%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW208+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 : n013.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 09:04:50 AM UTC 2026
% Result : Theorem 228.23s 228.60s
% Output : Proof 228.40s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [V_gb_2,V_fa_2] :
( ! [B_x] : hAPP(V_fa_2,B_x) = hAPP(V_gb_2,B_x)
=> V_fa_2 = V_gb_2 ),
file('theBenchmark.p',fact_ext) ).
fof(fact_rp,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
file('theBenchmark.p',fact_rp) ).
fof(fact_f_I1_J,axiom,
c_SEQ_Osubseq(v_f____),
file('theBenchmark.p',fact_f_I1_J) ).
fof(fact_th,axiom,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,B_n)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
file('theBenchmark.p',fact_th) ).
fof(fact_g_I1_J,axiom,
c_SEQ_Osubseq(v_ga____),
file('theBenchmark.p',fact_g_I1_J) ).
fof(fact_assms,axiom,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
file('theBenchmark.p',fact_assms) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(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] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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_zero__less__two,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ),
file('theBenchmark.p',fact_zero__less__two) ).
fof(fact_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_abs__triangle__ineq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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__not__less__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ~ hBOOL(hAPP(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_zero__less__abs__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(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__096cmod_A_Is_A0_J_A_060_061_Ar_096,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
file('theBenchmark.p',fact__096cmod_A_Is_A0_J_A_060_061_Ar_096) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [V_z,V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_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_linorder__neqE__linordered__idom,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( V_x != V_y
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__ab__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [V_c_2,V_a_2,V_b_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__left__cancel,axiom,
! [V_c_2,V_b_2,V_a_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)
<=> V_b_2 = V_c_2 ) ),
file('theBenchmark.p',fact_add__left__cancel) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_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_real__le__antisym,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w))
=> ( hBOOL(hAPP(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_real__le__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k)) ) ),
file('theBenchmark.p',fact_real__le__trans) ).
fof(fact_real__le__linear,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
file('theBenchmark.p',fact_real__le__linear) ).
fof(fact_real__le__refl,axiom,
! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)),
file('theBenchmark.p',fact_real__le__refl) ).
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_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add__0__right) ).
fof(fact_double__zero__sym,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(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,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_add__0__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__mono) ).
fof(fact_add__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
file('theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__le__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(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__le__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
<=> hBOOL(hAPP(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__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ),
file('theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
file('theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__less__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__less__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__right) ).
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_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__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__le__D1,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ),
file('theBenchmark.p',fact_abs__le__D1) ).
fof(fact_abs__ge__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(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_less__eq__real__def,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_real__less__def) ).
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,hAPP(hAPP(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))) = hAPP(hAPP(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_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__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__add__left__mono,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y))) ),
file('theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_add__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__increasing2,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__increasing) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
=> ( hAPP(hAPP(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__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
<=> hBOOL(hAPP(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_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
<=> hBOOL(hAPP(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_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
<=> hBOOL(hAPP(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_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
<=> hBOOL(hAPP(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_add__le__less__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_zero__le__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_zero__le__one) ).
fof(fact_not__one__le__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_zero__less__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_zero__less__one) ).
fof(fact_not__one__less__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ hBOOL(hAPP(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__add__one,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ),
file('theBenchmark.p',fact_less__add__one) ).
fof(fact_abs__of__nonneg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(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__le__zero__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(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__ge__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(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__of__pos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(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_abs__Im__le__cmod,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
file('theBenchmark.p',fact_abs__Im__le__cmod) ).
fof(fact_norm__add__less,axiom,
! [V_s,V_y,V_r,V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s))) ) ) ),
file('theBenchmark.p',fact_norm__add__less) ).
fof(fact_norm__triangle__ineq,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(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_zero__less__norm__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( hBOOL(hAPP(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_norm__le__zero__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( hBOOL(hAPP(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__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)
=> ~ hBOOL(hAPP(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_norm__ge__zero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> hBOOL(hAPP(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_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_even__less__0__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
<=> hBOOL(hAPP(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_order__refl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x)) ),
file('theBenchmark.p',fact_order__refl) ).
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_le__fun__def,axiom,
! [V_gb_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
<=> ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(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
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
& hBOOL(hAPP(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
=> hBOOL(hAPP(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_gb_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
=> ( hBOOL(hAPP(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
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
=> hBOOL(hAPP(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
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b))
=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
=> ( V_b = V_c
=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_order__antisym) ).
fof(fact_order__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(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_gb_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_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)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_order__less__irrefl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x)) ),
file('theBenchmark.p',fact_order__less__irrefl) ).
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
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(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__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
=> ( ~ hBOOL(hAPP(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__neqE,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x != V_y
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__neqE) ).
fof(fact_less__imp__neq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> V_x != V_y ) ),
file('theBenchmark.p',fact_less__imp__neq) ).
fof(fact_order__less__not__sym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_order__less__imp__not__less,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__imp__not__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> V_x != V_y ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> V_y != V_x ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__asym_H,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ),
file('theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_xt1_I9_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ),
file('theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_ord__eq__less__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__eq__less__trans) ).
fof(fact_xt1_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I1_J) ).
fof(fact_ord__less__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_ord__less__eq__trans) ).
fof(fact_xt1_I2_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
=> ( V_b = V_c
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I2_J) ).
fof(fact_order__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I10_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_order__less__asym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ),
file('theBenchmark.p',fact_order__less__asym) ).
fof(fact_linorder__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> ( V_x != V_y
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x)) ) ) ),
file('theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
& hBOOL(hAPP(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__le__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_leI,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x)) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ),
file('theBenchmark.p',fact_not__leE) ).
fof(fact_linorder__antisym__conv1,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
=> ( hBOOL(hAPP(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_order__neq__le__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_order__less__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y)) ) ),
file('theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
=> ( ~ hBOOL(hAPP(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__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
=> ( V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( V_a != V_b
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
=> ( V_a != V_b
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a)) ) ) ),
file('theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__less__le__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I7_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_xt1_I8_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x)) ) ) ),
file('theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_double__eq__0__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( hAPP(hAPP(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_Im_Ozero,axiom,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_Im_Ozero) ).
fof(fact_complex__Im__one,axiom,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_complex__Im__one) ).
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_Im_Oadd,axiom,
! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)),
file('theBenchmark.p',fact_Im_Oadd) ).
fof(fact_le0,axiom,
! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
file('theBenchmark.p',fact_le0) ).
fof(fact_less__zeroE,axiom,
! [V_n] : ~ hBOOL(hAPP(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_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__iff,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_b_2 = hAPP(hAPP(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_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_psize__eq__0__iff,axiom,
! [V_p_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> V_p_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_convex__bound__lt,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_g_I2_J,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
file('theBenchmark.p',fact_g_I2_J) ).
fof(fact_f_I2_J,axiom,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
file('theBenchmark.p',fact_f_I2_J) ).
fof(fact_not__add__less1,axiom,
! [V_j,V_i] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)),
file('theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [V_i,V_j] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
file('theBenchmark.p',fact_not__add__less2) ).
fof(fact_le__add2,axiom,
! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
file('theBenchmark.p',fact_le__add2) ).
fof(fact_le__add1,axiom,
! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))),
file('theBenchmark.p',fact_le__add1) ).
fof(fact_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_le__iff__add,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
<=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ),
file('theBenchmark.p',fact_le__iff__add) ).
fof(fact_less__fun__def,axiom,
! [V_gb_2,V_fa_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
<=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_gb_2),V_fa_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_trans__less__add1,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
file('theBenchmark.p',fact_trans__less__add1) ).
fof(fact_trans__less__add2,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
file('theBenchmark.p',fact_trans__less__add2) ).
fof(fact_trans__le__add1,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
file('theBenchmark.p',fact_trans__le__add1) ).
fof(fact_trans__le__add2,axiom,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
file('theBenchmark.p',fact_trans__le__add2) ).
fof(fact_add__less__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
file('theBenchmark.p',fact_add__less__mono1) ).
fof(fact_add__le__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
file('theBenchmark.p',fact_add__le__mono1) ).
fof(fact_add__less__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ),
file('theBenchmark.p',fact_add__less__mono) ).
fof(fact_add__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ),
file('theBenchmark.p',fact_add__le__mono) ).
fof(fact_less__add__eq__less,axiom,
! [V_n,V_m,V_l,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ),
file('theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__lessD1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k)) ),
file('theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__leD2,axiom,
! [V_n,V_k,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ),
file('theBenchmark.p',fact_add__leD2) ).
fof(fact_add__leD1,axiom,
! [V_n,V_k,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leE,axiom,
! [V_n,V_k,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
=> ~ ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ) ),
file('theBenchmark.p',fact_add__leE) ).
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_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_nat__less__cases,axiom,
! [V_P_2,V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> ( ( V_m_2 = V_n_2
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
fof(fact_less__or__eq__imp__le,axiom,
! [V_n,V_m] :
( ( V_m = V_n
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_mult__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ),
file('theBenchmark.p',fact_mult__le__mono) ).
fof(fact_le__antisym,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_le__antisym) ).
fof(fact_le__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ),
file('theBenchmark.p',fact_le__trans) ).
fof(fact_le__neq__implies__less,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> ( V_m != V_n
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ),
file('theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_mult__le__mono2,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ),
file('theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_mult__le__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ),
file('theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_less__imp__le__nat,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_eq__imp__le,axiom,
! [V_n,V_m] :
( V_m = V_n
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__not__refl3,axiom,
! [V_t,V_s] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t))
=> V_s != V_t ),
file('theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))
=> V_m != V_n ),
file('theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__irrefl__nat,axiom,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)),
file('theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_linorder__neqE__nat,axiom,
! [V_y,V_x] :
( V_x != V_y
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x)) ) ),
file('theBenchmark.p',fact_linorder__neqE__nat) ).
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_le__eq__less__or__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
<=> ( V_m_2 = V_n_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
<=> ( V_m_2 != V_n_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__less__le) ).
fof(fact_nat__le__linear,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_nat__le__linear) ).
fof(fact_nat__neq__iff,axiom,
! [V_n_2,V_m_2] :
( V_m_2 != V_n_2
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
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__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_le__cube,axiom,
! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))),
file('theBenchmark.p',fact_le__cube) ).
fof(fact_le__square,axiom,
! [V_m] : hBOOL(hAPP(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__refl,axiom,
! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)),
file('theBenchmark.p',fact_le__refl) ).
fof(fact_less__not__refl,axiom,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)),
file('theBenchmark.p',fact_less__not__refl) ).
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_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)
=> ( hAPP(hAPP(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)) = hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_crossproduct__noteq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(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_c_2)) ) ),
file('theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult__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_mult__less__mono2,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ),
file('theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ),
file('theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel2) ).
fof(fact_mult__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__le__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_mult__le__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
file('theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_mult__less__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
file('theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__is__0,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__0__right,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0__right) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
file('theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_mult__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_norm__mult__ineq,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hBOOL(hAPP(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_norm__mult__less,axiom,
! [V_s,V_y,V_r,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_r))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
=> hBOOL(hAPP(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_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__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__left) ).
fof(fact_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__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_combine__common__factor,axiom,
! [V_c,V_b,V_e,V_a,T_a] :
( class_Rings_Osemiring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ),
file('theBenchmark.p',fact_combine__common__factor) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(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_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(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_mult_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult__1__right) ).
fof(fact_mult__1,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1__left) ).
fof(fact_real__mult__left__cancel,axiom,
! [V_b_2,V_a_2,V_c_2] :
( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_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_c_2] :
( V_c_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_real__mult__right__cancel) ).
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_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w) = hAPP(hAPP(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_add__scale__eq__noteq,axiom,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_r != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( V_c != V_d
& V_a = V_b )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ),
file('theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [V_a,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_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_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__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__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_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_split__mult__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ),
file('theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_split__mult__pos__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_comm__mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__comm__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_mult__right__mono) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(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)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
& hBOOL(hAPP(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)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ),
file('theBenchmark.p',fact_zero__le__square) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__comm__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_mult__pos__neg2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(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_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_c_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ hBOOL(hAPP(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_less__1__mult,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ),
file('theBenchmark.p',fact_less__1__mult) ).
fof(fact_abs__mult__less,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),V_c))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d))
=> hBOOL(hAPP(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_real__mult__less__mono2,axiom,
! [V_y,V_x,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [V_y_2,V_x_2] :
( hAPP(hAPP(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_sgn__less,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
<=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2)))
<=> hBOOL(hAPP(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__left__le__imp__le,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__right__le__imp__le,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__left__less__imp__less,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_mult__right__less__imp__less,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__less__le__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(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_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
<=> hBOOL(hAPP(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_mult__left__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ),
file('theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_mult__right__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ),
file('theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_abs__eq__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring__abs(T_a)
=> ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_real__mult__le__cancel__iff2,axiom,
! [V_y_2,V_x_2,V_z_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_z_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(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_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_gr0I,axiom,
! [V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
file('theBenchmark.p',fact_gr0I) ).
fof(fact_add__eq__self__zero,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
=> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_gr__implies__not0,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_add__is__0,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_add__is__0) ).
fof(fact_le__0__eq,axiom,
! [V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_le__0__eq) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_less__nat__zero__code,axiom,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_add__gr__0,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
file('theBenchmark.p',fact_add__gr__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [V_n] : hBOOL(hAPP(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_neq0__conv,axiom,
! [V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_not__less0,axiom,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_not__less0) ).
fof(fact_real__sgn__pos,axiom,
! [V_x] :
( hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
<=> hBOOL(hAPP(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_convex__bound__le,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__le) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [B_g] :
( c_SEQ_Osubseq(B_g)
=> ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g)))) ),
file('theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [V_y,V_x,V_c,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> ( hBOOL(hAPP(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_sum__squares__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_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_not__sum__squares__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ),
file('theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_monoseq__def,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Omonoseq(T_a,V_X_2)
<=> ( ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m))) )
| ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) ) ) ) ),
file('theBenchmark.p',fact_monoseq__def) ).
fof(fact_rabs__ratiotest__lemma,axiom,
! [V_y,V_x,V_c] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> ( hBOOL(hAPP(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_nat__add__commute,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),
file('theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)),
file('theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_add__mult__distrib2,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
file('theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_nat__add__assoc,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_add__mult__distrib,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_nat__add__right__cancel,axiom,
! [V_n_2,V_k_2,V_m_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__mult__commute,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
file('theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_nat__mult__assoc,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_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_nat__mult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_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_nat__mult__1__right,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [V_n_2,V_m_2] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_nat__mult__1,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_nat__mult__1) ).
fof(fact_expand__complex__eq,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
<=> ( hAPP(c_Complex_OIm,V_x_2) = hAPP(c_Complex_OIm,V_y_2)
& hAPP(c_Complex_ORe,V_x_2) = hAPP(c_Complex_ORe,V_y_2) ) ),
file('theBenchmark.p',fact_expand__complex__eq) ).
fof(fact_complex__equality,axiom,
! [V_y,V_x] :
( hAPP(c_Complex_ORe,V_x) = hAPP(c_Complex_ORe,V_y)
=> ( hAPP(c_Complex_OIm,V_x) = hAPP(c_Complex_OIm,V_y)
=> V_x = V_y ) ),
file('theBenchmark.p',fact_complex__equality) ).
fof(fact_complex__Im__mult,axiom,
! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))),
file('theBenchmark.p',fact_complex__Im__mult) ).
fof(fact_complex__Re__le__cmod,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
file('theBenchmark.p',fact_complex__Re__le__cmod) ).
fof(fact_Re_Ozero,axiom,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_Re_Ozero) ).
