U_3137] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3137))
| ~ class_Rings_Olinordered__idom(U_3137) ),
inference(definitional_conversion,[status(esa)],[f_1217_2]) ).
cnf(f_1217_4,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3137))
| ~ class_Rings_Olinordered__idom(U_3137) ),
inference(clausify,[status(thm)],[f_1217_3]) ).
fof(f_1218_1,plain,
! [T_1] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1218_2,plain,
! [U_3138] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3138))
| ~ class_Rings_Olinordered__idom(U_3138) ),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
fof(f_1218_3,plain,
! [U_3138] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3138))
| ~ class_Rings_Olinordered__idom(U_3138) ),
inference(definitional_conversion,[status(esa)],[f_1218_2]) ).
cnf(f_1218_4,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3138))
| ~ class_Rings_Olinordered__idom(U_3138) ),
inference(clausify,[status(thm)],[f_1218_3]) ).
fof(f_1219_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict]) ).
fof(f_1219_2,plain,
! [U_3139] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3139))
| ~ class_Rings_Olinordered__idom(U_3139) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
fof(f_1219_3,plain,
! [U_3139] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3139))
| ~ class_Rings_Olinordered__idom(U_3139) ),
inference(definitional_conversion,[status(esa)],[f_1219_2]) ).
cnf(f_1219_4,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3139))
| ~ class_Rings_Olinordered__idom(U_3139) ),
inference(clausify,[status(thm)],[f_1219_3]) ).
fof(f_1220_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict]) ).
fof(f_1220_2,plain,
! [U_3140] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3140))
| ~ class_Rings_Olinordered__idom(U_3140) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
fof(f_1220_3,plain,
! [U_3140] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3140))
| ~ class_Rings_Olinordered__idom(U_3140) ),
inference(definitional_conversion,[status(esa)],[f_1220_2]) ).
cnf(f_1220_4,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3140))
| ~ class_Rings_Olinordered__idom(U_3140) ),
inference(clausify,[status(thm)],[f_1220_3]) ).
fof(f_1221_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1221_2,plain,
! [U_3141] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3141))
| ~ class_Rings_Olinordered__idom(U_3141) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
fof(f_1221_3,plain,
! [U_3141] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3141))
| ~ class_Rings_Olinordered__idom(U_3141) ),
inference(definitional_conversion,[status(esa)],[f_1221_2]) ).
cnf(f_1221_4,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3141))
| ~ class_Rings_Olinordered__idom(U_3141) ),
inference(clausify,[status(thm)],[f_1221_3]) ).
fof(f_1222_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs]) ).
fof(f_1222_2,plain,
! [U_3142] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3142))
| ~ class_Rings_Olinordered__idom(U_3142) ),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
fof(f_1222_3,plain,
! [U_3142] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3142))
| ~ class_Rings_Olinordered__idom(U_3142) ),
inference(definitional_conversion,[status(esa)],[f_1222_2]) ).
cnf(f_1222_4,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3142))
| ~ class_Rings_Olinordered__idom(U_3142) ),
inference(clausify,[status(thm)],[f_1222_3]) ).
fof(f_1223_1,plain,
! [T_1] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add]) ).
fof(f_1223_2,plain,
! [U_3143] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3143))
| ~ class_Rings_Olinordered__idom(U_3143) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
fof(f_1223_3,plain,
! [U_3143] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3143))
| ~ class_Rings_Olinordered__idom(U_3143) ),
inference(definitional_conversion,[status(esa)],[f_1223_2]) ).
cnf(f_1223_4,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3143))
| ~ class_Rings_Olinordered__idom(U_3143) ),
inference(clausify,[status(thm)],[f_1223_3]) ).
fof(f_1224_1,plain,
! [T_1] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add]) ).
fof(f_1224_2,plain,
! [U_3144] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3144))
| ~ class_Rings_Olinordered__idom(U_3144) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
fof(f_1224_3,plain,
! [U_3144] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3144))
| ~ class_Rings_Olinordered__idom(U_3144) ),
inference(definitional_conversion,[status(esa)],[f_1224_2]) ).
cnf(f_1224_4,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3144))
| ~ class_Rings_Olinordered__idom(U_3144) ),
inference(clausify,[status(thm)],[f_1224_3]) ).
fof(f_1225_1,plain,
! [T_1] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1225_2,plain,
! [U_3145] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3145))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3145) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
fof(f_1225_3,plain,
! [U_3145] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3145))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3145) ),
inference(definitional_conversion,[status(esa)],[f_1225_2]) ).
cnf(f_1225_4,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3145))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3145) ),
inference(clausify,[status(thm)],[f_1225_3]) ).
fof(f_1226_1,plain,
! [T_1] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors]) ).
fof(f_1226_2,plain,
! [U_3146] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3146))
| ~ class_Rings_Oidom(U_3146) ),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
fof(f_1226_3,plain,
! [U_3146] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3146))
| ~ class_Rings_Oidom(U_3146) ),
inference(definitional_conversion,[status(esa)],[f_1226_2]) ).
cnf(f_1226_4,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3146))
| ~ class_Rings_Oidom(U_3146) ),
inference(clausify,[status(thm)],[f_1226_3]) ).
fof(f_1227_1,plain,
! [T_1] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring]) ).
fof(f_1227_2,plain,
! [U_3147] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3147))
| ~ class_Rings_Olinordered__idom(U_3147) ),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
fof(f_1227_3,plain,
! [U_3147] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3147))
| ~ class_Rings_Olinordered__idom(U_3147) ),
inference(definitional_conversion,[status(esa)],[f_1227_2]) ).
cnf(f_1227_4,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3147))
| ~ class_Rings_Olinordered__idom(U_3147) ),
inference(clausify,[status(thm)],[f_1227_3]) ).
fof(f_1228_1,plain,
! [T_1] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict]) ).
fof(f_1228_2,plain,
! [U_3148] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3148))
| ~ class_Rings_Olinordered__idom(U_3148) ),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
fof(f_1228_3,plain,
! [U_3148] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3148))
| ~ class_Rings_Olinordered__idom(U_3148) ),
inference(definitional_conversion,[status(esa)],[f_1228_2]) ).
cnf(f_1228_4,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3148))
| ~ class_Rings_Olinordered__idom(U_3148) ),
inference(clausify,[status(thm)],[f_1228_3]) ).
fof(f_1229_1,plain,
! [T_1] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors]) ).
fof(f_1229_2,plain,
! [U_3149] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3149))
| ~ class_Rings_Oidom(U_3149) ),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
fof(f_1229_3,plain,
! [U_3149] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3149))
| ~ class_Rings_Oidom(U_3149) ),
inference(definitional_conversion,[status(esa)],[f_1229_2]) ).
cnf(f_1229_4,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3149))
| ~ class_Rings_Oidom(U_3149) ),
inference(clausify,[status(thm)],[f_1229_3]) ).
fof(f_1230_1,plain,
! [T_1] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring]) ).
fof(f_1230_2,plain,
! [U_3150] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3150))
| ~ class_Rings_Olinordered__idom(U_3150) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
fof(f_1230_3,plain,
! [U_3150] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3150))
| ~ class_Rings_Olinordered__idom(U_3150) ),
inference(definitional_conversion,[status(esa)],[f_1230_2]) ).
cnf(f_1230_4,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3150))
| ~ class_Rings_Olinordered__idom(U_3150) ),
inference(clausify,[status(thm)],[f_1230_3]) ).
fof(f_1231_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1]) ).
fof(f_1231_2,plain,
! [U_3151] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3151))
| ~ class_Rings_Olinordered__idom(U_3151) ),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
fof(f_1231_3,plain,
! [U_3151] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3151))
| ~ class_Rings_Olinordered__idom(U_3151) ),
inference(definitional_conversion,[status(esa)],[f_1231_2]) ).