fof(fact_Re_Oadd,axiom,
! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),
file('theBenchmark.p',fact_Re_Oadd) ).
fof(fact_complex__Re__one,axiom,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_complex__Re__one) ).
fof(fact_abs__Re__le__cmod,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
file('theBenchmark.p',fact_abs__Re__le__cmod) ).
fof(fact_le__Suc__ex__iff,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2))
<=> ? [B_n] : V_l_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n) ),
file('theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_subseq__def,axiom,
! [V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
<=> ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n))) ) ),
file('theBenchmark.p',fact_subseq__def) ).
fof(fact_seq__suble,axiom,
! [V_n_2,V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),hAPP(V_fa_2,V_n_2))) ),
file('theBenchmark.p',fact_seq__suble) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( hAPP(hAPP(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_conv1,axiom,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
file('theBenchmark.p',fact_conv1) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_not__real__square__gt__zero,axiom,
! [V_x_2] :
( ~ hBOOL(hAPP(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_nat__mult__eq__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_convergent__const,axiom,
! [V_c_2,T_a] :
( class_RealVector_Ometric__space(T_a)
=> c_SEQ_Oconvergent(T_a,c_COMBK(T_a,tc_Nat_Onat,V_c_2)) ),
file('theBenchmark.p',fact_convergent__const) ).
fof(fact_mult__right_Oconvergent,axiom,
! [V_x_2,V_X_2,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ( c_SEQ_Oconvergent(T_a,V_X_2)
=> c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2)) ) ),
file('theBenchmark.p',fact_mult__right_Oconvergent) ).
fof(fact_mult__left_Oconvergent,axiom,
! [V_y_2,V_X_2,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ( c_SEQ_Oconvergent(T_a,V_X_2)
=> c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2)) ) ),
file('theBenchmark.p',fact_mult__left_Oconvergent) ).
fof(fact_mult_Oconvergent,axiom,
! [V_Y_2,V_X_2,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ( c_SEQ_Oconvergent(T_a,V_X_2)
=> ( c_SEQ_Oconvergent(T_a,V_Y_2)
=> c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2)) ) ) ),
file('theBenchmark.p',fact_mult_Oconvergent) ).
fof(fact_convergent__add,axiom,
! [V_Y_2,V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_Oconvergent(T_a,V_X_2)
=> ( c_SEQ_Oconvergent(T_a,V_Y_2)
=> c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2)) ) ) ),
file('theBenchmark.p',fact_convergent__add) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_m_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_left__add__mult__distrib,axiom,
! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k),
file('theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_Im_Opos__bounded,axiom,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
file('theBenchmark.p',fact_Im_Opos__bounded) ).
fof(fact_Re_Opos__bounded,axiom,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
file('theBenchmark.p',fact_Re_Opos__bounded) ).
fof(fact_Im_Ononneg__bounded,axiom,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
file('theBenchmark.p',fact_Im_Ononneg__bounded) ).
fof(fact_Re_Ononneg__bounded,axiom,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
file('theBenchmark.p',fact_Re_Ononneg__bounded) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_Re_Oconvergent,axiom,
! [V_X_2] :
( c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2)) ),
file('theBenchmark.p',fact_Re_Oconvergent) ).
fof(fact_Im_Oconvergent,axiom,
! [V_X_2] :
( c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2)) ),
file('theBenchmark.p',fact_Im_Oconvergent) ).
fof(fact_mult_Opos__bounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_a,B_b] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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__right_Opos__bounded,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_termination__basic__simps_I4_J,axiom,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y)) ),
file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_Im_Obounded,axiom,
? [B_K] :
! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))),
file('theBenchmark.p',fact_Im_Obounded) ).
fof(fact_Re_Obounded,axiom,
? [B_K] :
! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))),
file('theBenchmark.p',fact_Re_Obounded) ).
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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
=> hBOOL(hAPP(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_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k))
=> ~ hBOOL(hAPP(V_P_2,B_i)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k),V_n_2)) ) ) ),
file('theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_mult_Ononneg__bounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_a,B_b] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_decseq__imp__monoseq,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Odecseq(T_a,V_X_2)
=> c_SEQ_Omonoseq(T_a,V_X_2) ) ),
file('theBenchmark.p',fact_decseq__imp__monoseq) ).
fof(fact_mult__left_Ononneg__bounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_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] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(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_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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
=> hBOOL(hAPP(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_Bseq__offset,axiom,
! [V_k_2,V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))
=> c_SEQ_OBseq(T_a,V_X_2) ) ),
file('theBenchmark.p',fact_Bseq__offset) ).
fof(fact_Bseq__ignore__initial__segment,axiom,
! [V_k_2,V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
=> c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2))) ) ),
file('theBenchmark.p',fact_Bseq__ignore__initial__segment) ).
fof(fact_Bseq__monoseq__convergent,axiom,
! [V_X_2] :
( c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2)
=> ( c_SEQ_Omonoseq(tc_RealDef_Oreal,V_X_2)
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2) ) ),
file('theBenchmark.p',fact_Bseq__monoseq__convergent) ).
fof(fact_incseq__imp__monoseq,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Oincseq(T_a,V_X_2)
=> c_SEQ_Omonoseq(T_a,V_X_2) ) ),
file('theBenchmark.p',fact_incseq__imp__monoseq) ).
fof(fact_BseqI,axiom,
! [V_X_2,V_K_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_K_2))
=> ( ! [B_n] : hBOOL(hAPP(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_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] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(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_expi__zero,axiom,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_expi__zero) ).
fof(fact_natceiling__add__one,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(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_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] : hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
=> hBOOL(hAPP(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_natceiling__neg,axiom,
! [V_x] :
( hBOOL(hAPP(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_natceiling__le__eq__one,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> hBOOL(hAPP(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_expi__add,axiom,
! [V_b,V_a] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)),
file('theBenchmark.p',fact_expi__add) ).
fof(fact_natfloor__add__one,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(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_natceiling__eq,axiom,
! [V_x,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(hAPP(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) = hAPP(hAPP(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_le__mult__natfloor,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b))
=> hBOOL(hAPP(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_Bseq__mono__convergent,axiom,
! [V_X_2] :
( c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2)
=> ( ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n))) )
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2) ) ),
file('theBenchmark.p',fact_Bseq__mono__convergent) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [V_n] : hBOOL(hAPP(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_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_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_le__natfloor,axiom,
! [V_a,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a))) ),
file('theBenchmark.p',fact_le__natfloor) ).
fof(fact_real__natfloor__le,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(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_real__of__nat__inject,axiom,
! [V_m_2,V_n_2] :
( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
<=> V_n_2 = V_m_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_le__natfloor__eq,axiom,
! [V_a_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))
<=> hBOOL(hAPP(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_real__natfloor__add__one__gt,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(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_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] : ~ hBOOL(hAPP(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_m_2,V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_real__of__nat__le__iff,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(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_m_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_less__natfloor,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_n)) ) ),
file('theBenchmark.p',fact_less__natfloor) ).
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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(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_natfloor__add,axiom,
! [V_a,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_z)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
=> hBOOL(hAPP(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_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_natfloor__eq,axiom,
! [V_x,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(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_real__natceiling__ge,axiom,
! [V_x] : hBOOL(hAPP(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_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] : hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y))
=> hBOOL(hAPP(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_real__of__nat__le__zero__cancel__iff,axiom,
! [V_n_2] :
( hBOOL(hAPP(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_natceiling__le,axiom,
! [V_a,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a)) ),
file('theBenchmark.p',fact_natceiling__le) ).
fof(fact_natfloor__neg,axiom,
! [V_x] :
( hBOOL(hAPP(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_real__of__nat__gt__zero__cancel__iff,axiom,
! [V_n_2] :
( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(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_m_2,V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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_m_2))) ),
file('theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
file('theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_natceiling__le__eq,axiom,
! [V_a_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))
<=> hBOOL(hAPP(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_le__natfloor__eq__one,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2)))
<=> hBOOL(hAPP(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__add,axiom,
! [V_a,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a) ),
file('theBenchmark.p',fact_natceiling__add) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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),hAPP(hAPP(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_BseqI2_H,axiom,
! [V_K_2,V_X_2,V_N_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( ! [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_N_2),B_n))
=> hBOOL(hAPP(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] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) )
<=> ? [B_N] :
! [B_n] : hBOOL(hAPP(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] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) )
<=> ? [B_N] :
! [B_n] : hBOOL(hAPP(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] : hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(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] : hBOOL(hAPP(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_realpow__Suc__le__self,axiom,
! [V_n,V_r,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_r))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(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_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_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_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_I31_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_Suc__less__SucD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__lessD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__lessD) ).
fof(fact_less__SucE,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
=> ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__SucE) ).
fof(fact_less__trans__Suc,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k)) ) ),
file('theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_Suc__lessI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> ( c_Nat_OSuc(V_m) != V_n
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n)) ) ),
file('theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__SucI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ),
file('theBenchmark.p',fact_less__SucI) ).
fof(fact_less__antisym,axiom,
! [V_m,V_n] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m))
=> ( hBOOL(hAPP(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_not__less__less__Suc__eq,axiom,
! [V_m_2,V_n_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
<=> V_n_2 = V_m_2 ) ),
file('theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_Suc__less__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
<=> ( V_m_2 = V_n_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_not__less__eq,axiom,
! [V_n_2,V_m_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) ),
file('theBenchmark.p',fact_not__less__eq) ).
fof(fact_add__Suc__shift,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_add__Suc,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_add__Suc__right) ).
fof(fact_Suc__leD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__leD) ).
fof(fact_le__SucE,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
=> ( ~ hBOOL(hAPP(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_le__SucI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n))) ),
file('theBenchmark.p',fact_le__SucI) ).
fof(fact_Suc__le__mono,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
<=> ( V_m_2 = c_Nat_OSuc(V_n_2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_not__less__eq__eq,axiom,
! [V_n_2,V_m_2] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_Suc__n__not__le__n,axiom,
! [V_n] : ~ hBOOL(hAPP(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_Suc__mult__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_Suc__mult__cancel1) ).
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_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__n__not__n,axiom,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
file('theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_nat_Oinject,axiom,
! [V_nat_H_2,V_nat_2] :
( 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__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_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_norm__power__ineq,axiom,
! [V_n,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_gr0__conv__Suc,axiom,
! [V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
<=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ),
file('theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_less__Suc0,axiom,
! [V_n_2] :
( hBOOL(hAPP(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_less__Suc__eq__0__disj,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
<=> ( ? [B_j] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2))
& V_m_2 = c_Nat_OSuc(B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_one__is__add,axiom,
! [V_n_2,V_m_2] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
<=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = 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_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_add__is__1) ).
fof(fact_mult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = 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_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_less__iff__Suc__add,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
<=> ? [B_k] : V_n_2 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ),
file('theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__add__Suc2,axiom,
! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))),
file('theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_less__add__Suc1,axiom,
! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))),
file('theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__eq__Suc__le,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) ),
file('theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_less__Suc__eq__le,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_Suc__le__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_le__imp__less__Suc,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(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__leI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(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__less__Suc__eq,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
<=> V_n_2 = V_m_2 ) ),
file('theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__le__lessD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__le__lessD) ).
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_Suc__mult__less__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(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_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_mult__Suc__right,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_mult__Suc,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_mult__Suc) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(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_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
file('theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_Suc__eq__plus1,axiom,
! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_monoseq__Suc,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Omonoseq(T_a,V_X_2)
<=> ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n)))
| ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n)))) ) ) ),
file('theBenchmark.p',fact_monoseq__Suc) ).
fof(fact_subseq__Suc__iff,axiom,
! [V_fa_2] :
( c_SEQ_Osubseq(V_fa_2)
<=> ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n)))) ),
file('theBenchmark.p',fact_subseq__Suc__iff) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [V_n_2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),
file('theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_one__less__mult,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ),
file('theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ),
file('theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_one__le__mult__iff,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(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_m_2),V_n_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) ) ),
file('theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_real__of__nat__Suc__gt__zero,axiom,
! [V_n] : hBOOL(hAPP(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_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)) = hAPP(hAPP(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_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] : hBOOL(hAPP(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] : hBOOL(hAPP(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_monoseq__realpow,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ),
file('theBenchmark.p',fact_monoseq__realpow) ).
fof(fact_convergent__realpow,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ),
file('theBenchmark.p',fact_convergent__realpow) ).
fof(fact_Bseq__realpow,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2)) ) ),
file('theBenchmark.p',fact_Bseq__realpow) ).
fof(fact_power__strict__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ),
file('theBenchmark.p',fact_power__strict__mono) ).
fof(fact_one__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
file('theBenchmark.p',fact_one__less__power) ).
fof(fact_power__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_zpower__zadd__distrib,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
file('theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zpower__zpower,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
file('theBenchmark.p',fact_zpower__zpower) ).
fof(fact_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_m_2,V_x_2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_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_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [V_n_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),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_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [V_n_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(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__one__le__power,axiom,
! [V_n,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
=> hBOOL(hAPP(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_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_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_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_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__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__mult,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ),
file('theBenchmark.p',fact_power__mult) ).
fof(fact_power__one__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
file('theBenchmark.p',fact_power__one__right) ).
fof(fact_zero__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_zero__le__power) ).
fof(fact_power__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ),
file('theBenchmark.p',fact_power__mono) ).
fof(fact_zero__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_zero__less__power) ).
fof(fact_one__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_one__le__power) ).
fof(fact_power__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_m_2,V_a_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(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_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
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__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__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__0,axiom,
! [V_a,T_a] :
( class_Power_Opower(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__0) ).
fof(fact_power__add,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__add) ).
fof(fact_power__less__imp__less__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_power__le__imp__le__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(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))))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_power__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> V_a = V_b ) ) ) ),
file('theBenchmark.p',fact_power__inject__base) ).
fof(fact_power__less__power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
file('theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_power__gt1__lemma,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
file('theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_power__0__left,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left) ).
fof(fact_zero__le__power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n))) ),
file('theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_power__gt1,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)))) ) ),
file('theBenchmark.p',fact_power__gt1) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_b_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_power__Suc__less,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
file('theBenchmark.p',fact_power__Suc__less) ).
fof(fact_power__Suc__less__one,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(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_power__strict__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ),
file('theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ),
file('theBenchmark.p',fact_power__decreasing) ).
fof(fact_reduce__poly__simple,axiom,
! [V_n,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [B_z] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
file('theBenchmark.p',fact_reduce__poly__simple) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [V_x] :
( hBOOL(hAPP(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_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] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))),
file('theBenchmark.p',fact_zero__le__zpower__abs) ).
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_zadd__zmult__distrib2,axiom,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
file('theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
file('theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_zmult__zless__mono2,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ),
file('theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_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_zmult__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
file('theBenchmark.p',fact_zmult__assoc) ).
fof(fact_zmult__commute,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
file('theBenchmark.p',fact_zmult__commute) ).
fof(fact_zadd__zless__mono,axiom,
! [V_z,V_z_H,V_w,V_w_H] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ),
file('theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_zadd__strict__right__mono,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ),
file('theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ),
file('theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_le__imp__0__less,axiom,
! [V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ),
file('theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_odd__less__0,axiom,
! [V_z_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(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_add1__zle__eq,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zabs__less__one__iff,axiom,
! [V_z_2] :
( hBOOL(hAPP(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_zless__add1__eq,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( V_w_2 = V_z_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(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_zless__linear,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y)) ),
file('theBenchmark.p',fact_zless__linear) ).
fof(fact_zless__le,axiom,
! [V_w_2,V_z_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))
<=> ( V_z_2 != V_w_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2)) ) ),
file('theBenchmark.p',fact_zless__le) ).
fof(fact_zadd__0__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zadd__0__right) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [V_z_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zadd__0,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zadd__0) ).
fof(fact_int__0__less__1,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('theBenchmark.p',fact_int__0__less__1) ).
fof(fact_odd__nonzero,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_odd__nonzero) ).
fof(fact_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_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_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_zero__less__power__nat__eq,axiom,
! [V_n_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_self__quotient__aux2,axiom,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_self__quotient__aux1,axiom,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_q__pos__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ),
file('theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_zadd__left__mono,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ),
file('theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_zadd__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)),
file('theBenchmark.p',fact_zadd__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)),
file('theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_zadd__commute,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_zle__antisym,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z))
=> V_z = V_w ) ),
file('theBenchmark.p',fact_zle__antisym) ).
fof(fact_zle__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) ),
file('theBenchmark.p',fact_zle__linear) ).
fof(fact_zle__refl,axiom,
! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w)),
file('theBenchmark.p',fact_zle__refl) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H)) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_unique__quotient__lemma,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q)) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_q__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_DeMoivre2,axiom,
! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)),
file('theBenchmark.p',fact_DeMoivre2) ).
fof(fact_reals__Archimedean6a,axiom,
! [V_r] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))
=> ? [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))
& hBOOL(hAPP(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_realpow__pos__nth__unique,axiom,
! [V_a,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(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
& hBOOL(hAPP(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
& hBOOL(hAPP(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_complex__mod__rcis,axiom,
! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
file('theBenchmark.p',fact_complex__mod__rcis) ).
fof(fact_rcis__zero__mod,axiom,
! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_rcis__zero__mod) ).
fof(fact_rcis__mult,axiom,
! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)),
file('theBenchmark.p',fact_rcis__mult) ).
fof(fact_realpow__pos__nth,axiom,
! [V_a,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(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
& hBOOL(hAPP(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_cis__real__of__nat__Suc__mult,axiom,
! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))),
file('theBenchmark.p',fact_cis__real__of__nat__Suc__mult) ).
fof(fact_reals__Archimedean4,axiom,
! [V_x,V_y] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> ? [B_n] :
( hBOOL(hAPP(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)))
& hBOOL(hAPP(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_cis__mult,axiom,
! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)),
file('theBenchmark.p',fact_cis__mult) ).
fof(fact_cis__zero,axiom,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_cis__zero) ).
fof(fact_cis__rcis__eq,axiom,
! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a),
file('theBenchmark.p',fact_cis__rcis__eq) ).
fof(fact_DeMoivre,axiom,
! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)),
file('theBenchmark.p',fact_DeMoivre) ).
fof(fact_ln__realpow,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(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_cos__n__Re__cis__pow__n,axiom,
! [V_a,V_n] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)),
file('theBenchmark.p',fact_cos__n__Re__cis__pow__n) ).
fof(fact_sin__n__Im__cis__pow__n,axiom,
! [V_a,V_n] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)),
file('theBenchmark.p',fact_sin__n__Im__cis__pow__n) ).
fof(fact_sin__add,axiom,
! [V_y,V_x] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))),
file('theBenchmark.p',fact_sin__add) ).
fof(fact_sin__cos__squared__add3,axiom,
! [V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_sin__cos__squared__add3) ).
fof(fact_sin__zero__abs__cos__one,axiom,
! [V_x] :
( c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_sin__zero__abs__cos__one) ).
fof(fact_cos__one__sin__zero,axiom,
! [V_x] :
( c_Transcendental_Ocos(V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_cos__one__sin__zero) ).
fof(fact_cos__zero,axiom,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_cos__zero) ).
fof(fact_cos__le__one,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('theBenchmark.p',fact_cos__le__one) ).
fof(fact_sin__le__one,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('theBenchmark.p',fact_sin__le__one) ).
fof(fact_sin__zero,axiom,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_sin__zero) ).
fof(fact_Im__cis,axiom,
! [V_a] : hAPP(c_Complex_OIm,c_Complex_Ocis(V_a)) = c_Transcendental_Osin(V_a),
file('theBenchmark.p',fact_Im__cis) ).
fof(fact_Re__cis,axiom,
! [V_a] : hAPP(c_Complex_ORe,c_Complex_Ocis(V_a)) = c_Transcendental_Ocos(V_a),
file('theBenchmark.p',fact_Re__cis) ).
fof(fact_ln__less__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
<=> hBOOL(hAPP(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__inj__iff,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(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__self,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(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__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_abs__sin__le__one,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('theBenchmark.p',fact_abs__sin__le__one) ).
fof(fact_abs__cos__le__one,axiom,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('theBenchmark.p',fact_abs__cos__le__one) ).
fof(fact_Im__rcis,axiom,
! [V_a,V_r] : hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)),
file('theBenchmark.p',fact_Im__rcis) ).
fof(fact_Re__rcis,axiom,
! [V_a,V_r] : hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)),
file('theBenchmark.p',fact_Re__rcis) ).
fof(fact_ln__le__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
<=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(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__imp__gt__one,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(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__less__zero,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> hBOOL(hAPP(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__less__zero__iff,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
<=> hBOOL(hAPP(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__eq__zero__iff,axiom,
! [V_x_2] :
( hBOOL(hAPP(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__gt__zero__iff,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
<=> hBOOL(hAPP(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__gt__zero,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(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__ge__zero__imp__ge__one,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(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__ge__zero__iff,axiom,
! [V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
<=> hBOOL(hAPP(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__mult,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> ( hBOOL(hAPP(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)) = hAPP(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(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_cos__arccos__abs,axiom,
! [V_y] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_Transcendental_Ocos(c_Transcendental_Oarccos(V_y)) = V_y ),
file('theBenchmark.p',fact_cos__arccos__abs) ).
fof(fact_reals__Archimedean3,axiom,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> ! [B_y] :
? [B_n] : hBOOL(hAPP(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_realpow__pos__nth2,axiom,
! [V_n,V_a] :
( hBOOL(hAPP(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),c_Nat_OSuc(V_n)) = V_a
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) ) ),
file('theBenchmark.p',fact_realpow__pos__nth2) ).
fof(fact_mult__left_Obounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
! [B_x] : hBOOL(hAPP(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_mult__right_Obounded,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
! [B_x] : hBOOL(hAPP(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_mult_Obounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
! [B_a,B_b] : hBOOL(hAPP(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_realpow__minus__mult,axiom,
! [V_x,V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( hBOOL(hAPP(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_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_norm__triangle__ineq3,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> hBOOL(hAPP(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)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
<=> hBOOL(hAPP(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_norm__triangle__ineq2,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> hBOOL(hAPP(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_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_c_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_c_2,V_d_2)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = V_a ),
file('theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__le__self,axiom,
! [V_n,V_m] : hBOOL(hAPP(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_diff__le__mono2,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(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_eq__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
<=> V_m_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_m))
=> ( hBOOL(hAPP(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_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ),
file('theBenchmark.p',fact_le__diff__iff) ).
fof(fact_diff__add__inverse2,axiom,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__add__inverse,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__diff__left,axiom,
! [V_k,V_j,V_i] : 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
file('theBenchmark.p',fact_diff__diff__left) ).
fof(fact_diff__cancel,axiom,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = 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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__cancel2) ).
fof(fact_less__iff__diff__less__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
<=> hBOOL(hAPP(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_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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(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)
<=> hAPP(hAPP(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_c_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oring(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(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_c_2 = hAPP(hAPP(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_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)) = hAPP(hAPP(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_abs__triangle__ineq2__sym,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(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)
=> hBOOL(hAPP(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)
=> hBOOL(hAPP(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_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__eq__diff__eq,axiom,
! [V_d_2,V_c_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_c_2,V_d_2)
=> ( V_a_2 = V_b_2
<=> V_c_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_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_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_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,axiom,
! [V_d_2,V_c_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_c_2,V_d_2)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
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_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_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_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_less__imp__diff__less,axiom,
! [V_n,V_k,V_j] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))
=> hBOOL(hAPP(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_diff__less__mono2,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))
=> hBOOL(hAPP(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_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_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_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_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__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__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_diff__diff__right,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j) ),
file('theBenchmark.p',fact_diff__diff__right) ).
fof(fact_le__diff__conv,axiom,
! [V_i_2,V_k_2,V_j_2] :
( hBOOL(hAPP(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))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ),
file('theBenchmark.p',fact_le__diff__conv) ).
fof(fact_le__add__diff,axiom,
! [V_m,V_n,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k))) ),
file('theBenchmark.p',fact_le__add__diff) ).
fof(fact_le__add__diff__inverse,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_add__diff__assoc,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_le__diff__conv2,axiom,
! [V_i_2,V_j_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ),
file('theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_le__add__diff__inverse2,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
=> hAPP(hAPP(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__imp__diff__is__add,axiom,
! [V_k_2,V_j_2,V_i_2] :
( hBOOL(hAPP(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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ),
file('theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_diff__add__assoc,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_add__diff__assoc2,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i) ),
file('theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_less__diff__iff,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ) ),
file('theBenchmark.p',fact_less__diff__iff) ).
fof(fact_diff__less__mono,axiom,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a))
=> hBOOL(hAPP(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_less__diff__conv,axiom,
! [V_k_2,V_j_2,V_i_2] :
( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ),
file('theBenchmark.p',fact_less__diff__conv) ).
fof(fact_add__diff__inverse,axiom,
! [V_n,V_m] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
=> hAPP(hAPP(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_Suc__diff__le,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(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_diff__is__0__eq_H,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(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_diff__is__0__eq,axiom,
! [V_n_2,V_m_2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_diff__add__0,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__less__Suc,axiom,
! [V_n,V_m] : hBOOL(hAPP(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_diff__less,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> hBOOL(hAPP(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_zero__less__diff,axiom,
! [V_m_2,V_n_2] :
( hBOOL(hAPP(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_m_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ),
file('theBenchmark.p',fact_zero__less__diff) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),hAPP(hAPP(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_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(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_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_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),hAPP(hAPP(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__triangle__ineq4,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(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))),hAPP(hAPP(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)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_abs__diff__less__iff,axiom,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(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))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2)))
& hBOOL(hAPP(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_norm__triangle__ineq4,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> hBOOL(hAPP(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))),hAPP(hAPP(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_Suc__pred,axiom,
! [V_n] :
( hBOOL(hAPP(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_diff__Suc__less,axiom,
! [V_i,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(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_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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
=> hBOOL(hAPP(V_P_2,B_d)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2))
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_nat__diff__split) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [V_m,V_j,V_k] :
( hBOOL(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [V_m,V_j,V_k] :
( hBOOL(hAPP(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,hAPP(hAPP(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_nat__eq__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
<=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2) ) ),
file('theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_nat__diff__add__eq2,axiom,
! [V_n,V_m,V_u,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n)) ),
file('theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_nat__le__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) ) ),
file('theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__eq__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ),
file('theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__diff__add__eq1,axiom,
! [V_n,V_m,V_u,V_i,V_j] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_i))
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_m_2,V_u_2,V_i_2,V_j_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_norm__diff__triangle__ineq,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_lemma__realpow__diff,axiom,
! [V_y,V_n,V_p,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( hBOOL(hAPP(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] :
( hBOOL(hAPP(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] :
( hBOOL(hAPP(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)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = c_Nat_OSuc(hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) ),
file('theBenchmark.p',fact_add__eq__if) ).
fof(fact_nat__less__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),V_i_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__less__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_mult__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_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_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)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) ),
file('theBenchmark.p',fact_realpow__two__diff) ).
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_reals__Archimedean6,axiom,
! [V_r] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_r))
=> ? [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,B_n)))
& hBOOL(hAPP(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_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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(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_real__le__eq__diff,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
<=> hBOOL(hAPP(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_Im_Odiff,axiom,
! [V_y,V_x] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)),
file('theBenchmark.p',fact_Im_Odiff) ).
fof(fact_Re_Odiff,axiom,
! [V_y,V_x] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)),
file('theBenchmark.p',fact_Re_Odiff) ).
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_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_less__bin__lemma,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))
<=> hBOOL(hAPP(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_norm__diff__ineq,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))) ),
file('theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_metric__bound__lemma,axiom,
! [V_y,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)))))),
file('theBenchmark.p',fact_metric__bound__lemma) ).
fof(fact_zle__diff1__eq,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(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))))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_real__of__nat__diff,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(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_sin__diff,axiom,
! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))),
file('theBenchmark.p',fact_sin__diff) ).
fof(fact_sin__diff2,axiom,
! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x))),
file('theBenchmark.p',fact_sin__diff2) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [V_a,V_b] : hBOOL(hAPP(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,hAPP(hAPP(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_cos__add,axiom,
! [V_y,V_x] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))),
file('theBenchmark.p',fact_cos__add) ).
fof(fact_cos__diff,axiom,
! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))),
file('theBenchmark.p',fact_cos__diff) ).
fof(fact_cos__diff2,axiom,
! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x))),
file('theBenchmark.p',fact_cos__diff2) ).
fof(fact_natfloor__subtract,axiom,
! [V_x,V_a] :
( hBOOL(hAPP(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] : hBOOL(hAPP(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] :
( hBOOL(hAPP(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_complex__Re__mult,axiom,
! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),
file('theBenchmark.p',fact_complex__Re__mult) ).
fof(fact_decr__lemma,axiom,
! [V_z,V_x,V_d] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
=> hBOOL(hAPP(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),hAPP(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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_unimodular__reduce__norm,axiom,
! [V_z] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ),
file('theBenchmark.p',fact_unimodular__reduce__norm) ).
fof(fact_tsub__def,axiom,
! [V_x,V_y] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x))
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hBOOL(hAPP(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_complex__Re__i,axiom,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_complex__Re__i) ).
fof(fact_complex__i__not__zero,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_complex__i__not__zero) ).
fof(fact_complex__i__not__one,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_complex__i__not__one) ).
fof(fact_complex__Im__i,axiom,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_complex__Im__i) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_tsub__eq,axiom,
! [V_x,V_y] :
( hBOOL(hAPP(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_int__power__div__base,axiom,
! [V_k,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> ( hBOOL(hAPP(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_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) = hAPP(hAPP(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_int__div__less__self,axiom,
! [V_k,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
=> hBOOL(hAPP(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] :
( hBOOL(hAPP(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__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_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__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__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__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__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__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_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> hBOOL(hAPP(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__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_div__neg__pos__less0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(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_neg__imp__zdiv__neg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_zdiv__self,axiom,
! [V_a] :
( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_zdiv__self) ).
fof(fact_div__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_zdiv__mono1__neg,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(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_zdiv__mono1,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(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_div__neg__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(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__mono2__neg,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
=> hBOOL(hAPP(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__nonpos__pos__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(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_neg__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_div__pos__pos__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(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_div__nonneg__neg__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(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_zdiv__mono2,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
=> hBOOL(hAPP(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_nonneg1__imp__zdiv__pos__iff,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
=> ( hBOOL(hAPP(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)))
<=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [V_i_2,V_k_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
=> ( hBOOL(hAPP(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)))
<=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_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)
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ),
file('theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ),
file('theBenchmark.p',fact_div__mult__self1) ).
fof(fact_div__add__self2,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_div__add__self2) ).