cnf(f_1231_4,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3151))
| ~ class_Rings_Olinordered__idom(U_3151) ),
inference(clausify,[status(thm)],[f_1231_3]) ).
fof(f_1232_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add]) ).
fof(f_1232_2,plain,
! [U_3152] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3152))
| ~ class_Rings_Olinordered__idom(U_3152) ),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
fof(f_1232_3,plain,
! [U_3152] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3152))
| ~ class_Rings_Olinordered__idom(U_3152) ),
inference(definitional_conversion,[status(esa)],[f_1232_2]) ).
cnf(f_1232_4,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3152))
| ~ class_Rings_Olinordered__idom(U_3152) ),
inference(clausify,[status(thm)],[f_1232_3]) ).
fof(f_1233_1,plain,
! [T_1] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add]) ).
fof(f_1233_2,plain,
! [U_3153] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3153))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3153) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
fof(f_1233_3,plain,
! [U_3153] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3153))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3153) ),
inference(definitional_conversion,[status(esa)],[f_1233_2]) ).
cnf(f_1233_4,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3153))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3153) ),
inference(clausify,[status(thm)],[f_1233_3]) ).
fof(f_1234_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring]) ).
fof(f_1234_2,plain,
! [U_3154] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3154))
| ~ class_Rings_Olinordered__idom(U_3154) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
fof(f_1234_3,plain,
! [U_3154] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3154))
| ~ class_Rings_Olinordered__idom(U_3154) ),
inference(definitional_conversion,[status(esa)],[f_1234_2]) ).
cnf(f_1234_4,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3154))
| ~ class_Rings_Olinordered__idom(U_3154) ),
inference(clausify,[status(thm)],[f_1234_3]) ).
fof(f_1235_1,plain,
! [T_1] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom]) ).
fof(f_1235_2,plain,
! [U_3155] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3155))
| ~ class_Rings_Olinordered__idom(U_3155) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
fof(f_1235_3,plain,
! [U_3155] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3155))
| ~ class_Rings_Olinordered__idom(U_3155) ),
inference(definitional_conversion,[status(esa)],[f_1235_2]) ).
cnf(f_1235_4,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3155))
| ~ class_Rings_Olinordered__idom(U_3155) ),
inference(clausify,[status(thm)],[f_1235_3]) ).
fof(f_1236_1,plain,
! [T_1] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult]) ).
fof(f_1236_2,plain,
! [U_3156] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3156))
| ~ class_Rings_Ocomm__semiring__0(U_3156) ),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
fof(f_1236_3,plain,
! [U_3156] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3156))
| ~ class_Rings_Ocomm__semiring__0(U_3156) ),
inference(definitional_conversion,[status(esa)],[f_1236_2]) ).
cnf(f_1236_4,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3156))
| ~ class_Rings_Ocomm__semiring__0(U_3156) ),
inference(clausify,[status(thm)],[f_1236_3]) ).
fof(f_1237_1,plain,
! [T_1] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult]) ).
fof(f_1237_2,plain,
! [U_3157] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3157))
| ~ class_Rings_Ocomm__semiring__1(U_3157) ),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
fof(f_1237_3,plain,
! [U_3157] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3157))
| ~ class_Rings_Ocomm__semiring__1(U_3157) ),
inference(definitional_conversion,[status(esa)],[f_1237_2]) ).
cnf(f_1237_4,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3157))
| ~ class_Rings_Ocomm__semiring__1(U_3157) ),
inference(clausify,[status(thm)],[f_1237_3]) ).
fof(f_1238_1,plain,
! [T_1] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add]) ).
fof(f_1238_2,plain,
! [U_3158] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3158))
| ~ class_Groups_Ocomm__monoid__add(U_3158) ),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
fof(f_1238_3,plain,
! [U_3158] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3158))
| ~ class_Groups_Ocomm__monoid__add(U_3158) ),
inference(definitional_conversion,[status(esa)],[f_1238_2]) ).
cnf(f_1238_4,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3158))
| ~ class_Groups_Ocomm__monoid__add(U_3158) ),
inference(clausify,[status(thm)],[f_1238_3]) ).
fof(f_1239_1,plain,
! [T_1] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring]) ).
fof(f_1239_2,plain,
! [U_3159] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3159))
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
fof(f_1239_3,plain,
! [U_3159] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3159))
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(definitional_conversion,[status(esa)],[f_1239_2]) ).
cnf(f_1239_4,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3159))
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(clausify,[status(thm)],[f_1239_3]) ).
fof(f_1240_1,plain,
! [T_1] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs]) ).
fof(f_1240_2,plain,
! [U_3160] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3160))
| ~ class_Rings_Olinordered__idom(U_3160) ),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
fof(f_1240_3,plain,
! [U_3160] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3160))
| ~ class_Rings_Olinordered__idom(U_3160) ),
inference(definitional_conversion,[status(esa)],[f_1240_2]) ).
cnf(f_1240_4,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3160))
| ~ class_Rings_Olinordered__idom(U_3160) ),
inference(clausify,[status(thm)],[f_1240_3]) ).
fof(f_1241_1,plain,
! [T_1] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors]) ).
fof(f_1241_2,plain,
! [U_3161] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3161))
| ~ class_Rings_Oidom(U_3161) ),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
fof(f_1241_3,plain,
! [U_3161] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3161))
| ~ class_Rings_Oidom(U_3161) ),
inference(definitional_conversion,[status(esa)],[f_1241_2]) ).
cnf(f_1241_4,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3161))
| ~ class_Rings_Oidom(U_3161) ),
inference(clausify,[status(thm)],[f_1241_3]) ).
fof(f_1242_1,plain,
! [T_1] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add]) ).
fof(f_1242_2,plain,
! [U_3162] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3162))
| ~ class_Groups_Ocomm__monoid__add(U_3162) ),
inference(variable_rename,[status(thm)],[f_1242_1]) ).
fof(f_1242_3,plain,
! [U_3162] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3162))
| ~ class_Groups_Ocomm__monoid__add(U_3162) ),
inference(definitional_conversion,[status(esa)],[f_1242_2]) ).
cnf(f_1242_4,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3162))
| ~ class_Groups_Ocomm__monoid__add(U_3162) ),
inference(clausify,[status(thm)],[f_1242_3]) ).
fof(f_1243_1,plain,
! [T_1] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring]) ).
fof(f_1243_2,plain,
! [U_3163] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3163))
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
fof(f_1243_3,plain,
! [U_3163] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3163))
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(definitional_conversion,[status(esa)],[f_1243_2]) ).
cnf(f_1243_4,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3163))
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(clausify,[status(thm)],[f_1243_3]) ).
fof(f_1244_1,plain,
! [T_1] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom]) ).
fof(f_1244_2,plain,
! [U_3164] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3164))
| ~ class_Rings_Olinordered__idom(U_3164) ),
inference(variable_rename,[status(thm)],[f_1244_1]) ).
fof(f_1244_3,plain,
! [U_3164] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3164))
| ~ class_Rings_Olinordered__idom(U_3164) ),
inference(definitional_conversion,[status(esa)],[f_1244_2]) ).
cnf(f_1244_4,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3164))
| ~ class_Rings_Olinordered__idom(U_3164) ),
inference(clausify,[status(thm)],[f_1244_3]) ).
fof(f_1245_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1]) ).
fof(f_1245_2,plain,
! [U_3165] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3165))
| ~ class_Rings_Ocomm__semiring__1(U_3165) ),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
fof(f_1245_3,plain,
! [U_3165] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3165))
| ~ class_Rings_Ocomm__semiring__1(U_3165) ),
inference(definitional_conversion,[status(esa)],[f_1245_2]) ).
cnf(f_1245_4,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3165))
| ~ class_Rings_Ocomm__semiring__1(U_3165) ),
inference(clausify,[status(thm)],[f_1245_3]) ).