fof(fact_div__add__self1,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_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)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [B_i] :
( ? [B_j] :
( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j)) )
=> hBOOL(hAPP(V_P_2,B_i)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ! [B_i] :
( ? [B_j] :
( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
=> hBOOL(hAPP(V_P_2,B_i)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_split__zdiv) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [V_r_1,V_y,V_b_1,V_a_1] :
( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
=> ( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) ) ) )
=> ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> 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_complex__mult__def,axiom,
! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))),
file('theBenchmark.p',fact_complex__mult__def) ).
fof(fact_lemma__interval,axiom,
! [V_b,V_x,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_b))
=> ? [B_d] :
( ! [B_y] :
( hBOOL(hAPP(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))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y),V_b))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a),B_y)) ) )
& hBOOL(hAPP(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_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] :
( hBOOL(hAPP(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_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] : hBOOL(hAPP(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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(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_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_div__less__dividend,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> hBOOL(hAPP(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__mult__self__is__m,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(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] :
( hBOOL(hAPP(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_nat__mult__div__cancel1,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(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__le__mono2,axiom,
! [V_k,V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> hBOOL(hAPP(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_complex__diff,axiom,
! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)),
file('theBenchmark.p',fact_complex__diff) ).
fof(fact_complex__surj,axiom,
! [V_z] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z)) = V_z,
file('theBenchmark.p',fact_complex__surj) ).
fof(fact_complex_Oinject,axiom,
! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] :
( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)
<=> ( V_real2_2 = V_real2_H_2
& V_real1_2 = V_real1_H_2 ) ),
file('theBenchmark.p',fact_complex_Oinject) ).
fof(fact_Im,axiom,
! [V_y,V_x] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_y,
file('theBenchmark.p',fact_Im) ).
fof(fact_Re,axiom,
! [V_y,V_x] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_x,
file('theBenchmark.p',fact_Re) ).
fof(fact_complex__add,axiom,
! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d)),
file('theBenchmark.p',fact_complex__add) ).
fof(fact_Complex__eq__0,axiom,
! [V_b_2,V_a_2] :
( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_Complex__eq__0) ).
fof(fact_complex__zero__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_complex__zero__def) ).
fof(fact_Complex__eq__i,axiom,
! [V_y_2,V_x_2] :
( c_Complex_Ocomplex_OComplex(V_x_2,V_y_2) = c_Complex_Oii
<=> ( V_y_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_Complex__eq__i) ).
fof(fact_i__def,axiom,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_i__def) ).
fof(fact_Complex__eq__1,axiom,
! [V_b_2,V_a_2] :
( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_Complex__eq__1) ).
fof(fact_complex__one__def,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_complex__one__def) ).
fof(fact_cis__def,axiom,
! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)),
file('theBenchmark.p',fact_cis__def) ).
fof(fact_div__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( ~ hBOOL(hAPP(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_div__if,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( ( ~ hBOOL(hAPP(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)) )
& ( hBOOL(hAPP(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_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] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_k_2))
=> ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
=> hBOOL(hAPP(V_P_2,B_i)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_split__div) ).
fof(fact_complex__mult,axiom,
! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))),
file('theBenchmark.p',fact_complex__mult) ).
fof(fact_cmod__unit__one,axiom,
! [V_a] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_cmod__unit__one) ).
fof(fact_complex__add__def,axiom,
! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),
file('theBenchmark.p',fact_complex__add__def) ).
fof(fact_split__div_H,axiom,
! [V_n_2,V_m_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
<=> ( ? [B_q] :
( hBOOL(hAPP(V_P_2,B_q))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_split__div_H) ).
fof(fact_split__div__lemma,axiom,
! [V_m_2,V_q_2,V_n_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) )
<=> V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) ) ),
file('theBenchmark.p',fact_split__div__lemma) ).
fof(fact_le__div__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
=> 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_le__div__geq) ).
fof(fact_complex_Osize_I1_J,axiom,
! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_complex_Osize_I1_J) ).
fof(fact_cos__arg__i__mult__zero__pos,axiom,
! [V_y] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_cos__arg__i__mult__zero__pos) ).
fof(fact_cos__arg__i__mult__zero,axiom,
! [V_y] :
( V_y != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_cos__arg__i__mult__zero) ).
fof(fact_cos__arg__i__mult__zero__neg,axiom,
! [V_y] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
=> c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_cos__arg__i__mult__zero__neg) ).
fof(fact_complex_Osize_I2_J,axiom,
! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_complex_Osize_I2_J) ).
fof(fact_complex_Orecs,axiom,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
file('theBenchmark.p',fact_complex_Orecs) ).
fof(fact_complex_Osimps_I2_J,axiom,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
file('theBenchmark.p',fact_complex_Osimps_I2_J) ).
fof(fact_natfloor__div__nat,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y) ) ),
file('theBenchmark.p',fact_natfloor__div__nat) ).
fof(fact_real__sgn__eq,axiom,
! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),
file('theBenchmark.p',fact_real__sgn__eq) ).
fof(fact_divide_Oadd,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_divide_Oadd) ).
fof(fact_add__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_divide__1,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_divide__1) ).
fof(fact_right__inverse__eq,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
<=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_divide__self,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_divide__self) ).
fof(fact_divide__self__if,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) )
& ( V_a = c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divide__self__if) ).
fof(fact_nonzero__power__divide,axiom,
! [V_n,V_a,V_b,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
file('theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_power__one__over,axiom,
! [V_n,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ),
file('theBenchmark.p',fact_power__one__over) ).
fof(fact_divide_Oconvergent,axiom,
! [V_y_2,V_X_2,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> ( c_SEQ_Oconvergent(T_a,V_X_2)
=> c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_y_2)) ) ),
file('theBenchmark.p',fact_divide_Oconvergent) ).
fof(fact_norm__divide,axiom,
! [V_b,V_a,T_a] :
( ( class_RealVector_Oreal__normed__field(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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__divide) ).
fof(fact_eq__divide__imp,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
=> V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ),
file('theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_divide__eq__imp,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ),
file('theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ),
file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_nonzero__norm__divide,axiom,
! [V_a,V_b,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_nonzero__norm__divide) ).
fof(fact_divide_Ozero,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide_Ozero) ).
fof(fact_divide__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__zero__left) ).
fof(fact_divide__zero,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__zero) ).
fof(fact_times__divide__eq__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ),
file('theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_real__divide__square__eq,axiom,
! [V_a,V_r] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_a),V_r),
file('theBenchmark.p',fact_real__divide__square__eq) ).
fof(fact_power__divide,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
file('theBenchmark.p',fact_power__divide) ).
fof(fact_real__0__le__divide__iff,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x_2),V_y_2)))
<=> ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ) ),
file('theBenchmark.p',fact_real__0__le__divide__iff) ).
fof(fact_Im__sgn,axiom,
! [V_z] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)),
file('theBenchmark.p',fact_Im__sgn) ).
fof(fact_Re__sgn,axiom,
! [V_z] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)),
file('theBenchmark.p',fact_Re__sgn) ).
fof(fact_divide_Odiff,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_divide_Odiff) ).
fof(fact_diff__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_c) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_diff__divide__distrib) ).
fof(fact_DERIV__mult__lemma,axiom,
! [V_h,V_d,V_c,V_b,V_a,T_a] :
( class_RealVector_Oreal__field(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),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_c),V_d))),V_h) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)),V_h))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),V_h)),V_d)) ),
file('theBenchmark.p',fact_DERIV__mult__lemma) ).
fof(fact_lemma__MVT,axiom,
! [V_b_2,V_a_2,V_fa_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_a_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_b_2)),
file('theBenchmark.p',fact_lemma__MVT) ).
fof(fact_real__of__nat__div4,axiom,
! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)))),
file('theBenchmark.p',fact_real__of__nat__div4) ).
fof(fact_power__diff,axiom,
! [V_m,V_n,V_a,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
file('theBenchmark.p',fact_power__diff) ).
fof(fact_ln__div,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
=> c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y)) ) ),
file('theBenchmark.p',fact_ln__div) ).
fof(fact_real__of__nat__div2,axiom,
! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))))),
file('theBenchmark.p',fact_real__of__nat__div2) ).
fof(fact_real__of__nat__div3,axiom,
! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('theBenchmark.p',fact_real__of__nat__div3) ).
fof(fact_divide__left__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_divide__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono) ).
fof(fact_cis__divide,axiom,
! [V_b,V_a] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_b)),
file('theBenchmark.p',fact_cis__divide) ).
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_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_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__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_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
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_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__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
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_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_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__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
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_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_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
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_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__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
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_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__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__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
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_Osgn__if,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Osgn__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__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__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__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__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__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_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__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
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__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
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__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
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__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Ometric__space) ).
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__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
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__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
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_Osgn__if,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__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__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__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__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
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__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
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__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
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__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Ometric__space) ).
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__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
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_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
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__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__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__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__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__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_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__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__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__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(help_c__COMBK__1,axiom,
! [V_Q,V_P,T_b,T_a] : hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P,
file('theBenchmark.p',help_c__COMBK__1) ).
fof(help_c__COMBB__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBB__1) ).
fof(help_c__COMBC__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
file('theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBS__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
fof(conj_0,conjecture,
( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
file('theBenchmark.p',conj_0) ).
fof(f_1_1,plain,
! [V_gb_2,V_fa_2] :
( V_fa_2 = V_gb_2
| ? [B_x] : hAPP(V_fa_2,B_x) != hAPP(V_gb_2,B_x) ),
inference(fof_nnf,[status(thm)],[fact_ext]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = U_2
| ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
hBOOL(hAPP(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_rp]) ).
cnf(f_2_2,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),v_r)),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
c_SEQ_Osubseq(v_f____),
inference(fof_nnf,[status(thm)],[fact_f_I1_J]) ).
cnf(f_3_2,plain,
c_SEQ_Osubseq(v_f____),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,B_n)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(fof_nnf,[status(thm)],[fact_th]) ).
fof(f_4_2,plain,
! [U_3] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,U_3)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,U_3)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
c_SEQ_Osubseq(v_ga____),
inference(fof_nnf,[status(thm)],[fact_g_I1_J]) ).
cnf(f_5_2,plain,
c_SEQ_Osubseq(v_ga____),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,B_n))),v_r)),
inference(fof_nnf,[status(thm)],[fact_assms]) ).
fof(f_6_2,plain,
! [U_4] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,U_4))),v_r)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,U_4))),v_r)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(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_7_2,plain,
! [U_5] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(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_5)))),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(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_5)))),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [V_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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_8_2,plain,
! [U_6] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_6)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_6)),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_6)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_6)),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__two]) ).
fof(f_9_2,plain,
! [U_7] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_7,c_Groups_Ozero__class_Ozero(U_7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7),c_Groups_Oone__class_Oone(U_7)),c_Groups_Oone__class_Oone(U_7))))
| ~ class_Rings_Olinordered__semidom(U_7) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_7,c_Groups_Ozero__class_Ozero(U_7)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7),c_Groups_Oone__class_Oone(U_7)),c_Groups_Oone__class_Oone(U_7))))
| ~ class_Rings_Olinordered__semidom(U_7) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg]) ).
fof(f_10_2,plain,
! [U_10,U_9,U_8] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_8,c_Groups_Ozero__class_Ozero(U_8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8),U_9),U_10)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_8,c_Groups_Ozero__class_Ozero(U_8)),U_10))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_8,c_Groups_Ozero__class_Ozero(U_8)),U_9))
| ~ class_Groups_Oordered__comm__monoid__add(U_8) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_8,c_Groups_Ozero__class_Ozero(U_8)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8),U_9),U_10)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_8,c_Groups_Ozero__class_Ozero(U_8)),U_10))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_8,c_Groups_Ozero__class_Ozero(U_8)),U_9))
| ~ class_Groups_Oordered__comm__monoid__add(U_8) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos]) ).
fof(f_11_2,plain,
! [U_13,U_12,U_11] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_11,c_Groups_Ozero__class_Ozero(U_11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11),U_12),U_13)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_11,c_Groups_Ozero__class_Ozero(U_11)),U_13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Ozero__class_Ozero(U_11)),U_12))
| ~ class_Groups_Oordered__comm__monoid__add(U_11) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_11,c_Groups_Ozero__class_Ozero(U_11)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11),U_12),U_13)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_11,c_Groups_Ozero__class_Ozero(U_11)),U_13))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_11,c_Groups_Ozero__class_Ozero(U_11)),U_12))
| ~ class_Groups_Oordered__comm__monoid__add(U_11) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing]) ).
fof(f_12_2,plain,
! [U_17,U_16,U_15,U_14] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_14,U_16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14),U_15),U_17)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_14,U_16),U_17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_14,c_Groups_Ozero__class_Ozero(U_14)),U_15))
| ~ class_Groups_Oordered__comm__monoid__add(U_14) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_14,U_16),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_14),U_15),U_17)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_14,U_16),U_17))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_14,c_Groups_Ozero__class_Ozero(U_14)),U_15))
| ~ class_Groups_Oordered__comm__monoid__add(U_14) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2]) ).
fof(f_13_2,plain,
! [U_21,U_20,U_19,U_18] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_18,U_20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18),U_19),U_21)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_18,U_20),U_21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_18,c_Groups_Ozero__class_Ozero(U_18)),U_19))
| ~ class_Groups_Oordered__comm__monoid__add(U_18) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_18,U_20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18),U_19),U_21)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_18,U_20),U_21))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_18,c_Groups_Ozero__class_Ozero(U_18)),U_19))
| ~ class_Groups_Oordered__comm__monoid__add(U_18) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos]) ).
fof(f_14_2,plain,
! [U_24,U_23,U_22] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_22),U_23),U_24)),c_Groups_Ozero__class_Ozero(U_22)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_22,U_24),c_Groups_Ozero__class_Ozero(U_22)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_22,U_23),c_Groups_Ozero__class_Ozero(U_22)))
| ~ class_Groups_Oordered__comm__monoid__add(U_22) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_22,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_22),U_23),U_24)),c_Groups_Ozero__class_Ozero(U_22)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_22,U_24),c_Groups_Ozero__class_Ozero(U_22)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_22,U_23),c_Groups_Ozero__class_Ozero(U_22)))
| ~ class_Groups_Oordered__comm__monoid__add(U_22) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg]) ).
fof(f_15_2,plain,
! [U_27,U_26,U_25] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_25,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_25),U_26),U_27)),c_Groups_Ozero__class_Ozero(U_25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_25,U_27),c_Groups_Ozero__class_Ozero(U_25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_25,U_26),c_Groups_Ozero__class_Ozero(U_25)))
| ~ class_Groups_Oordered__comm__monoid__add(U_25) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_25,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_25),U_26),U_27)),c_Groups_Ozero__class_Ozero(U_25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_25,U_27),c_Groups_Ozero__class_Ozero(U_25)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_25,U_26),c_Groups_Ozero__class_Ozero(U_25)))
| ~ class_Groups_Oordered__comm__monoid__add(U_25) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_16_2,plain,
! [U_30,U_29,U_28] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oabs__class_Oabs(U_28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_28),U_29),U_30))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_28),c_Groups_Oabs__class_Oabs(U_28,U_29)),c_Groups_Oabs__class_Oabs(U_28,U_30))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oabs__class_Oabs(U_28,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_28),U_29),U_30))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_28),c_Groups_Oabs__class_Oabs(U_28,U_29)),c_Groups_Oabs__class_Oabs(U_28,U_30))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [V_a,T_a] :
( ~ hBOOL(hAPP(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_17_2,plain,
! [U_32,U_31] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_31,c_Groups_Oabs__class_Oabs(U_31,U_32)),c_Groups_Ozero__class_Ozero(U_31)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_31) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_31,c_Groups_Oabs__class_Oabs(U_31,U_32)),c_Groups_Ozero__class_Ozero(U_31)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_31) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_18_2,plain,
! [U_34,U_33] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_33,c_Groups_Ozero__class_Ozero(U_33)),c_Groups_Oabs__class_Oabs(U_33,U_34)))
| U_34 = c_Groups_Ozero__class_Ozero(U_33) )
& ( U_34 != c_Groups_Ozero__class_Ozero(U_33)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_33,c_Groups_Ozero__class_Ozero(U_33)),c_Groups_Oabs__class_Oabs(U_33,U_34))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_33) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( U_34 != c_Groups_Ozero__class_Ozero(U_33)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_33,c_Groups_Ozero__class_Ozero(U_33)),c_Groups_Oabs__class_Oabs(U_33,U_34)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_33) ),
inference(clausify,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_33,c_Groups_Ozero__class_Ozero(U_33)),c_Groups_Oabs__class_Oabs(U_33,U_34)))
| U_34 = c_Groups_Ozero__class_Ozero(U_33)
| ~ class_Groups_Oordered__ab__group__add__abs(U_33) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(fof_nnf,[status(thm)],[fact__096cmod_A_Is_A0_J_A_060_061_Ar_096]) ).