fof(f_1246_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0]) ).
fof(f_1246_2,plain,
! [U_3166] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3166))
| ~ class_Rings_Ocomm__semiring__0(U_3166) ),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
fof(f_1246_3,plain,
! [U_3166] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3166))
| ~ class_Rings_Ocomm__semiring__0(U_3166) ),
inference(definitional_conversion,[status(esa)],[f_1246_2]) ).
cnf(f_1246_4,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3166))
| ~ class_Rings_Ocomm__semiring__0(U_3166) ),
inference(clausify,[status(thm)],[f_1246_3]) ).
fof(f_1247_1,plain,
! [T_1] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div]) ).
fof(f_1247_2,plain,
! [U_3167] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3167))
| ~ class_Fields_Ofield(U_3167) ),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
fof(f_1247_3,plain,
! [U_3167] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3167))
| ~ class_Fields_Ofield(U_3167) ),
inference(definitional_conversion,[status(esa)],[f_1247_2]) ).
cnf(f_1247_4,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3167))
| ~ class_Fields_Ofield(U_3167) ),
inference(clausify,[status(thm)],[f_1247_3]) ).
fof(f_1248_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring]) ).
fof(f_1248_2,plain,
! [U_3168] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3168))
| ~ class_Rings_Ocomm__semiring__0(U_3168) ),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
fof(f_1248_3,plain,
! [U_3168] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3168))
| ~ class_Rings_Ocomm__semiring__0(U_3168) ),
inference(definitional_conversion,[status(esa)],[f_1248_2]) ).
cnf(f_1248_4,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3168))
| ~ class_Rings_Ocomm__semiring__0(U_3168) ),
inference(clausify,[status(thm)],[f_1248_3]) ).
fof(f_1249_1,plain,
! [T_1] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add]) ).
fof(f_1249_2,plain,
! [U_3169] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3169))
| ~ class_Groups_Oab__group__add(U_3169) ),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
fof(f_1249_3,plain,
! [U_3169] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3169))
| ~ class_Groups_Oab__group__add(U_3169) ),
inference(definitional_conversion,[status(esa)],[f_1249_2]) ).
cnf(f_1249_4,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3169))
| ~ class_Groups_Oab__group__add(U_3169) ),
inference(clausify,[status(thm)],[f_1249_3]) ).
fof(f_1250_1,plain,
! [T_1] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one]) ).
fof(f_1250_2,plain,
! [U_3170] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3170))
| ~ class_Rings_Ocomm__semiring__1(U_3170) ),
inference(variable_rename,[status(thm)],[f_1250_1]) ).
fof(f_1250_3,plain,
! [U_3170] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3170))
| ~ class_Rings_Ocomm__semiring__1(U_3170) ),
inference(definitional_conversion,[status(esa)],[f_1250_2]) ).
cnf(f_1250_4,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3170))
| ~ class_Rings_Ocomm__semiring__1(U_3170) ),
inference(clausify,[status(thm)],[f_1250_3]) ).
fof(f_1251_1,plain,
! [T_1] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring]) ).
fof(f_1251_2,plain,
! [U_3171] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
fof(f_1251_3,plain,
! [U_3171] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(definitional_conversion,[status(esa)],[f_1251_2]) ).
cnf(f_1251_4,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(clausify,[status(thm)],[f_1251_3]) ).
fof(f_1252_1,plain,
! [T_1] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder]) ).
fof(f_1252_2,plain,
! [U_3172] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3172))
| ~ class_Rings_Olinordered__idom(U_3172) ),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
fof(f_1252_3,plain,
! [U_3172] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3172))
| ~ class_Rings_Olinordered__idom(U_3172) ),
inference(definitional_conversion,[status(esa)],[f_1252_2]) ).
cnf(f_1252_4,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3172))
| ~ class_Rings_Olinordered__idom(U_3172) ),
inference(clausify,[status(thm)],[f_1252_3]) ).
fof(f_1253_1,plain,
! [T_1] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder]) ).
fof(f_1253_2,plain,
! [U_3173] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3173))
| ~ class_Rings_Olinordered__idom(U_3173) ),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
fof(f_1253_3,plain,
! [U_3173] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3173))
| ~ class_Rings_Olinordered__idom(U_3173) ),
inference(definitional_conversion,[status(esa)],[f_1253_2]) ).
cnf(f_1253_4,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3173))
| ~ class_Rings_Olinordered__idom(U_3173) ),
inference(clausify,[status(thm)],[f_1253_3]) ).
fof(f_1254_1,plain,
! [T_1] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult]) ).
fof(f_1254_2,plain,
! [U_3174] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3174))
| ~ class_Rings_Ocomm__semiring__1(U_3174) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
fof(f_1254_3,plain,
! [U_3174] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3174))
| ~ class_Rings_Ocomm__semiring__1(U_3174) ),
inference(definitional_conversion,[status(esa)],[f_1254_2]) ).
cnf(f_1254_4,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3174))
| ~ class_Rings_Ocomm__semiring__1(U_3174) ),
inference(clausify,[status(thm)],[f_1254_3]) ).
fof(f_1255_1,plain,
! [T_1] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1]) ).
fof(f_1255_2,plain,
! [U_3175] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3175))
| ~ class_Rings_Ocomm__ring__1(U_3175) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
fof(f_1255_3,plain,
! [U_3175] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3175))
| ~ class_Rings_Ocomm__ring__1(U_3175) ),
inference(definitional_conversion,[status(esa)],[f_1255_2]) ).
cnf(f_1255_4,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3175))
| ~ class_Rings_Ocomm__ring__1(U_3175) ),
inference(clausify,[status(thm)],[f_1255_3]) ).
fof(f_1256_1,plain,
! [T_1] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add]) ).
fof(f_1256_2,plain,
! [U_3176] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3176))
| ~ class_Groups_Ocomm__monoid__add(U_3176) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
fof(f_1256_3,plain,
! [U_3176] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3176))
| ~ class_Groups_Ocomm__monoid__add(U_3176) ),
inference(definitional_conversion,[status(esa)],[f_1256_2]) ).
cnf(f_1256_4,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3176))
| ~ class_Groups_Ocomm__monoid__add(U_3176) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
fof(f_1257_1,plain,
! [T_1] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0]) ).
fof(f_1257_2,plain,
! [U_3177] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3177))
| ~ class_Rings_Ocomm__semiring__0(U_3177) ),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
fof(f_1257_3,plain,
! [U_3177] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3177))
| ~ class_Rings_Ocomm__semiring__0(U_3177) ),
inference(definitional_conversion,[status(esa)],[f_1257_2]) ).
cnf(f_1257_4,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3177))
| ~ class_Rings_Ocomm__semiring__0(U_3177) ),
inference(clausify,[status(thm)],[f_1257_3]) ).
fof(f_1258_1,plain,
! [T_1] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add]) ).
fof(f_1258_2,plain,
! [U_3178] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3178))
| ~ class_Groups_Oab__group__add(U_3178) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
fof(f_1258_3,plain,
! [U_3178] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3178))
| ~ class_Groups_Oab__group__add(U_3178) ),
inference(definitional_conversion,[status(esa)],[f_1258_2]) ).
cnf(f_1258_4,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3178))
| ~ class_Groups_Oab__group__add(U_3178) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
fof(f_1259_1,plain,
! [T_1] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero]) ).
fof(f_1259_2,plain,
! [U_3179] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3179))
| ~ class_Rings_Ocomm__semiring__0(U_3179) ),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
fof(f_1259_3,plain,
! [U_3179] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3179))
| ~ class_Rings_Ocomm__semiring__0(U_3179) ),
inference(definitional_conversion,[status(esa)],[f_1259_2]) ).
cnf(f_1259_4,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3179))
| ~ class_Rings_Ocomm__semiring__0(U_3179) ),
inference(clausify,[status(thm)],[f_1259_3]) ).
fof(f_1260_1,plain,
! [T_1] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring]) ).
fof(f_1260_2,plain,
! [U_3180] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3180))
| ~ class_Rings_Ocomm__ring(U_3180) ),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
fof(f_1260_3,plain,
! [U_3180] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3180))
| ~ class_Rings_Ocomm__ring(U_3180) ),
inference(definitional_conversion,[status(esa)],[f_1260_2]) ).
cnf(f_1260_4,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3180))
| ~ class_Rings_Ocomm__ring(U_3180) ),
inference(clausify,[status(thm)],[f_1260_3]) ).
fof(f_1261_1,plain,
! [T_1] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder]) ).
fof(f_1261_2,plain,
! [U_3181] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3181))
| ~ class_Rings_Olinordered__idom(U_3181) ),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
fof(f_1261_3,plain,
! [U_3181] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3181))
| ~ class_Rings_Olinordered__idom(U_3181) ),
inference(definitional_conversion,[status(esa)],[f_1261_2]) ).
cnf(f_1261_4,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3181))
| ~ class_Rings_Olinordered__idom(U_3181) ),
inference(clausify,[status(thm)],[f_1261_3]) ).
fof(f_1262_1,plain,
! [T_1] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0]) ).
fof(f_1262_2,plain,
! [U_3182] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3182))
| ~ class_Rings_Olinordered__idom(U_3182) ),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
fof(f_1262_3,plain,
! [U_3182] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3182))
| ~ class_Rings_Olinordered__idom(U_3182) ),
inference(definitional_conversion,[status(esa)],[f_1262_2]) ).
cnf(f_1262_4,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3182))
| ~ class_Rings_Olinordered__idom(U_3182) ),
inference(clausify,[status(thm)],[f_1262_3]) ).
fof(f_1263_1,plain,
! [T_1] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring]) ).
fof(f_1263_2,plain,
! [U_3183] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3183))
| ~ class_Rings_Ocomm__semiring__0(U_3183) ),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
fof(f_1263_3,plain,
! [U_3183] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3183))
| ~ class_Rings_Ocomm__semiring__0(U_3183) ),
inference(definitional_conversion,[status(esa)],[f_1263_2]) ).
cnf(f_1263_4,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3183))
| ~ class_Rings_Ocomm__semiring__0(U_3183) ),
inference(clausify,[status(thm)],[f_1263_3]) ).
fof(f_1264_1,plain,
! [T_1] :
( class_Orderings_Oord(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord]) ).
fof(f_1264_2,plain,
! [U_3184] :
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3184))
| ~ class_Rings_Olinordered__idom(U_3184) ),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
fof(f_1264_3,plain,
! [U_3184] :
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3184))
| ~ class_Rings_Olinordered__idom(U_3184) ),
inference(definitional_conversion,[status(esa)],[f_1264_2]) ).
cnf(f_1264_4,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3184))
| ~ class_Rings_Olinordered__idom(U_3184) ),
inference(clausify,[status(thm)],[f_1264_3]) ).
fof(f_1265_1,plain,
! [T_1] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus]) ).
fof(f_1265_2,plain,
! [U_3185] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3185))
| ~ class_Groups_Oab__group__add(U_3185) ),
inference(variable_rename,[status(thm)],[f_1265_1]) ).
fof(f_1265_3,plain,
! [U_3185] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3185))
| ~ class_Groups_Oab__group__add(U_3185) ),
inference(definitional_conversion,[status(esa)],[f_1265_2]) ).
cnf(f_1265_4,plain,
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3185))
| ~ class_Groups_Oab__group__add(U_3185) ),
inference(clausify,[status(thm)],[f_1265_3]) ).
fof(f_1266_1,plain,
! [T_1] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Osgn__if]) ).
fof(f_1266_2,plain,
! [U_3186] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3186))
| ~ class_Rings_Olinordered__idom(U_3186) ),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
fof(f_1266_3,plain,
! [U_3186] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3186))
| ~ class_Rings_Olinordered__idom(U_3186) ),
inference(definitional_conversion,[status(esa)],[f_1266_2]) ).
cnf(f_1266_4,plain,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3186))
| ~ class_Rings_Olinordered__idom(U_3186) ),
inference(clausify,[status(thm)],[f_1266_3]) ).
fof(f_1267_1,plain,
! [T_1] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if]) ).
fof(f_1267_2,plain,
! [U_3187] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_3187))
| ~ class_Rings_Olinordered__idom(U_3187) ),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
fof(f_1267_3,plain,
! [U_3187] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_3187))
| ~ class_Rings_Olinordered__idom(U_3187) ),
inference(definitional_conversion,[status(esa)],[f_1267_2]) ).
cnf(f_1267_4,plain,
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_3187))
| ~ class_Rings_Olinordered__idom(U_3187) ),
inference(clausify,[status(thm)],[f_1267_3]) ).
fof(f_1268_1,plain,
! [T_1] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1]) ).
fof(f_1268_2,plain,
! [U_3188] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3188))
| ~ class_Rings_Ocomm__ring__1(U_3188) ),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
fof(f_1268_3,plain,
! [U_3188] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3188))
| ~ class_Rings_Ocomm__ring__1(U_3188) ),
inference(definitional_conversion,[status(esa)],[f_1268_2]) ).
cnf(f_1268_4,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3188))
| ~ class_Rings_Ocomm__ring__1(U_3188) ),
inference(clausify,[status(thm)],[f_1268_3]) ).
fof(f_1269_1,plain,
! [T_1] :
( class_Groups_Ominus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus]) ).
fof(f_1269_2,plain,
! [U_3189] :
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3189))
| ~ class_Groups_Oab__group__add(U_3189) ),
inference(variable_rename,[status(thm)],[f_1269_1]) ).
fof(f_1269_3,plain,
! [U_3189] :
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3189))
| ~ class_Groups_Oab__group__add(U_3189) ),
inference(definitional_conversion,[status(esa)],[f_1269_2]) ).
cnf(f_1269_4,plain,
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3189))
| ~ class_Groups_Oab__group__add(U_3189) ),
inference(clausify,[status(thm)],[f_1269_3]) ).
fof(f_1270_1,plain,
! [T_1] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower]) ).
fof(f_1270_2,plain,
! [U_3190] :
( class_Power_Opower(tc_Polynomial_Opoly(U_3190))
| ~ class_Rings_Ocomm__semiring__1(U_3190) ),
inference(variable_rename,[status(thm)],[f_1270_1]) ).
fof(f_1270_3,plain,
! [U_3190] :
( class_Power_Opower(tc_Polynomial_Opoly(U_3190))
| ~ class_Rings_Ocomm__semiring__1(U_3190) ),
inference(definitional_conversion,[status(esa)],[f_1270_2]) ).
cnf(f_1270_4,plain,
( class_Power_Opower(tc_Polynomial_Opoly(U_3190))
| ~ class_Rings_Ocomm__semiring__1(U_3190) ),
inference(clausify,[status(thm)],[f_1270_3]) ).
fof(f_1271_1,plain,
! [T_1] :
( class_Groups_Ozero(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ozero(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero]) ).
fof(f_1271_2,plain,
! [U_3191] :
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3191))
| ~ class_Groups_Ozero(U_3191) ),
inference(variable_rename,[status(thm)],[f_1271_1]) ).
fof(f_1271_3,plain,
! [U_3191] :
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3191))
| ~ class_Groups_Ozero(U_3191) ),
inference(definitional_conversion,[status(esa)],[f_1271_2]) ).
cnf(f_1271_4,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3191))
| ~ class_Groups_Ozero(U_3191) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
fof(f_1272_1,plain,
! [T_1] :
( class_Rings_Oring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring]) ).