cnf(f_19_2,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(v_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),v_r)),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
! [V_z,V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(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_20_2,plain,
! [U_36,U_35] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_35),U_36))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_36)))),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_35),U_36))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_36)))),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_38,U_37] :
( ( ( c_Groups_Ozero__class_Ozero(U_37) = U_38
| U_38 != c_Groups_Ozero__class_Ozero(U_37) )
& ( U_38 = c_Groups_Ozero__class_Ozero(U_37)
| c_Groups_Ozero__class_Ozero(U_37) != U_38 ) )
| ~ class_Groups_Ozero(U_37) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( U_38 = c_Groups_Ozero__class_Ozero(U_37)
| c_Groups_Ozero__class_Ozero(U_37) != U_38
| ~ class_Groups_Ozero(U_37) ),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( c_Groups_Ozero__class_Ozero(U_37) = U_38
| U_38 != c_Groups_Ozero__class_Ozero(U_37)
| ~ class_Groups_Ozero(U_37) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| V_x = V_y
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(f_22_2,plain,
! [U_41,U_40,U_39] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_39,U_41),U_40))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_39,U_40),U_41))
| U_40 = U_41
| ~ class_Rings_Olinordered__idom(U_39) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_39,U_41),U_40))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_39,U_40),U_41))
| U_40 = U_41
| ~ class_Rings_Olinordered__idom(U_39) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [V_c,V_a,V_b,T_a] :
( V_b = V_c
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq]) ).
fof(f_23_2,plain,
! [U_45,U_44,U_43,U_42] :
( U_43 = U_45
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_42),U_43),U_44) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_42),U_45),U_44)
| ~ class_Groups_Ocancel__semigroup__add(U_42) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( U_43 = U_45
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_42),U_43),U_44) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_42),U_45),U_44)
| ~ class_Groups_Ocancel__semigroup__add(U_42) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
| ~ class_Groups_Ocancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__imp__eq]) ).
fof(f_24_2,plain,
! [U_49,U_48,U_47,U_46] :
( U_48 = U_49
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_46),U_47),U_48) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_46),U_47),U_49)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_46) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( U_48 = U_49
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_46),U_47),U_48) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_46),U_47),U_49)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_46) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).
fof(f_25_2,plain,
! [U_53,U_52,U_51,U_50] :
( U_52 = U_53
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_50),U_51),U_52) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_50),U_51),U_53)
| ~ class_Groups_Ocancel__semigroup__add(U_50) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( U_52 = U_53
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_50),U_51),U_52) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_50),U_51),U_53)
| ~ class_Groups_Ocancel__semigroup__add(U_50) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [V_c_2,V_a_2,V_b_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_26_2,plain,
! [U_57,U_56,U_55,U_54] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_55),U_56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_57),U_56)
| U_55 != U_57 )
& ( U_55 = U_57
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_55),U_56) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_57),U_56) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_54) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( U_55 = U_57
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_55),U_56) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_57),U_56)
| ~ class_Groups_Ocancel__semigroup__add(U_54) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_55),U_56) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_54),U_57),U_56)
| U_55 != U_57
| ~ class_Groups_Ocancel__semigroup__add(U_54) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [V_c_2,V_b_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_27_2,plain,
! [U_61,U_60,U_59,U_58] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_60) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_61)
| U_60 != U_61 )
& ( U_60 = U_61
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_60) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_61) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_58) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( U_60 = U_61
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_60) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_61)
| ~ class_Groups_Ocancel__semigroup__add(U_58) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_60) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_58),U_59),U_61)
| U_60 != U_61
| ~ class_Groups_Ocancel__semigroup__add(U_58) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
| ~ class_Groups_Oab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J]) ).
fof(f_28_2,plain,
! [U_65,U_64,U_63,U_62] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),U_63),U_64)),U_65) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),U_63),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),U_64),U_65))
| ~ class_Groups_Oab__semigroup__add(U_62) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),U_63),U_64)),U_65) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),U_63),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_62),U_64),U_65))
| ~ class_Groups_Oab__semigroup__add(U_62) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_67,U_66] :
( ( ( c_Groups_Oone__class_Oone(U_66) = U_67
| U_67 != c_Groups_Oone__class_Oone(U_66) )
& ( U_67 = c_Groups_Oone__class_Oone(U_66)
| c_Groups_Oone__class_Oone(U_66) != U_67 ) )
| ~ class_Groups_Oone(U_66) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( U_67 = c_Groups_Oone__class_Oone(U_66)
| c_Groups_Oone__class_Oone(U_66) != U_67
| ~ class_Groups_Oone(U_66) ),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
( c_Groups_Oone__class_Oone(U_66) = U_67
| U_67 != c_Groups_Oone__class_Oone(U_66)
| ~ class_Groups_Oone(U_66) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_real__le__antisym]) ).
fof(f_30_2,plain,
! [U_69,U_68] :
( U_68 = U_69
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_69),U_68))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_68),U_69)) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( U_68 = U_69
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_69),U_68))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_68),U_69)) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_real__le__trans]) ).
fof(f_31_2,plain,
! [U_72,U_71,U_70] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_70),U_72))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_71),U_72))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_70),U_71)) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_70),U_72))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_71),U_72))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_70),U_71)) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_real__le__linear]) ).
fof(f_32_2,plain,
! [U_74,U_73] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_74),U_73))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_73),U_74)) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_74),U_73))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_73),U_74)) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w),V_w)),
inference(fof_nnf,[status(thm)],[fact_real__le__refl]) ).
fof(f_33_2,plain,
! [U_75] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_75),U_75)),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_75),U_75)),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
! [U_77,U_76] :
( c_Groups_Oabs__class_Oabs(U_76,c_Groups_Oabs__class_Oabs(U_76,U_77)) = c_Groups_Oabs__class_Oabs(U_76,U_77)
| ~ class_Groups_Oordered__ab__group__add__abs(U_76) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( c_Groups_Oabs__class_Oabs(U_76,c_Groups_Oabs__class_Oabs(U_76,U_77)) = c_Groups_Oabs__class_Oabs(U_76,U_77)
| ~ class_Groups_Oordered__ab__group__add__abs(U_76) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral]) ).
fof(f_35_2,plain,
! [U_79,U_78] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_78),U_79),c_Groups_Ozero__class_Ozero(U_78)) = U_79
| ~ class_Groups_Ocomm__monoid__add(U_78) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_78),U_79),c_Groups_Ozero__class_Ozero(U_78)) = U_79
| ~ class_Groups_Ocomm__monoid__add(U_78) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__right]) ).
fof(f_36_2,plain,
! [U_81,U_80] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_80),U_81),c_Groups_Ozero__class_Ozero(U_80)) = U_81
| ~ class_Groups_Omonoid__add(U_80) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_80),U_81),c_Groups_Ozero__class_Ozero(U_80)) = U_81
| ~ class_Groups_Omonoid__add(U_80) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(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) != hAPP(hAPP(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_37_2,plain,
! [U_83,U_82] :
( ( ( c_Groups_Ozero__class_Ozero(U_82) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_82),U_83),U_83)
| U_83 != c_Groups_Ozero__class_Ozero(U_82) )
& ( U_83 = c_Groups_Ozero__class_Ozero(U_82)
| c_Groups_Ozero__class_Ozero(U_82) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_82),U_83),U_83) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_82) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_83 = c_Groups_Ozero__class_Ozero(U_82)
| c_Groups_Ozero__class_Ozero(U_82) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_82),U_83),U_83)
| ~ class_Groups_Olinordered__ab__group__add(U_82) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( c_Groups_Ozero__class_Ozero(U_82) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_82),U_83),U_83)
| U_83 != c_Groups_Ozero__class_Ozero(U_82)
| ~ class_Groups_Olinordered__ab__group__add(U_82) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0]) ).
fof(f_38_2,plain,
! [U_85,U_84] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_84),c_Groups_Ozero__class_Ozero(U_84)),U_85) = U_85
| ~ class_Groups_Ocomm__monoid__add(U_84) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_84),c_Groups_Ozero__class_Ozero(U_84)),U_85) = U_85
| ~ class_Groups_Ocomm__monoid__add(U_84) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__left]) ).
fof(f_39_2,plain,
! [U_87,U_86] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_86),c_Groups_Ozero__class_Ozero(U_86)),U_87) = U_87
| ~ class_Groups_Omonoid__add(U_86) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_86),c_Groups_Ozero__class_Ozero(U_86)),U_87) = U_87
| ~ class_Groups_Omonoid__add(U_86) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left]) ).
fof(f_40_2,plain,
! [U_91,U_90,U_89,U_88] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_88,U_90),U_91))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_88,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_88),U_89),U_90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_88),U_89),U_91)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_88) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_88,U_90),U_91))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_88,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_88),U_89),U_90)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_88),U_89),U_91)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_88) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right]) ).
fof(f_41_2,plain,
! [U_95,U_94,U_93,U_92] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_92,U_93),U_95))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_92,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_92),U_93),U_94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_92),U_95),U_94)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_92) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_92,U_93),U_95))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_92,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_92),U_93),U_94)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_92),U_95),U_94)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_92) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__mono]) ).
fof(f_42_2,plain,
! [U_100,U_99,U_98,U_97,U_96] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_96,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_96),U_97),U_99)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_96),U_98),U_100)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_96,U_99),U_100))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_96,U_97),U_98))
| ~ class_Groups_Oordered__ab__semigroup__add(U_96) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_96,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_96),U_97),U_99)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_96),U_98),U_100)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_96,U_99),U_100))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_96,U_97),U_98))
| ~ class_Groups_Oordered__ab__semigroup__add(U_96) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(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_43_2,plain,
! [U_104,U_103,U_102,U_101] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_101,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_101),U_104),U_102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_101),U_104),U_103)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_101,U_102),U_103))
| ~ class_Groups_Oordered__ab__semigroup__add(U_101) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_101,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_101),U_104),U_102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_101),U_104),U_103)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_101,U_102),U_103))
| ~ class_Groups_Oordered__ab__semigroup__add(U_101) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(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_44_2,plain,
! [U_108,U_107,U_106,U_105] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_105,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_105),U_106),U_108)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_105),U_107),U_108)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_105,U_106),U_107))
| ~ class_Groups_Oordered__ab__semigroup__add(U_105) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_105,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_105),U_106),U_108)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_105),U_107),U_108)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_105,U_106),U_107))
| ~ class_Groups_Oordered__ab__semigroup__add(U_105) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_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_45_2,plain,
! [U_112,U_111,U_110,U_109] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_111)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_112)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,U_111),U_112)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,U_111),U_112))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_111)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_112))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_109) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,U_111),U_112))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_111)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_112)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_109) ),
inference(clausify,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_111)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_109),U_110),U_112)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_109,U_111),U_112))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_109) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_46_2,plain,
! [U_116,U_115,U_114,U_113] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_114),U_115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_116),U_115)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,U_114),U_116)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,U_114),U_116))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_114),U_115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_116),U_115))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_113) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,U_114),U_116))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_114),U_115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_116),U_115)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_113) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_114),U_115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_113),U_116),U_115)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_113,U_114),U_116))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_113) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left]) ).
fof(f_47_2,plain,
! [U_120,U_119,U_118,U_117] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_117,U_119),U_120))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_117,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_117),U_118),U_119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_117),U_118),U_120)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_117) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_117,U_119),U_120))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_117,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_117),U_118),U_119)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_117),U_118),U_120)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_117) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right]) ).
fof(f_48_2,plain,
! [U_124,U_123,U_122,U_121] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_121,U_122),U_124))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_121,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_121),U_122),U_123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_121),U_124),U_123)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_121) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_121,U_122),U_124))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_121,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_121),U_122),U_123)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_121),U_124),U_123)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_121) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__mono]) ).
fof(f_49_2,plain,
! [U_129,U_128,U_127,U_126,U_125] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_125,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_125),U_126),U_128)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_125),U_127),U_129)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_125,U_128),U_129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_125,U_126),U_127))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_125) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_125,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_125),U_126),U_128)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_125),U_127),U_129)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_125,U_128),U_129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_125,U_126),U_127))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_125) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(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_50_2,plain,
! [U_133,U_132,U_131,U_130] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_130,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_130),U_133),U_131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_130),U_133),U_132)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_130,U_131),U_132))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_130) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_130,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_130),U_133),U_131)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_130),U_133),U_132)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_130,U_131),U_132))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_130) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(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_51_2,plain,
! [U_137,U_136,U_135,U_134] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_134,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_134),U_135),U_137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_134),U_136),U_137)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_134,U_135),U_136))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_134) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_134,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_134),U_135),U_137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_134),U_136),U_137)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_134,U_135),U_136))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_134) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_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_52_2,plain,
! [U_141,U_140,U_139,U_138] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_140)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_141)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,U_140),U_141)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,U_140),U_141))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_140)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_141))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_138) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,U_140),U_141))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_140)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_141)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_138) ),
inference(clausify,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_140)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_138),U_139),U_141)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_138,U_140),U_141))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_138) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_53_2,plain,
! [U_145,U_144,U_143,U_142] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_143),U_144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_145),U_144)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,U_143),U_145)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,U_143),U_145))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_143),U_144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_145),U_144))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_142) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,U_143),U_145))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_143),U_144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_145),U_144)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_142) ),
inference(clausify,[status(thm)],[f_53_2]) ).
cnf(f_53_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_143),U_144)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_142),U_145),U_144)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_142,U_143),U_145))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_142) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_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_54_2,plain,
! [U_146] :
( c_Groups_Ozero__class_Ozero(U_146) != c_Groups_Oone__class_Oone(U_146)
| ~ class_Rings_Ozero__neq__one(U_146) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( c_Groups_Ozero__class_Ozero(U_146) != c_Groups_Oone__class_Oone(U_146)
| ~ class_Rings_Ozero__neq__one(U_146) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_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_55_2,plain,
! [U_147] :
( c_Groups_Oone__class_Oone(U_147) != c_Groups_Ozero__class_Ozero(U_147)
| ~ class_Rings_Ozero__neq__one(U_147) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( c_Groups_Oone__class_Oone(U_147) != c_Groups_Ozero__class_Ozero(U_147)
| ~ class_Rings_Ozero__neq__one(U_147) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_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_56_2,plain,
! [U_149,U_148] :
( ( ( c_Groups_Oabs__class_Oabs(U_148,U_149) = c_Groups_Ozero__class_Ozero(U_148)
| U_149 != c_Groups_Ozero__class_Ozero(U_148) )
& ( U_149 = c_Groups_Ozero__class_Ozero(U_148)
| c_Groups_Oabs__class_Oabs(U_148,U_149) != c_Groups_Ozero__class_Ozero(U_148) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_148) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( U_149 = c_Groups_Ozero__class_Ozero(U_148)
| c_Groups_Oabs__class_Oabs(U_148,U_149) != c_Groups_Ozero__class_Ozero(U_148)
| ~ class_Groups_Oordered__ab__group__add__abs(U_148) ),
inference(clausify,[status(thm)],[f_56_2]) ).