fof(f_1272_2,plain,
! [U_3192] :
( class_Rings_Oring(tc_Polynomial_Opoly(U_3192))
| ~ class_Rings_Ocomm__ring(U_3192) ),
inference(variable_rename,[status(thm)],[f_1272_1]) ).
fof(f_1272_3,plain,
! [U_3192] :
( class_Rings_Oring(tc_Polynomial_Opoly(U_3192))
| ~ class_Rings_Ocomm__ring(U_3192) ),
inference(definitional_conversion,[status(esa)],[f_1272_2]) ).
cnf(f_1272_4,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(U_3192))
| ~ class_Rings_Ocomm__ring(U_3192) ),
inference(clausify,[status(thm)],[f_1272_3]) ).
fof(f_1273_1,plain,
! [T_1] :
( class_Rings_Oidom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom]) ).
fof(f_1273_2,plain,
! [U_3193] :
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3193))
| ~ class_Rings_Oidom(U_3193) ),
inference(variable_rename,[status(thm)],[f_1273_1]) ).
fof(f_1273_3,plain,
! [U_3193] :
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3193))
| ~ class_Rings_Oidom(U_3193) ),
inference(definitional_conversion,[status(esa)],[f_1273_2]) ).
cnf(f_1273_4,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3193))
| ~ class_Rings_Oidom(U_3193) ),
inference(clausify,[status(thm)],[f_1273_3]) ).
fof(f_1274_1,plain,
! [T_1] :
( class_Groups_Oone(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone]) ).
fof(f_1274_2,plain,
! [U_3194] :
( class_Groups_Oone(tc_Polynomial_Opoly(U_3194))
| ~ class_Rings_Ocomm__semiring__1(U_3194) ),
inference(variable_rename,[status(thm)],[f_1274_1]) ).
fof(f_1274_3,plain,
! [U_3194] :
( class_Groups_Oone(tc_Polynomial_Opoly(U_3194))
| ~ class_Rings_Ocomm__semiring__1(U_3194) ),
inference(definitional_conversion,[status(esa)],[f_1274_2]) ).
cnf(f_1274_4,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(U_3194))
| ~ class_Rings_Ocomm__semiring__1(U_3194) ),
inference(clausify,[status(thm)],[f_1274_3]) ).
fof(f_1275_1,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_1275_2,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(definitional_conversion,[status(esa)],[f_1275_1]) ).
cnf(f_1275_3,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(clausify,[status(thm)],[f_1275_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_Groups_Ozero__class_Ozero(Eq_x_0) = c_Groups_Ozero__class_Ozero(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c_RealVector_Onorm__class_Onorm(Eq_x_0,Eq_x_1) = c_RealVector_Onorm__class_Onorm(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_Groups_Otimes__class_Otimes(Eq_x_0) = c_Groups_Otimes__class_Otimes(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_Groups_Oabs__class_Oabs(Eq_x_0,Eq_x_1) = c_Groups_Oabs__class_Oabs(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_Groups_Oone__class_Oone(Eq_x_0) = c_Groups_Oone__class_Oone(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( c_Groups_Oplus__class_Oplus(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Oplus__class_Oplus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_Polynomial_Opoly(Eq_x_0,Eq_x_1) = c_Polynomial_Opoly(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( tc_Polynomial_Opoly(Eq_x_0) = tc_Polynomial_Opoly(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_Polynomial_Oorder(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Oorder(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( c_Groups_Osgn__class_Osgn(Eq_x_0,Eq_x_1) = c_Groups_Osgn__class_Osgn(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_Polynomial_Opoly__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Polynomial_Opoly__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_Polynomial_Ocoeff(Eq_x_0,Eq_x_1) = c_Polynomial_Ocoeff(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Groups_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Ominus__class_Ominus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( c_Groups_Ouminus__class_Ouminus(Eq_x_0,Eq_x_1) = c_Groups_Ouminus__class_Ouminus(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_RComplete_Onatceiling(Eq_x_0) = c_RComplete_Onatceiling(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_RComplete_Onatfloor(Eq_x_0) = c_RComplete_Onatfloor(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_RealDef_Oreal(Eq_x_0,Eq_x_1) = c_RealDef_Oreal(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_Power_Opower__class_Opower(Eq_x_0) = c_Power_Opower__class_Opower(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_24,axiom,
( c_Power_Opower_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_Nat__Transfer_Otsub(Eq_x_0,Eq_x_1) = c_Nat__Transfer_Otsub(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_Transcendental_Oln(Eq_x_0) = c_Transcendental_Oln(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( c_Nat_OSuc(Eq_x_0) = c_Nat_OSuc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_Divides_Odiv__class_Odiv(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Odiv(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_SMT_Oz3div(Eq_x_0,Eq_x_1) = c_SMT_Oz3div(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_41,axiom,
( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_49,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK26(Eq_x_0,Eq_x_1) = sK26(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_55,axiom,
( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_64,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_66,axiom,
( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK42(Eq_x_0,Eq_x_1) = sK42(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK44(Eq_x_0,Eq_x_1) = sK44(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_73,axiom,
( sK46(Eq_x_0,Eq_x_1,Eq_x_2) = sK46(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_78,axiom,
( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_79,axiom,
( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_80,axiom,
( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK55(Eq_x_0,Eq_x_1) = sK55(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_83,axiom,
( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK57(Eq_x_0,Eq_x_1) = sK57(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_85,axiom,
( sK58(Eq_x_0,Eq_x_1) = sK58(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_87,axiom,
( sK60(Eq_x_0) = sK60(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_88,axiom,
( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_89,axiom,
( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_90,axiom,
( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_91,axiom,
( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK65(Eq_x_0,Eq_x_1) = sK65(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_93,axiom,
( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_94,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_95,axiom,
( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_96,axiom,
( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,axiom,
( sK70(Eq_x_0) = sK70(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_98,axiom,
( sK71(Eq_x_0,Eq_x_1,Eq_x_2) = sK71(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,axiom,
( c_Orderings_Oord__class_Oless__eq(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_101,axiom,
( c_Orderings_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_102,axiom,
( class_RealVector_Oreal__normed__vector(Eq_y_0)
| ~ class_RealVector_Oreal__normed__vector(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_103,axiom,
( class_RealVector_Oreal__normed__algebra(Eq_y_0)
| ~ class_RealVector_Oreal__normed__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,axiom,
( class_Rings_Olinordered__semidom(Eq_y_0)
| ~ class_Rings_Olinordered__semidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,axiom,
( class_Rings_Olinordered__ring(Eq_y_0)
| ~ class_Rings_Olinordered__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_106,axiom,
( class_Rings_Olinordered__ring__strict(Eq_y_0)
| ~ class_Rings_Olinordered__ring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( class_RealVector_Oreal__normed__algebra__1(Eq_y_0)
| ~ class_RealVector_Oreal__normed__algebra__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_108,axiom,
( class_Rings_Oordered__cancel__semiring(Eq_y_0)
| ~ class_Rings_Oordered__cancel__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_109,axiom,
( class_Rings_Oordered__ring(Eq_y_0)
| ~ class_Rings_Oordered__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_110,axiom,
( class_Rings_Oordered__semiring(Eq_y_0)
| ~ class_Rings_Oordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_111,axiom,
( class_Rings_Oordered__comm__semiring(Eq_y_0)
| ~ class_Rings_Oordered__comm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_112,axiom,
( class_Rings_Olinordered__semiring__strict(Eq_y_0)
| ~ class_Rings_Olinordered__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_113,axiom,
( class_Rings_Olinordered__semiring(Eq_y_0)
| ~ class_Rings_Olinordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_114,axiom,
( class_Rings_Olinordered__idom(Eq_y_0)
| ~ class_Rings_Olinordered__idom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_115,axiom,
( class_Rings_Oordered__ring__abs(Eq_y_0)
| ~ class_Rings_Oordered__ring__abs(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_116,axiom,
( class_Rings_Olinordered__semiring__1(Eq_y_0)
| ~ class_Rings_Olinordered__semiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_117,axiom,
( class_Rings_Olinordered__semiring__1__strict(Eq_y_0)
| ~ class_Rings_Olinordered__semiring__1__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_118,axiom,
( class_Rings_Ono__zero__divisors(Eq_y_0)
| ~ class_Rings_Ono__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_119,axiom,
( class_Rings_Oring__no__zero__divisors(Eq_y_0)
| ~ class_Rings_Oring__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_120,axiom,
( class_Rings_Omult__zero(Eq_y_0)
| ~ class_Rings_Omult__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_121,axiom,
( class_Rings_Ozero__neq__one(Eq_y_0)
| ~ class_Rings_Ozero__neq__one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_122,axiom,
( class_Rings_Osemiring(Eq_y_0)
| ~ class_Rings_Osemiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_123,axiom,
( class_Rings_Ocomm__semiring(Eq_y_0)
| ~ class_Rings_Ocomm__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_124,axiom,
( class_Rings_Olinordered__comm__semiring__strict(Eq_y_0)
| ~ class_Rings_Olinordered__comm__semiring__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_125,axiom,
( class_RealVector_Oreal__normed__div__algebra(Eq_y_0)
| ~ class_RealVector_Oreal__normed__div__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_126,axiom,
( class_Groups_Oordered__comm__monoid__add(Eq_y_0)
| ~ class_Groups_Oordered__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_127,axiom,
( class_Groups_Oordered__ab__group__add__abs(Eq_y_0)
| ~ class_Groups_Oordered__ab__group__add__abs(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_128,axiom,
( class_Groups_Ozero(Eq_y_0)
| ~ class_Groups_Ozero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_129,axiom,
( class_Groups_Oab__semigroup__mult(Eq_y_0)
| ~ class_Groups_Oab__semigroup__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_130,axiom,