cnf(f_56_4,plain,
( c_Groups_Oabs__class_Oabs(U_148,U_149) = c_Groups_Ozero__class_Ozero(U_148)
| U_149 != c_Groups_Ozero__class_Ozero(U_148)
| ~ class_Groups_Oordered__ab__group__add__abs(U_148) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_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_57_2,plain,
! [U_150] :
( c_Groups_Oabs__class_Oabs(U_150,c_Groups_Ozero__class_Ozero(U_150)) = c_Groups_Ozero__class_Ozero(U_150)
| ~ class_Groups_Oordered__ab__group__add__abs(U_150) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( c_Groups_Oabs__class_Oabs(U_150,c_Groups_Ozero__class_Ozero(U_150)) = c_Groups_Ozero__class_Ozero(U_150)
| ~ class_Groups_Oordered__ab__group__add__abs(U_150) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(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_58_2,plain,
! [U_153,U_152,U_151] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_151,U_152),U_153))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_151,c_Groups_Oabs__class_Oabs(U_151,U_152)),U_153))
| ~ class_Groups_Oordered__ab__group__add__abs(U_151) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_151,U_152),U_153))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_151,c_Groups_Oabs__class_Oabs(U_151,U_152)),U_153))
| ~ class_Groups_Oordered__ab__group__add__abs(U_151) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(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_59_2,plain,
! [U_155,U_154] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_154,U_155),c_Groups_Oabs__class_Oabs(U_154,U_155)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_154) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_154,U_155),c_Groups_Oabs__class_Oabs(U_154,U_155)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_154) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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_60_2,plain,
! [U_157,U_156] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_156),U_157))
| ( U_156 != U_157
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_156),U_157)) ) )
& ( U_156 = U_157
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_156),U_157))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_156),U_157)) ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( ! [U_161,U_159] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_159),U_161))
| ( U_159 != U_161
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_159),U_161)) ) )
& ! [U_160,U_158] :
( U_158 = U_160
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_158),U_160))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_158),U_160)) ) ),
inference(miniscope,[status(thm)],[f_60_2]) ).
cnf(f_60_4,plain,
( U_158 = U_160
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_158),U_160))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_158),U_160)) ),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_159),U_161))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_159),U_161)) ),
inference(clausify,[status(thm)],[f_60_3]) ).
cnf(f_60_6,plain,
( U_159 != U_161
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_159),U_161)) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(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_61_2,plain,
! [U_163,U_162] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_162),U_163))
| U_162 = U_163
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_162),U_163)) )
& ( ( U_162 != U_163
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_162),U_163)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_162),U_163)) ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ! [U_167,U_165] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_165),U_167))
| U_165 = U_167
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_165),U_167)) )
& ! [U_166,U_164] :
( ( U_164 != U_166
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_164),U_166)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_164),U_166)) ) ),
inference(miniscope,[status(thm)],[f_61_2]) ).
cnf(f_61_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_164),U_166))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_164),U_166)) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_5,plain,
( U_164 != U_166
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_164),U_166)) ),
inference(clausify,[status(thm)],[f_61_3]) ).
cnf(f_61_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_165),U_167))
| U_165 = U_167
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_165),U_167)) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(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))) = hAPP(hAPP(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_62_2,plain,
! [U_170,U_169,U_168] :
( c_Groups_Oabs__class_Oabs(U_168,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_168),c_Groups_Oabs__class_Oabs(U_168,U_169)),c_Groups_Oabs__class_Oabs(U_168,U_170))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_168),c_Groups_Oabs__class_Oabs(U_168,U_169)),c_Groups_Oabs__class_Oabs(U_168,U_170))
| ~ class_Groups_Oordered__ab__group__add__abs(U_168) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( c_Groups_Oabs__class_Oabs(U_168,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_168),c_Groups_Oabs__class_Oabs(U_168,U_169)),c_Groups_Oabs__class_Oabs(U_168,U_170))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_168),c_Groups_Oabs__class_Oabs(U_168,U_169)),c_Groups_Oabs__class_Oabs(U_168,U_170))
| ~ class_Groups_Oordered__ab__group__add__abs(U_168) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_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_63_2,plain,
! [U_171] :
( c_Groups_Oabs__class_Oabs(U_171,c_Groups_Oone__class_Oone(U_171)) = c_Groups_Oone__class_Oone(U_171)
| ~ class_Rings_Olinordered__idom(U_171) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( c_Groups_Oabs__class_Oabs(U_171,c_Groups_Oone__class_Oone(U_171)) = c_Groups_Oone__class_Oone(U_171)
| ~ class_Rings_Olinordered__idom(U_171) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_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]) ).
cnf(f_64_2,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_64_1]) ).
fof(f_65_1,plain,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_x)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z),V_y)))
| ~ hBOOL(hAPP(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_65_2,plain,
! [U_174,U_173,U_172] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_174),U_172)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_174),U_173)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_172),U_173)) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_174),U_172)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_174),U_173)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_172),U_173)) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos]) ).
fof(f_66_2,plain,
! [U_177,U_176,U_175] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_175,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_175),U_176),U_177)),c_Groups_Ozero__class_Ozero(U_175)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_175,U_177),c_Groups_Ozero__class_Ozero(U_175)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_175,U_176),c_Groups_Ozero__class_Ozero(U_175)))
| ~ class_Groups_Oordered__comm__monoid__add(U_175) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_175,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_175),U_176),U_177)),c_Groups_Ozero__class_Ozero(U_175)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_175,U_177),c_Groups_Ozero__class_Ozero(U_175)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_175,U_176),c_Groups_Ozero__class_Ozero(U_175)))
| ~ class_Groups_Oordered__comm__monoid__add(U_175) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [V_a,V_b,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing2]) ).
fof(f_67_2,plain,
! [U_181,U_180,U_179,U_178] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_178,U_180),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_178),U_181),U_179)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_178,U_180),U_181))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_178,c_Groups_Ozero__class_Ozero(U_178)),U_179))
| ~ class_Groups_Oordered__comm__monoid__add(U_178) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_178,U_180),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_178),U_181),U_179)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_178,U_180),U_181))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_178,c_Groups_Ozero__class_Ozero(U_178)),U_179))
| ~ class_Groups_Oordered__comm__monoid__add(U_178) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing]) ).
fof(f_68_2,plain,
! [U_185,U_184,U_183,U_182] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_182,U_184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_182),U_183),U_185)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_182,U_184),U_185))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_182,c_Groups_Ozero__class_Ozero(U_182)),U_183))
| ~ class_Groups_Oordered__comm__monoid__add(U_182) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_182,U_184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_182),U_183),U_185)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_182,U_184),U_185))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_182,c_Groups_Ozero__class_Ozero(U_182)),U_183))
| ~ class_Groups_Oordered__comm__monoid__add(U_182) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hAPP(hAPP(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) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y_2))
| ~ hBOOL(hAPP(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_69_2,plain,
! [U_188,U_187,U_186] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_186),U_187),U_188) = c_Groups_Ozero__class_Ozero(U_186)
| U_188 != c_Groups_Ozero__class_Ozero(U_186)
| U_187 != c_Groups_Ozero__class_Ozero(U_186) )
& ( ( U_188 = c_Groups_Ozero__class_Ozero(U_186)
& U_187 = c_Groups_Ozero__class_Ozero(U_186) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_186),U_187),U_188) != c_Groups_Ozero__class_Ozero(U_186) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_188))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_187))
| ~ class_Groups_Oordered__comm__monoid__add(U_186) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( U_187 = c_Groups_Ozero__class_Ozero(U_186)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_186),U_187),U_188) != c_Groups_Ozero__class_Ozero(U_186)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_188))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_187))
| ~ class_Groups_Oordered__comm__monoid__add(U_186) ),
inference(clausify,[status(thm)],[f_69_2]) ).
cnf(f_69_4,plain,
( U_188 = c_Groups_Ozero__class_Ozero(U_186)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_186),U_187),U_188) != c_Groups_Ozero__class_Ozero(U_186)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_188))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_187))
| ~ class_Groups_Oordered__comm__monoid__add(U_186) ),
inference(clausify,[status(thm)],[f_69_2]) ).
cnf(f_69_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_186),U_187),U_188) = c_Groups_Ozero__class_Ozero(U_186)
| U_188 != c_Groups_Ozero__class_Ozero(U_186)
| U_187 != c_Groups_Ozero__class_Ozero(U_186)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_188))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_186,c_Groups_Ozero__class_Ozero(U_186)),U_187))
| ~ class_Groups_Oordered__comm__monoid__add(U_186) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg]) ).
fof(f_70_2,plain,
! [U_191,U_190,U_189] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_189),U_190),U_191)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189)),U_191))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189)),U_190))
| ~ class_Groups_Oordered__comm__monoid__add(U_189) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_189),U_190),U_191)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189)),U_191))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_189,c_Groups_Ozero__class_Ozero(U_189)),U_190))
| ~ class_Groups_Oordered__comm__monoid__add(U_189) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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_71_2,plain,
! [U_193,U_192] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_192),U_193),U_193)),c_Groups_Ozero__class_Ozero(U_192)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,U_193),c_Groups_Ozero__class_Ozero(U_192))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,U_193),c_Groups_Ozero__class_Ozero(U_192)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_192),U_193),U_193)),c_Groups_Ozero__class_Ozero(U_192))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_192) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,U_193),c_Groups_Ozero__class_Ozero(U_192)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_192),U_193),U_193)),c_Groups_Ozero__class_Ozero(U_192)))
| ~ class_Groups_Olinordered__ab__group__add(U_192) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_192),U_193),U_193)),c_Groups_Ozero__class_Ozero(U_192)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_192,U_193),c_Groups_Ozero__class_Ozero(U_192)))
| ~ class_Groups_Olinordered__ab__group__add(U_192) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_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_72_2,plain,
! [U_195,U_194] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_194),U_195),U_195)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),U_195)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),U_195))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_194),U_195),U_195))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_194) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),U_195))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_194),U_195),U_195)))
| ~ class_Groups_Olinordered__ab__group__add(U_194) ),
inference(clausify,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_194),U_195),U_195)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_194,c_Groups_Ozero__class_Ozero(U_194)),U_195))
| ~ class_Groups_Olinordered__ab__group__add(U_194) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__neg]) ).
fof(f_73_2,plain,
! [U_198,U_197,U_196] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_196,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_196),U_197),U_198)),c_Groups_Ozero__class_Ozero(U_196)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_196,U_198),c_Groups_Ozero__class_Ozero(U_196)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_196,U_197),c_Groups_Ozero__class_Ozero(U_196)))
| ~ class_Groups_Oordered__comm__monoid__add(U_196) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_196,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_196),U_197),U_198)),c_Groups_Ozero__class_Ozero(U_196)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_196,U_198),c_Groups_Ozero__class_Ozero(U_196)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_196,U_197),c_Groups_Ozero__class_Ozero(U_196)))
| ~ class_Groups_Oordered__comm__monoid__add(U_196) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__add__strict]) ).
fof(f_74_2,plain,
! [U_202,U_201,U_200,U_199] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_199,U_201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_199),U_200),U_202)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_199,U_201),U_202))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_199,c_Groups_Ozero__class_Ozero(U_199)),U_200))
| ~ class_Rings_Olinordered__semidom(U_199) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_199,U_201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_199),U_200),U_202)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_199,U_201),U_202))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_199,c_Groups_Ozero__class_Ozero(U_199)),U_200))
| ~ class_Rings_Olinordered__semidom(U_199) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__pos]) ).
fof(f_75_2,plain,
! [U_205,U_204,U_203] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_203,c_Groups_Ozero__class_Ozero(U_203)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_203),U_204),U_205)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_203,c_Groups_Ozero__class_Ozero(U_203)),U_205))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_203,c_Groups_Ozero__class_Ozero(U_203)),U_204))
| ~ class_Groups_Oordered__comm__monoid__add(U_203) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_203,c_Groups_Ozero__class_Ozero(U_203)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_203),U_204),U_205)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_203,c_Groups_Ozero__class_Ozero(U_203)),U_205))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_203,c_Groups_Ozero__class_Ozero(U_203)),U_204))
| ~ class_Groups_Oordered__comm__monoid__add(U_203) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_76_2,plain,
! [U_207,U_206] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_206),U_207),U_207)),c_Groups_Ozero__class_Ozero(U_206)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,U_207),c_Groups_Ozero__class_Ozero(U_206))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,U_207),c_Groups_Ozero__class_Ozero(U_206)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_206),U_207),U_207)),c_Groups_Ozero__class_Ozero(U_206))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_206) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,U_207),c_Groups_Ozero__class_Ozero(U_206)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_206),U_207),U_207)),c_Groups_Ozero__class_Ozero(U_206)))
| ~ class_Groups_Olinordered__ab__group__add(U_206) ),
inference(clausify,[status(thm)],[f_76_2]) ).
cnf(f_76_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_206),U_207),U_207)),c_Groups_Ozero__class_Ozero(U_206)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_206,U_207),c_Groups_Ozero__class_Ozero(U_206)))
| ~ class_Groups_Olinordered__ab__group__add(U_206) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_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_77_2,plain,
! [U_209,U_208] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_208),U_209),U_209)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),U_209)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),U_209))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_208),U_209),U_209))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_208) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),U_209))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_208),U_209),U_209)))
| ~ class_Groups_Olinordered__ab__group__add(U_208) ),
inference(clausify,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_208),U_209),U_209)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_208,c_Groups_Ozero__class_Ozero(U_208)),U_209))
| ~ class_Groups_Olinordered__ab__group__add(U_208) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__less__mono]) ).
fof(f_78_2,plain,
! [U_214,U_213,U_212,U_211,U_210] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_210,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_210),U_211),U_213)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_210),U_212),U_214)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_210,U_213),U_214))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_210,U_211),U_212))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_210) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_210,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_210),U_211),U_213)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_210),U_212),U_214)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_210,U_213),U_214))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_210,U_211),U_212))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_210) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__le__mono]) ).
fof(f_79_2,plain,
! [U_219,U_218,U_217,U_216,U_215] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_215,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_215),U_216),U_218)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_215),U_217),U_219)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_215,U_218),U_219))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_215,U_216),U_217))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_215) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_215,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_215),U_216),U_218)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_215),U_217),U_219)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_215,U_218),U_219))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_215,U_216),U_217))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_215) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__one]) ).
fof(f_80_2,plain,
! [U_220] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_220,c_Groups_Ozero__class_Ozero(U_220)),c_Groups_Oone__class_Oone(U_220)))
| ~ class_Rings_Olinordered__semidom(U_220) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_220,c_Groups_Ozero__class_Ozero(U_220)),c_Groups_Oone__class_Oone(U_220)))
| ~ class_Rings_Olinordered__semidom(U_220) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_1,plain,
! [T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__le__zero]) ).