( class_Groups_Oab__semigroup__add(Eq_y_0)
| ~ class_Groups_Oab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_131,axiom,
( class_Groups_Ocancel__semigroup__add(Eq_y_0)
| ~ class_Groups_Ocancel__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_132,axiom,
( class_Groups_Ocancel__ab__semigroup__add(Eq_y_0)
| ~ class_Groups_Ocancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_133,axiom,
( class_Groups_Oone(Eq_y_0)
| ~ class_Groups_Oone(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_134,axiom,
( class_Groups_Omonoid__add(Eq_y_0)
| ~ class_Groups_Omonoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_135,axiom,
( class_Groups_Ocomm__monoid__add(Eq_y_0)
| ~ class_Groups_Ocomm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_136,axiom,
( class_Groups_Olinordered__ab__group__add(Eq_y_0)
| ~ class_Groups_Olinordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,axiom,
( class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_y_0)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_138,axiom,
( class_Groups_Oordered__ab__semigroup__add(Eq_y_0)
| ~ class_Groups_Oordered__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_139,axiom,
( class_Groups_Oordered__cancel__ab__semigroup__add(Eq_y_0)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_140,axiom,
( class_Groups_Omonoid__mult(Eq_y_0)
| ~ class_Groups_Omonoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_141,axiom,
( class_Groups_Ocomm__monoid__mult(Eq_y_0)
| ~ class_Groups_Ocomm__monoid__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_142,axiom,
( class_Rings_Ocomm__semiring__1(Eq_y_0)
| ~ class_Rings_Ocomm__semiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_143,axiom,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_y_0)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_144,axiom,
( class_Orderings_Opreorder(Eq_y_0)
| ~ class_Orderings_Opreorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_145,axiom,
( class_Rings_Ocomm__semiring__0(Eq_y_0)
| ~ class_Rings_Ocomm__semiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_146,axiom,
( class_Orderings_Oord(Eq_y_0)
| ~ class_Orderings_Oord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_147,axiom,
( class_Orderings_Olinorder(Eq_y_0)
| ~ class_Orderings_Olinorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_148,axiom,
( class_Orderings_Oorder(Eq_y_0)
| ~ class_Orderings_Oorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_149,axiom,
( class_Int_Oring__char__0(Eq_y_0)
| ~ class_Int_Oring__char__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_150,axiom,
( class_Rings_Oidom(Eq_y_0)
| ~ class_Rings_Oidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_151,axiom,
( class_Fields_Olinordered__field__inverse__zero(Eq_y_0)
| ~ class_Fields_Olinordered__field__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_152,axiom,
( class_Groups_Osgn__if(Eq_y_0)
| ~ class_Groups_Osgn__if(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_153,axiom,
( class_Fields_Olinordered__field(Eq_y_0)
| ~ class_Fields_Olinordered__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_154,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_155,axiom,
( class_Groups_Oab__group__add(Eq_y_0)
| ~ class_Groups_Oab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_156,axiom,
( class_Groups_Ogroup__add(Eq_y_0)
| ~ class_Groups_Ogroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_157,axiom,
( class_Rings_Ocomm__ring__1(Eq_y_0)
| ~ class_Rings_Ocomm__ring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_158,axiom,
( class_Rings_Ocomm__ring(Eq_y_0)
| ~ class_Rings_Ocomm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_159,axiom,
( class_Groups_Oordered__ab__group__add(Eq_y_0)
| ~ class_Groups_Oordered__ab__group__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_160,axiom,
( class_Rings_Oring(Eq_y_0)
| ~ class_Rings_Oring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_161,axiom,
( class_Rings_Oring__1__no__zero__divisors(Eq_y_0)
| ~ class_Rings_Oring__1__no__zero__divisors(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_162,axiom,
( class_Rings_Oring__1(Eq_y_0)
| ~ class_Rings_Oring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_163,axiom,
( class_Groups_Oabs__if(Eq_y_0)
| ~ class_Groups_Oabs__if(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,axiom,
( class_Lattices_Oboolean__algebra(Eq_y_0)
| ~ class_Lattices_Oboolean__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_165,axiom,
( class_Lattices_Oab__semigroup__idem__mult(Eq_y_0)
| ~ class_Lattices_Oab__semigroup__idem__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_166,axiom,
( class_Groups_Ominus(Eq_y_0)
| ~ class_Groups_Ominus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( class_Groups_Ouminus(Eq_y_0)
| ~ class_Groups_Ouminus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_168,axiom,
( c_Polynomial_Opos__poly(Eq_y_0,Eq_y_1)
| ~ c_Polynomial_Opos__poly(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_169,axiom,
( c_SEQ_Odecseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_Odecseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( c_SEQ_OBseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_OBseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_171,axiom,
( class_Power_Opower(Eq_y_0)
| ~ class_Power_Opower(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_172,axiom,
( class_Rings_Osemiring__0(Eq_y_0)
| ~ class_Rings_Osemiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_173,axiom,
( c_SEQ_Oincseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_Oincseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_174,axiom,
( class_Divides_Osemiring__div(Eq_y_0)
| ~ class_Divides_Osemiring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_175,axiom,
( class_Fields_Ofield(Eq_y_0)
| ~ class_Fields_Ofield(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_176,axiom,
( class_Groups_Ocancel__comm__monoid__add(Eq_y_0)
| ~ class_Groups_Ocancel__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_177,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_178,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_179,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP2(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_180,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_181,axiom,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_182,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_184,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_187,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_191,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_196,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_197,axiom,
( sP20(Eq_y_0,Eq_y_1)
| ~ sP20(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_198,axiom,
( sP21(Eq_y_0,Eq_y_1)
| ~ sP21(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( sP22(Eq_y_0,Eq_y_1)
| ~ sP22(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_205,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_206,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_207,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_208,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_209,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_210,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_212,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_213,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_214,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_217,axiom,
( sP40(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_218,axiom,
( sP41(Eq_y_0,Eq_y_1)
| ~ sP41(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_220,axiom,
( sP43(Eq_y_0,Eq_y_1)
| ~ sP43(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_221,axiom,
( sP44(Eq_y_0,Eq_y_1)
| ~ sP44(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_224,axiom,
( sP47(Eq_y_0,Eq_y_1)
| ~ sP47(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_225,axiom,
( sP48(Eq_y_0,Eq_y_1)
| ~ sP48(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_226,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_227,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_228,axiom,
( sP51(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_229,axiom,
( sP52(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_230,axiom,
( sP53(Eq_y_0,Eq_y_1)
| ~ sP53(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_231,axiom,
( sP54(Eq_y_0,Eq_y_1)
| ~ sP54(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_232,axiom,
( sP55(Eq_y_0,Eq_y_1)
| ~ sP55(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_233,axiom,
( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_234,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_235,axiom,
( sP58(Eq_y_0,Eq_y_1)
| ~ sP58(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_236,axiom,
( sP59(Eq_y_0,Eq_y_1)
| ~ sP59(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_237,axiom,
( sP60(Eq_y_0,Eq_y_1)
| ~ sP60(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_238,axiom,
( sP61(Eq_y_0,Eq_y_1)
| ~ sP61(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_239,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_240,axiom,
( sP63(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_241,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_242,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_243,axiom,
( sP66(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_244,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_245,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_246,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_247,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_248,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_249,axiom,
( sP72(Eq_y_0,Eq_y_1)
| ~ sP72(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_250,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_251,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_252,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_253,axiom,
( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_254,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_255,axiom,
( sP78(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_256,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_257,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_258,axiom,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_259,axiom,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_260,axiom,
( sP83(Eq_y_0,Eq_y_1)
| ~ sP83(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_261,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_262,axiom,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_263,axiom,
( sP86(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP86(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_264,axiom,
( sP87(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_265,axiom,
( sP88(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_266,axiom,
( sP89(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_267,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_268,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_269,axiom,
( sP92(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP92(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_270,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_271,axiom,
( sP94(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_272,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_273,axiom,
( sP96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_274,axiom,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_275,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_276,axiom,
( sP99(Eq_y_0,Eq_y_1)
| ~ sP99(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_277,axiom,
( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_278,axiom,
( sP101(Eq_y_0,Eq_y_1)
| ~ sP101(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_279,axiom,
( sP102(Eq_y_0,Eq_y_1)
| ~ sP102(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_280,axiom,
( sP103(Eq_y_0,Eq_y_1)
| ~ sP103(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_281,axiom,
( sP104(Eq_y_0,Eq_y_1)
| ~ sP104(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_282,axiom,
( sP105(Eq_y_0,Eq_y_1)
| ~ sP105(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_283,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_284,axiom,
( sP107(Eq_y_0,Eq_y_1)
| ~ sP107(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_285,axiom,
( sP108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_286,axiom,
( sP109(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP109(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_287,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP110(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_288,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_289,axiom,
( sP112(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP112(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_290,axiom,
( sP113(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP113(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_291,axiom,
( sP114(Eq_y_0,Eq_y_1)
| ~ sP114(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_292,axiom,
( sP115(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_293,axiom,
( sP116(Eq_y_0,Eq_y_1)
| ~ sP116(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_294,axiom,
( sP117(Eq_y_0,Eq_y_1)
| ~ sP117(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_295,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_296,axiom,
( sP119(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_297,axiom,
( sP120(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_298,axiom,
( sP121(Eq_y_0,Eq_y_1)
| ~ sP121(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_299,axiom,
( sP122(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP122(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_300,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_301,axiom,
( sP124(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP124(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_302,axiom,
( sP125(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_303,axiom,
( sP126(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP126(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_304,axiom,
( sP127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_305,axiom,
( sP128(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_306,axiom,
( sP129(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP129(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_307,axiom,
( sP130(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP130(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_308,axiom,
( sP131(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_309,axiom,
( sP132(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_310,axiom,
( sP133(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_311,axiom,
( sP134(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_312,axiom,
( sP135(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_313,axiom,
( sP136(Eq_y_0,Eq_y_1)
| ~ sP136(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_314,axiom,
( sP137(Eq_y_0,Eq_y_1)
| ~ sP137(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_315,axiom,
( sP138(Eq_y_0,Eq_y_1)
| ~ sP138(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_316,axiom,
( sP139(Eq_y_0,Eq_y_1)
| ~ sP139(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_317,axiom,
( sP140(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP140(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_318,axiom,
( sP141(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP141(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_319,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_320,axiom,
( sP143(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_321,axiom,
( sP144(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_322,axiom,
( sP145(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP145(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_323,axiom,
( sP146(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP146(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_324,axiom,
( sP147(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP147(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_325,axiom,
( sP148(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP148(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_326,axiom,
( sP149(Eq_y_0,Eq_y_1)
| ~ sP149(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_327,axiom,
( sP150(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_328,axiom,
( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_329,axiom,
( sP152(Eq_y_0,Eq_y_1)
| ~ sP152(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_330,axiom,
( sP153(Eq_y_0,Eq_y_1)
| ~ sP153(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_331,axiom,
( sP154(Eq_y_0,Eq_y_1)
| ~ sP154(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_332,axiom,
( sP155(Eq_y_0,Eq_y_1)
| ~ sP155(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_333,axiom,
( sP156(Eq_y_0,Eq_y_1)
| ~ sP156(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_334,axiom,
( sP157(Eq_y_0,Eq_y_1)
| ~ sP157(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_335,axiom,
( sP158(Eq_y_0,Eq_y_1)
| ~ sP158(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_336,axiom,
( sP159(Eq_y_0,Eq_y_1)
| ~ sP159(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_337,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_338,axiom,
( sP161(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP161(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_339,axiom,
( sP162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_340,axiom,
( sP163(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP163(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_341,axiom,
( sP164(Eq_y_0,Eq_y_1)
| ~ sP164(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_342,axiom,
( sP165(Eq_y_0,Eq_y_1)
| ~ sP165(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_343,axiom,
( sP166(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP166(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_344,axiom,
( sP167(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP167(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_345,axiom,
( sP168(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP168(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_346,axiom,
( sP169(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP169(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_347,axiom,
( sP170(Eq_y_0,Eq_y_1)
| ~ sP170(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_348,axiom,
( sP171(Eq_y_0,Eq_y_1)
| ~ sP171(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_349,axiom,
( sP172(Eq_y_0,Eq_y_1)
| ~ sP172(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_350,axiom,
( sP173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_351,axiom,
( sP174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_352,axiom,
( sP175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_353,axiom,
( sP176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_354,axiom,
( sP177(Eq_y_0,Eq_y_1)
| ~ sP177(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_355,axiom,
( sP178(Eq_y_0)
| ~ sP178(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_356,axiom,
( sP179(Eq_y_0)
| ~ sP179(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_357,axiom,
( sP180(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP180(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_358,axiom,
( sP181(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP181(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_359,axiom,
( sP182(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP182(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_360,axiom,
( sP183(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP183(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_361,axiom,
( sP184(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP184(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_362,axiom,
( sP185(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP185(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_363,axiom,
( sP186(Eq_y_0,Eq_y_1)
| ~ sP186(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_364,axiom,
( sP187(Eq_y_0,Eq_y_1)
| ~ sP187(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_365,axiom,
( sP188(Eq_y_0,Eq_y_1)
| ~ sP188(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_366,axiom,
( sP189(Eq_y_0,Eq_y_1)
| ~ sP189(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_367,axiom,
( sP190(Eq_y_0,Eq_y_1)
| ~ sP190(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_368,axiom,
( sP191(Eq_y_0,Eq_y_1)
| ~ sP191(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_369,axiom,
( sP192(Eq_y_0,Eq_y_1)
| ~ sP192(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_370,axiom,
( sP193(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP193(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_371,axiom,
( sP194(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP194(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_372,axiom,
( sP195(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP195(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_373,axiom,
( sP196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP196(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_374,axiom,
( sP197(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP197(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_375,axiom,
( sP198(Eq_y_0,Eq_y_1)
| ~ sP198(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_376,axiom,
( sP199(Eq_y_0,Eq_y_1)
| ~ sP199(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_377,axiom,
( sP200(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP200(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_378,axiom,
( sP201(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_379,axiom,
( sP202(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP202(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_380,axiom,
( sP203(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP203(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_381,axiom,