fof(f_81_2,plain,
! [U_221] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_221,c_Groups_Oone__class_Oone(U_221)),c_Groups_Ozero__class_Ozero(U_221)))
| ~ class_Rings_Olinordered__semidom(U_221) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_221,c_Groups_Oone__class_Oone(U_221)),c_Groups_Ozero__class_Ozero(U_221)))
| ~ class_Rings_Olinordered__semidom(U_221) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__one]) ).
fof(f_82_2,plain,
! [U_222] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_222,c_Groups_Ozero__class_Ozero(U_222)),c_Groups_Oone__class_Oone(U_222)))
| ~ class_Rings_Olinordered__semidom(U_222) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_222,c_Groups_Ozero__class_Ozero(U_222)),c_Groups_Oone__class_Oone(U_222)))
| ~ class_Rings_Olinordered__semidom(U_222) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__less__zero]) ).
fof(f_83_2,plain,
! [U_223] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_223,c_Groups_Oone__class_Oone(U_223)),c_Groups_Ozero__class_Ozero(U_223)))
| ~ class_Rings_Olinordered__semidom(U_223) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_223,c_Groups_Oone__class_Oone(U_223)),c_Groups_Ozero__class_Ozero(U_223)))
| ~ class_Rings_Olinordered__semidom(U_223) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__one]) ).
fof(f_84_2,plain,
! [U_225,U_224] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_224,U_225),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_224),U_225),c_Groups_Oone__class_Oone(U_224))))
| ~ class_Rings_Olinordered__semidom(U_224) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_224,U_225),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_224),U_225),c_Groups_Oone__class_Oone(U_224))))
| ~ class_Rings_Olinordered__semidom(U_224) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg]) ).
fof(f_85_2,plain,
! [U_227,U_226] :
( c_Groups_Oabs__class_Oabs(U_226,U_227) = U_227
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_226,c_Groups_Ozero__class_Ozero(U_226)),U_227))
| ~ class_Groups_Oordered__ab__group__add__abs(U_226) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( c_Groups_Oabs__class_Oabs(U_226,U_227) = U_227
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_226,c_Groups_Ozero__class_Ozero(U_226)),U_227))
| ~ class_Groups_Oordered__ab__group__add__abs(U_226) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_86_2,plain,
! [U_229,U_228] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_228,c_Groups_Oabs__class_Oabs(U_228,U_229)),c_Groups_Ozero__class_Ozero(U_228)))
| U_229 != c_Groups_Ozero__class_Ozero(U_228) )
& ( U_229 = c_Groups_Ozero__class_Ozero(U_228)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_228,c_Groups_Oabs__class_Oabs(U_228,U_229)),c_Groups_Ozero__class_Ozero(U_228))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_228) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( U_229 = c_Groups_Ozero__class_Ozero(U_228)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_228,c_Groups_Oabs__class_Oabs(U_228,U_229)),c_Groups_Ozero__class_Ozero(U_228)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_228) ),
inference(clausify,[status(thm)],[f_86_2]) ).
cnf(f_86_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_228,c_Groups_Oabs__class_Oabs(U_228,U_229)),c_Groups_Ozero__class_Ozero(U_228)))
| U_229 != c_Groups_Ozero__class_Ozero(U_228)
| ~ class_Groups_Oordered__ab__group__add__abs(U_228) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(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_87_2,plain,
! [U_231,U_230] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_230,c_Groups_Ozero__class_Ozero(U_230)),c_Groups_Oabs__class_Oabs(U_230,U_231)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_230) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_230,c_Groups_Ozero__class_Ozero(U_230)),c_Groups_Oabs__class_Oabs(U_230,U_231)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_230) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__pos]) ).
fof(f_88_2,plain,
! [U_233,U_232] :
( c_Groups_Oabs__class_Oabs(U_232,U_233) = U_233
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_232,c_Groups_Ozero__class_Ozero(U_232)),U_233))
| ~ class_Groups_Oordered__ab__group__add__abs(U_232) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( c_Groups_Oabs__class_Oabs(U_232,U_233) = U_233
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_232,c_Groups_Ozero__class_Ozero(U_232)),U_233))
| ~ class_Groups_Oordered__ab__group__add__abs(U_232) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
inference(fof_nnf,[status(thm)],[fact_abs__Im__le__cmod]) ).
fof(f_89_2,plain,
! [U_234] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_234))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_234))),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_234))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_234))),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [V_s,V_y,V_r,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_r),V_s)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
| ~ hBOOL(hAPP(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_90_2,plain,
! [U_239,U_238,U_237,U_236,U_235] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_235,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_235),U_236),U_238))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_237),U_239)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_235,U_238)),U_239))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_235,U_236)),U_237))
| ~ class_RealVector_Oreal__normed__vector(U_235) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_235,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_235),U_236),U_238))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_237),U_239)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_235,U_238)),U_239))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_235,U_236)),U_237))
| ~ class_RealVector_Oreal__normed__vector(U_235) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y))),hAPP(hAPP(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_91_2,plain,
! [U_242,U_241,U_240] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_240,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_240),U_241),U_242))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_240,U_241)),c_RealVector_Onorm__class_Onorm(U_240,U_242))))
| ~ class_RealVector_Oreal__normed__vector(U_240) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_240,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_240),U_241),U_242))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_240,U_241)),c_RealVector_Onorm__class_Onorm(U_240,U_242))))
| ~ class_RealVector_Oreal__normed__vector(U_240) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [V_x_2,T_a] :
( ( ( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_92_2,plain,
! [U_244,U_243] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_243,U_244)))
| U_244 = c_Groups_Ozero__class_Ozero(U_243) )
& ( U_244 != c_Groups_Ozero__class_Ozero(U_243)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_243,U_244))) ) )
| ~ class_RealVector_Oreal__normed__vector(U_243) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( U_244 != c_Groups_Ozero__class_Ozero(U_243)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_243,U_244)))
| ~ class_RealVector_Oreal__normed__vector(U_243) ),
inference(clausify,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_243,U_244)))
| U_244 = c_Groups_Ozero__class_Ozero(U_243)
| ~ class_RealVector_Oreal__normed__vector(U_243) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [V_x_2,T_a] :
( ( ( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_93_2,plain,
! [U_246,U_245] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_245,U_246)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| U_246 != c_Groups_Ozero__class_Ozero(U_245) )
& ( U_246 = c_Groups_Ozero__class_Ozero(U_245)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_245,U_246)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
| ~ class_RealVector_Oreal__normed__vector(U_245) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( U_246 = c_Groups_Ozero__class_Ozero(U_245)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_245,U_246)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_RealVector_Oreal__normed__vector(U_245) ),
inference(clausify,[status(thm)],[f_93_2]) ).
cnf(f_93_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_245,U_246)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| U_246 != c_Groups_Ozero__class_Ozero(U_245)
| ~ class_RealVector_Oreal__normed__vector(U_245) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_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_94_2,plain,
! [U_247] :
( c_RealVector_Onorm__class_Onorm(U_247,c_Groups_Oone__class_Oone(U_247)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_247) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( c_RealVector_Onorm__class_Onorm(U_247,c_Groups_Oone__class_Oone(U_247)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_247) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [V_x,T_a] :
( ~ hBOOL(hAPP(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_95_2,plain,
! [U_249,U_248] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_248,U_249)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_RealVector_Oreal__normed__vector(U_248) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_248,U_249)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_RealVector_Oreal__normed__vector(U_248) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [V_x,T_a] :
( hBOOL(hAPP(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_96_2,plain,
! [U_251,U_250] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_250,U_251)))
| ~ class_RealVector_Oreal__normed__vector(U_250) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_250,U_251)))
| ~ class_RealVector_Oreal__normed__vector(U_250) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_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_97_2,plain,
! [U_253,U_252] :
( ( ( c_RealVector_Onorm__class_Onorm(U_252,U_253) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_253 != c_Groups_Ozero__class_Ozero(U_252) )
& ( U_253 = c_Groups_Ozero__class_Ozero(U_252)
| c_RealVector_Onorm__class_Onorm(U_252,U_253) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(U_252) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( U_253 = c_Groups_Ozero__class_Ozero(U_252)
| c_RealVector_Onorm__class_Onorm(U_252,U_253) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_252) ),
inference(clausify,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( c_RealVector_Onorm__class_Onorm(U_252,U_253) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_253 != c_Groups_Ozero__class_Ozero(U_252)
| ~ class_RealVector_Oreal__normed__vector(U_252) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_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_98_2,plain,
! [U_254] :
( c_RealVector_Onorm__class_Onorm(U_254,c_Groups_Ozero__class_Ozero(U_254)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_254) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( c_RealVector_Onorm__class_Onorm(U_254,c_Groups_Ozero__class_Ozero(U_254)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_254) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_99_2,plain,
! [U_256,U_255] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_255),U_256),U_256)),c_Groups_Ozero__class_Ozero(U_255)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,U_256),c_Groups_Ozero__class_Ozero(U_255))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,U_256),c_Groups_Ozero__class_Ozero(U_255)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_255),U_256),U_256)),c_Groups_Ozero__class_Ozero(U_255))) ) )
| ~ class_Rings_Olinordered__idom(U_255) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,U_256),c_Groups_Ozero__class_Ozero(U_255)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_255),U_256),U_256)),c_Groups_Ozero__class_Ozero(U_255)))
| ~ class_Rings_Olinordered__idom(U_255) ),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_255),U_256),U_256)),c_Groups_Ozero__class_Ozero(U_255)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_255,U_256),c_Groups_Ozero__class_Ozero(U_255)))
| ~ class_Rings_Olinordered__idom(U_255) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_x))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__refl]) ).
fof(f_100_2,plain,
! [U_258,U_257] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_257,U_258),U_258))
| ~ class_Orderings_Opreorder(U_257) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_257,U_258),U_258))
| ~ class_Orderings_Opreorder(U_257) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_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_101_2,plain,
! [U_259] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_259) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_259),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_259) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_259),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [V_gb_2,V_fa_2,T_a,T_b] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
| ? [B_x] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_2,B_x))) )
& ( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,B_x)),hAPP(V_gb_2,B_x)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_102_2,plain,
! [U_265,U_264,U_263,U_262] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_263,U_262),U_264),U_265))
| ? [U_261] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_262,hAPP(U_264,U_261)),hAPP(U_265,U_261))) )
& ( ! [U_260] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_262,hAPP(U_264,U_260)),hAPP(U_265,U_260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_263,U_262),U_264),U_265)) ) )
| ~ class_Orderings_Oord(U_262) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_265,U_264,U_263,U_262] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_263,U_262),U_264),U_265))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_262,hAPP(U_264,sK2(U_265,U_264,U_263,U_262))),hAPP(U_265,sK2(U_265,U_264,U_263,U_262)))) )
& ( ! [U_260] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_262,hAPP(U_264,U_260)),hAPP(U_265,U_260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_263,U_262),U_264),U_265)) ) )
| ~ class_Orderings_Oord(U_262) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_261,sK2(U_265,U_264,U_263,U_262))],[f_102_2]) ).
cnf(f_102_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_262,hAPP(U_264,U_260)),hAPP(U_265,U_260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_263,U_262),U_264),U_265))
| ~ class_Orderings_Oord(U_262) ),
inference(clausify,[status(thm)],[f_102_3]) ).
cnf(f_102_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_263,U_262),U_264),U_265))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_262,hAPP(U_264,sK2(U_265,U_264,U_263,U_262))),hAPP(U_265,sK2(U_265,U_264,U_263,U_262))))
| ~ class_Orderings_Oord(U_262) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__linear]) ).
fof(f_103_2,plain,
! [U_268,U_267,U_266] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_266,U_268),U_267))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_266,U_267),U_268))
| ~ class_Orderings_Olinorder(U_266) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_266,U_268),U_267))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_266,U_267),U_268))
| ~ class_Orderings_Olinorder(U_266) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
& hBOOL(hAPP(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_104_2,plain,
! [U_271,U_270,U_269] :
( ( ( U_270 = U_271
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_271),U_270))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_270),U_271)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_271),U_270))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_270),U_271)) )
| U_270 != U_271 ) )
| ~ class_Orderings_Oorder(U_269) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_270),U_271))
| U_270 != U_271
| ~ class_Orderings_Oorder(U_269) ),
inference(clausify,[status(thm)],[f_104_2]) ).
cnf(f_104_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_271),U_270))
| U_270 != U_271
| ~ class_Orderings_Oorder(U_269) ),
inference(clausify,[status(thm)],[f_104_2]) ).
cnf(f_104_5,plain,
( U_270 = U_271
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_271),U_270))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_269,U_270),U_271))
| ~ class_Orderings_Oorder(U_269) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| V_x != V_y
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__refl]) ).
fof(f_105_2,plain,
! [U_274,U_273,U_272] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_272,U_273),U_274))
| U_273 != U_274
| ~ class_Orderings_Opreorder(U_272) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
cnf(f_105_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_272,U_273),U_274))
| U_273 != U_274
| ~ class_Orderings_Opreorder(U_272) ),
inference(clausify,[status(thm)],[f_105_2]) ).
fof(f_106_1,plain,
! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_106_2,plain,
! [U_279,U_278,U_277,U_276,U_275] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_275,hAPP(U_277,U_279)),hAPP(U_278,U_279)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_276,U_275),U_277),U_278))
| ~ class_Orderings_Oord(U_275) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_275,hAPP(U_277,U_279)),hAPP(U_278,U_279)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_276,U_275),U_277),U_278))
| ~ class_Orderings_Oord(U_275) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( hBOOL(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(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_107_2,plain,
! [U_282,U_281,U_280] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_280,U_282),U_281))
| U_282 != U_281 )
& ( U_282 = U_281
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_280,U_282),U_281)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_280,U_281),U_282))
| ~ class_Orderings_Oorder(U_280) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( U_282 = U_281
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_280,U_282),U_281))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_280,U_281),U_282))
| ~ class_Orderings_Oorder(U_280) ),
inference(clausify,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_280,U_282),U_281))
| U_282 != U_281
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_280,U_281),U_282))
| ~ class_Orderings_Oorder(U_280) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_c))
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__le__trans]) ).
fof(f_108_2,plain,
! [U_286,U_285,U_284,U_283] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_283,U_284),U_286))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_283,U_285),U_286))
| U_284 != U_285
| ~ class_Orderings_Oord(U_283) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_283,U_284),U_286))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_283,U_285),U_286))
| U_284 != U_285
| ~ class_Orderings_Oord(U_283) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_b))
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I3_J]) ).
fof(f_109_2,plain,
! [U_290,U_289,U_288,U_287] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_287,U_290),U_288))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_287,U_290),U_289))
| U_288 != U_289
| ~ class_Orderings_Oorder(U_287) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_287,U_290),U_288))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_287,U_290),U_289))
| U_288 != U_289
| ~ class_Orderings_Oorder(U_287) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_c))
| V_b != V_c
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__le__eq__trans]) ).
fof(f_110_2,plain,
! [U_294,U_293,U_292,U_291] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_291,U_292),U_294))
| U_293 != U_294
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_291,U_292),U_293))
| ~ class_Orderings_Oord(U_291) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_291,U_292),U_294))
| U_293 != U_294
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_291,U_292),U_293))
| ~ class_Orderings_Oord(U_291) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_a))
| V_b != V_c
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I4_J]) ).