( sP204(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP204(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_382,axiom,
( sP205(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP205(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_383,axiom,
( sP206(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP206(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_384,axiom,
( sP207(Eq_y_0,Eq_y_1)
| ~ sP207(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_385,axiom,
( sP208(Eq_y_0,Eq_y_1)
| ~ sP208(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_386,axiom,
( sP209(Eq_y_0)
| ~ sP209(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_387,axiom,
( sP210(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP210(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_388,axiom,
( sP211(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_389,axiom,
( sP212(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP212(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_390,axiom,
( sP213(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_391,axiom,
( sP214(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP214(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_392,axiom,
( sP215(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP215(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_393,axiom,
( sP216(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP216(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_394,axiom,
( sP217(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP217(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_395,axiom,
( sP218(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP218(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_396,axiom,
( sP219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_397,axiom,
( sP220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_398,axiom,
( sP221(Eq_y_0,Eq_y_1)
| ~ sP221(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_399,axiom,
( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_400,axiom,
( sP223(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_401,axiom,
( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_402,axiom,
( sP225(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_403,axiom,
( sP226(Eq_y_0,Eq_y_1)
| ~ sP226(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_404,axiom,
( sP227(Eq_y_0,Eq_y_1)
| ~ sP227(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_405,axiom,
( sP228(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_406,axiom,
( sP229(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP229(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_407,axiom,
( sP230(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_408,axiom,
( sP231(Eq_y_0,Eq_y_1)
| ~ sP231(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_409,axiom,
( sP232(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP232(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_410,axiom,
( sP233(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_411,axiom,
( sP234(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP234(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_412,axiom,
( sP235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_413,axiom,
( sP236(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_414,axiom,
( sP237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_415,axiom,
( sP238(Eq_y_0,Eq_y_1)
| ~ sP238(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_416,axiom,
( sP239(Eq_y_0,Eq_y_1)
| ~ sP239(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_417,axiom,
( sP240(Eq_y_0,Eq_y_1)
| ~ sP240(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_418,axiom,
( sP241(Eq_y_0,Eq_y_1)
| ~ sP241(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_419,axiom,
( sP242(Eq_y_0)
| ~ sP242(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_420,axiom,
( sP243(Eq_y_0,Eq_y_1)
| ~ sP243(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_421,axiom,
( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_422,axiom,
( sP245(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP245(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_423,axiom,
( sP246(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP246(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_424,axiom,
( sP247(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP247(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_425,axiom,
( sP248(Eq_y_0,Eq_y_1)
| ~ sP248(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_426,axiom,
( sP249(Eq_y_0,Eq_y_1)
| ~ sP249(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_427,axiom,
( sP250(Eq_y_0,Eq_y_1)
| ~ sP250(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_428,axiom,
( sP251(Eq_y_0,Eq_y_1)
| ~ sP251(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_429,axiom,
( sP252(Eq_y_0)
| ~ sP252(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_430,axiom,
( sP253(Eq_y_0)
| ~ sP253(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_431,axiom,
( sP254(Eq_y_0)
| ~ sP254(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_432,axiom,
( sP255(Eq_y_0)
| ~ sP255(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_433,axiom,
( sP256(Eq_y_0,Eq_y_1)
| ~ sP256(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_434,axiom,
( sP257(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP257(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_435,axiom,
( sP258(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP258(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_436,axiom,
( sP259(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP259(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_437,axiom,
( sP260(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP260(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_438,axiom,
( sP261(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP261(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_439,axiom,
( sP262(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP262(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_440,axiom,
( sP263(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP263(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_441,axiom,
( sP264(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_442,axiom,
( sP265(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP265(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_443,axiom,
( sP266(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_444,axiom,
( sP267(Eq_y_0,Eq_y_1)
| ~ sP267(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_445,axiom,
( sP268(Eq_y_0,Eq_y_1)
| ~ sP268(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_446,axiom,
( sP269(Eq_y_0,Eq_y_1)
| ~ sP269(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_447,axiom,
( sP270(Eq_y_0,Eq_y_1)
| ~ sP270(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_448,axiom,
( sP271(Eq_y_0,Eq_y_1)
| ~ sP271(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_449,axiom,
( sP272(Eq_y_0,Eq_y_1)
| ~ sP272(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_450,axiom,
( sP273(Eq_y_0,Eq_y_1)
| ~ sP273(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_451,axiom,
( sP274(Eq_y_0,Eq_y_1)
| ~ sP274(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_452,axiom,
( sP275(Eq_y_0,Eq_y_1)
| ~ sP275(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_453,axiom,
( sP276(Eq_y_0,Eq_y_1)
| ~ sP276(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_454,axiom,
( sP277(Eq_y_0,Eq_y_1)
| ~ sP277(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_455,axiom,
( sP278(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_456,axiom,
( sP279(Eq_y_0,Eq_y_1)
| ~ sP279(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_457,axiom,
( sP280(Eq_y_0,Eq_y_1)
| ~ sP280(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_458,axiom,
( sP281(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP281(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_459,axiom,
( sP282(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP282(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_460,axiom,
( sP283(Eq_y_0,Eq_y_1)
| ~ sP283(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_461,axiom,
( sP284(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_462,axiom,
( sP285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_463,axiom,
( sP286(Eq_y_0,Eq_y_1)
| ~ sP286(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_464,axiom,
( sP287(Eq_y_0,Eq_y_1)
| ~ sP287(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_465,axiom,
( sP288(Eq_y_0,Eq_y_1)
| ~ sP288(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_466,axiom,
( sP289(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP289(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_467,axiom,
( sP290(Eq_y_0,Eq_y_1)
| ~ sP290(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_468,axiom,
( sP291(Eq_y_0,Eq_y_1)
| ~ sP291(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_469,axiom,
( sP292(Eq_y_0,Eq_y_1)
| ~ sP292(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_470,axiom,
( sP293(Eq_y_0,Eq_y_1)
| ~ sP293(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_471,axiom,
( sP294(Eq_y_0,Eq_y_1)
| ~ sP294(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_472,axiom,
( sP295(Eq_y_0,Eq_y_1)
| ~ sP295(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_473,axiom,
( sP296(Eq_y_0,Eq_y_1)
| ~ sP296(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_474,axiom,
( sP297(Eq_y_0,Eq_y_1)
| ~ sP297(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_475,axiom,
( sP298(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
| ~ sP298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
| Eq_x_6 != Eq_y_6
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_476,axiom,
( sP299(Eq_y_0,Eq_y_1)
| ~ sP299(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_477,axiom,
( sP300(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP300(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_478,axiom,
( sP301(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP301(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_479,axiom,
( sP302(Eq_y_0,Eq_y_1)
| ~ sP302(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_480,axiom,
( sP303(Eq_y_0,Eq_y_1)
| ~ sP303(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_481,axiom,
( sP304(Eq_y_0)
| ~ sP304(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_482,axiom,
( sP305(Eq_y_0,Eq_y_1)
| ~ sP305(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_483,axiom,
( sP306(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_484,axiom,
( sP307(Eq_y_0,Eq_y_1)
| ~ sP307(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_485,axiom,
( sP308(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP308(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW179+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun Sep 20 05:10:05 UTC 2026
% 0.12/0.36 % CPUTime :
% 270.34/270.64 % SZS status Theorem for theBenchmark
% 270.34/270.64 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------