fof(f_111_2,plain,
! [U_298,U_297,U_296,U_295] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_295,U_298),U_297))
| U_296 != U_298
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_295,U_296),U_297))
| ~ class_Orderings_Oorder(U_295) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_295,U_298),U_297))
| U_296 != U_298
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_295,U_296),U_297))
| ~ class_Orderings_Oorder(U_295) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym]) ).
fof(f_112_2,plain,
! [U_301,U_300,U_299] :
( U_300 = U_301
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_299,U_301),U_300))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_299,U_300),U_301))
| ~ class_Orderings_Oorder(U_299) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( U_300 = U_301
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_299,U_301),U_300))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_299,U_300),U_301))
| ~ class_Orderings_Oorder(U_299) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__trans]) ).
fof(f_113_2,plain,
! [U_305,U_304,U_303,U_302] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_302,U_303),U_305))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_302,U_304),U_305))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_302,U_303),U_304))
| ~ class_Orderings_Opreorder(U_302) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_302,U_303),U_305))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_302,U_304),U_305))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_302,U_303),U_304))
| ~ class_Orderings_Opreorder(U_302) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
! [V_x,V_y,T_a] :
( V_x = V_y
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I5_J]) ).
fof(f_114_2,plain,
! [U_308,U_307,U_306] :
( U_308 = U_307
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_306,U_308),U_307))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_306,U_307),U_308))
| ~ class_Orderings_Oorder(U_306) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( U_308 = U_307
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_306,U_308),U_307))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_306,U_307),U_308))
| ~ class_Orderings_Oorder(U_306) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).
fof(f_115_2,plain,
! [U_312,U_311,U_310,U_309] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_309,U_312),U_311))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_309,U_312),U_310))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_309,U_310),U_311))
| ~ class_Orderings_Oorder(U_309) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_309,U_312),U_311))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_309,U_312),U_310))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_309,U_310),U_311))
| ~ class_Orderings_Oorder(U_309) ),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_1,plain,
! [V_x_2,V_gb_2,V_fa_2,T_a,T_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_fa_2,V_x_2)),hAPP(V_gb_2,V_x_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_116_2,plain,
! [U_317,U_316,U_315,U_314,U_313] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_313,hAPP(U_315,U_317)),hAPP(U_316,U_317)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_314,U_313),U_315),U_316))
| ~ class_Orderings_Oord(U_313) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_313,hAPP(U_315,U_317)),hAPP(U_316,U_317)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_314,U_313),U_315),U_316))
| ~ class_Orderings_Oord(U_313) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__cases]) ).
fof(f_117_2,plain,
! [U_320,U_319,U_318] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_318,U_320),U_319))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_318,U_319),U_320))
| ~ class_Orderings_Olinorder(U_318) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_318,U_320),U_319))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_318,U_319),U_320))
| ~ class_Orderings_Olinorder(U_318) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_1,plain,
! [V_x,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_x))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__irrefl]) ).
fof(f_118_2,plain,
! [U_322,U_321] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_321,U_322),U_322))
| ~ class_Orderings_Opreorder(U_321) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_321,U_322),U_322))
| ~ class_Orderings_Opreorder(U_321) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 != V_y_2
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
| hBOOL(hAPP(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_119_2,plain,
! [U_325,U_324,U_323] :
( ( ( U_324 != U_325
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_325),U_324))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_324),U_325)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_325),U_324))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_324),U_325))
| U_324 = U_325 ) )
| ~ class_Orderings_Olinorder(U_323) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_325),U_324))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_324),U_325))
| U_324 = U_325
| ~ class_Orderings_Olinorder(U_323) ),
inference(clausify,[status(thm)],[f_119_2]) ).
cnf(f_119_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_324),U_325))
| U_324 != U_325
| ~ class_Orderings_Olinorder(U_323) ),
inference(clausify,[status(thm)],[f_119_2]) ).
cnf(f_119_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_323,U_325),U_324))
| U_324 != U_325
| ~ class_Orderings_Olinorder(U_323) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
| hBOOL(hAPP(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_120_2,plain,
! [U_328,U_327,U_326] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_327),U_328))
| ( U_327 != U_328
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_328),U_327)) ) )
& ( U_327 = U_328
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_328),U_327))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_327),U_328)) ) )
| ~ class_Orderings_Olinorder(U_326) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( U_327 = U_328
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_328),U_327))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_327),U_328))
| ~ class_Orderings_Olinorder(U_326) ),
inference(clausify,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_328),U_327))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_327),U_328))
| ~ class_Orderings_Olinorder(U_326) ),
inference(clausify,[status(thm)],[f_120_2]) ).
cnf(f_120_5,plain,
( U_327 != U_328
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_326,U_327),U_328))
| ~ class_Orderings_Olinorder(U_326) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__less__linear]) ).
fof(f_121_2,plain,
! [U_331,U_330,U_329] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_329,U_331),U_330))
| U_330 = U_331
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_329,U_330),U_331))
| ~ class_Orderings_Olinorder(U_329) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_329,U_331),U_330))
| U_330 = U_331
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_329,U_330),U_331))
| ~ class_Orderings_Olinorder(U_329) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( ~ hBOOL(hAPP(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
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) ) )
| hBOOL(hAPP(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_122_2,plain,
! [U_334,U_333,U_332] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_332,U_334),U_333))
| U_334 != U_333 )
& ( U_334 = U_333
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_332,U_334),U_333)) ) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_332,U_333),U_334))
| ~ class_Orderings_Olinorder(U_332) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( U_334 = U_333
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_332,U_334),U_333))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_332,U_333),U_334))
| ~ class_Orderings_Olinorder(U_332) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_332,U_334),U_333))
| U_334 != U_333
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_332,U_333),U_334))
| ~ class_Orderings_Olinorder(U_332) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE]) ).
fof(f_123_2,plain,
! [U_337,U_336,U_335] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_335,U_337),U_336))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_335,U_336),U_337))
| U_336 = U_337
| ~ class_Orderings_Olinorder(U_335) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_335,U_337),U_336))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_335,U_336),U_337))
| U_336 = U_337
| ~ class_Orderings_Olinorder(U_335) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__neq]) ).
fof(f_124_2,plain,
! [U_340,U_339,U_338] :
( U_339 != U_340
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_338,U_339),U_340))
| ~ class_Orderings_Oorder(U_338) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( U_339 != U_340
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_338,U_339),U_340))
| ~ class_Orderings_Oorder(U_338) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [V_y,V_x,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__not__sym]) ).
fof(f_125_2,plain,
! [U_343,U_342,U_341] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_341,U_343),U_342))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_341,U_342),U_343))
| ~ class_Orderings_Opreorder(U_341) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_341,U_343),U_342))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_341,U_342),U_343))
| ~ class_Orderings_Opreorder(U_341) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [V_y,V_x,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(f_126_2,plain,
! [U_346,U_345,U_344] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_344,U_346),U_345))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_344,U_345),U_346))
| ~ class_Orderings_Opreorder(U_344) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_344,U_346),U_345))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_344,U_345),U_346))
| ~ class_Orderings_Opreorder(U_344) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq]) ).
fof(f_127_2,plain,
! [U_349,U_348,U_347] :
( U_348 != U_349
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_347,U_348),U_349))
| ~ class_Orderings_Oorder(U_347) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( U_348 != U_349
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_347,U_348),U_349))
| ~ class_Orderings_Oorder(U_347) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [V_y,V_x,T_a] :
( V_y != V_x
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2]) ).
fof(f_128_2,plain,
! [U_352,U_351,U_350] :
( U_352 != U_351
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_350,U_351),U_352))
| ~ class_Orderings_Oorder(U_350) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( U_352 != U_351
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_350,U_351),U_352))
| ~ class_Orderings_Oorder(U_350) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [V_b,V_a,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym_H]) ).
fof(f_129_2,plain,
! [U_355,U_354,U_353] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_353,U_355),U_354))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_353,U_354),U_355))
| ~ class_Orderings_Opreorder(U_353) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_353,U_355),U_354))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_353,U_354),U_355))
| ~ class_Orderings_Opreorder(U_353) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [V_a,V_b,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I9_J]) ).
fof(f_130_2,plain,
! [U_358,U_357,U_356] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_356,U_358),U_357))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_356,U_357),U_358))
| ~ class_Orderings_Oorder(U_356) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_356,U_358),U_357))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_356,U_357),U_358))
| ~ class_Orderings_Oorder(U_356) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_c))
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__less__trans]) ).
fof(f_131_2,plain,
! [U_362,U_361,U_360,U_359] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_359,U_360),U_362))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_359,U_361),U_362))
| U_360 != U_361
| ~ class_Orderings_Oord(U_359) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_359,U_360),U_362))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_359,U_361),U_362))
| U_360 != U_361
| ~ class_Orderings_Oord(U_359) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_b))
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I1_J]) ).
fof(f_132_2,plain,
! [U_366,U_365,U_364,U_363] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_363,U_366),U_364))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_363,U_366),U_365))
| U_364 != U_365
| ~ class_Orderings_Oorder(U_363) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_363,U_366),U_364))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_363,U_366),U_365))
| U_364 != U_365
| ~ class_Orderings_Oorder(U_363) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_c))
| V_b != V_c
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__less__eq__trans]) ).
fof(f_133_2,plain,
! [U_370,U_369,U_368,U_367] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_367,U_368),U_370))
| U_369 != U_370
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_367,U_368),U_369))
| ~ class_Orderings_Oord(U_367) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_367,U_368),U_370))
| U_369 != U_370
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_367,U_368),U_369))
| ~ class_Orderings_Oord(U_367) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_a))
| V_b != V_c
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I2_J]) ).
fof(f_134_2,plain,
! [U_374,U_373,U_372,U_371] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_371,U_374),U_373))
| U_372 != U_374
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_371,U_372),U_373))
| ~ class_Orderings_Oorder(U_371) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_371,U_374),U_373))
| U_372 != U_374
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_371,U_372),U_373))
| ~ class_Orderings_Oorder(U_371) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__trans]) ).
fof(f_135_2,plain,
! [U_378,U_377,U_376,U_375] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_375,U_376),U_378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_375,U_377),U_378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_375,U_376),U_377))
| ~ class_Orderings_Opreorder(U_375) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_375,U_376),U_378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_375,U_377),U_378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_375,U_376),U_377))
| ~ class_Orderings_Opreorder(U_375) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I10_J]) ).
fof(f_136_2,plain,
! [U_382,U_381,U_380,U_379] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_379,U_382),U_381))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_379,U_382),U_380))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_379,U_380),U_381))
| ~ class_Orderings_Oorder(U_379) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_379,U_382),U_381))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_379,U_382),U_380))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_379,U_380),U_381))
| ~ class_Orderings_Oorder(U_379) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [V_y,V_x,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym]) ).
fof(f_137_2,plain,
! [U_385,U_384,U_383] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_383,U_385),U_384))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_383,U_384),U_385))
| ~ class_Orderings_Opreorder(U_383) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_383,U_385),U_384))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_383,U_384),U_385))
| ~ class_Orderings_Opreorder(U_383) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__cases]) ).
fof(f_138_2,plain,
! [U_388,U_387,U_386] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_386,U_388),U_387))
| U_387 = U_388
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_386,U_387),U_388))
| ~ class_Orderings_Olinorder(U_386) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_386,U_388),U_387))
| U_387 = U_388
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_386,U_387),U_388))
| ~ class_Orderings_Olinorder(U_386) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
| hBOOL(hAPP(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_139_2,plain,
! [U_391,U_390,U_389] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_389,U_390),U_391))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_389,U_391),U_390)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_389,U_391),U_390))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_389,U_390),U_391)) ) )
| ~ class_Orderings_Olinorder(U_389) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_389,U_391),U_390))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_389,U_390),U_391))
| ~ class_Orderings_Olinorder(U_389) ),
inference(clausify,[status(thm)],[f_139_2]) ).
cnf(f_139_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_389,U_390),U_391))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_389,U_391),U_390))
| ~ class_Orderings_Olinorder(U_389) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y_2),V_x_2))
| hBOOL(hAPP(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_140_2,plain,
! [U_394,U_393,U_392] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_392,U_393),U_394))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_392,U_394),U_393)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_392,U_394),U_393))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_392,U_393),U_394)) ) )
| ~ class_Orderings_Olinorder(U_392) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_392,U_394),U_393))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_392,U_393),U_394))
| ~ class_Orderings_Olinorder(U_392) ),
inference(clausify,[status(thm)],[f_140_2]) ).
cnf(f_140_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_392,U_393),U_394))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_392,U_394),U_393))
| ~ class_Orderings_Olinorder(U_392) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear]) ).
fof(f_141_2,plain,
! [U_397,U_396,U_395] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_395,U_397),U_396))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_395,U_396),U_397))
| ~ class_Orderings_Olinorder(U_395) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_395,U_397),U_396))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_395,U_396),U_397))
| ~ class_Orderings_Olinorder(U_395) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(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_142_2,plain,
! [U_400,U_399,U_398] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_398,U_399),U_400))
| U_399 = U_400
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_398,U_399),U_400)) )
& ( ( U_399 != U_400
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_398,U_399),U_400)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_398,U_399),U_400)) ) )
| ~ class_Orderings_Oorder(U_398) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_398,U_399),U_400))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_398,U_399),U_400))
| ~ class_Orderings_Oorder(U_398) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( U_399 != U_400
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_398,U_399),U_400))
| ~ class_Orderings_Oorder(U_398) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_398,U_399),U_400))
| U_399 = U_400
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_398,U_399),U_400))
| ~ class_Orderings_Oorder(U_398) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) )
& ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y_2),V_x_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(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_143_2,plain,
! [U_403,U_402,U_401] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_401,U_402),U_403))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_403),U_402))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_402),U_403)) )
& ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_403),U_402))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_402),U_403)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_401,U_402),U_403)) ) )
| ~ class_Orderings_Opreorder(U_401) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_402),U_403))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_401,U_402),U_403))
| ~ class_Orderings_Opreorder(U_401) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_403),U_402))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_401,U_402),U_403))
| ~ class_Orderings_Opreorder(U_401) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_401,U_402),U_403))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_403),U_402))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_401,U_402),U_403))
| ~ class_Orderings_Opreorder(U_401) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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_144_2,plain,
! [U_406,U_405,U_404] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_404,U_405),U_406))
| ( U_405 != U_406
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_404,U_405),U_406)) ) )
& ( U_405 = U_406
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_404,U_405),U_406))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_404,U_405),U_406)) ) )
| ~ class_Orderings_Oorder(U_404) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( U_405 = U_406
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_404,U_405),U_406))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_404,U_405),U_406))
| ~ class_Orderings_Oorder(U_404) ),
inference(clausify,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_404,U_405),U_406))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_404,U_405),U_406))
| ~ class_Orderings_Oorder(U_404) ),
inference(clausify,[status(thm)],[f_144_2]) ).
cnf(f_144_5,plain,
( U_405 != U_406
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_404,U_405),U_406))
| ~ class_Orderings_Oorder(U_404) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leI]) ).
fof(f_145_2,plain,
! [U_409,U_408,U_407] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_407,U_409),U_408))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_407,U_408),U_409))
| ~ class_Orderings_Olinorder(U_407) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_407,U_409),U_408))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_407,U_408),U_409))
| ~ class_Orderings_Olinorder(U_407) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [V_x,V_y,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__leE]) ).
fof(f_146_2,plain,
! [U_412,U_411,U_410] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_410,U_412),U_411))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_410,U_411),U_412))
| ~ class_Orderings_Olinorder(U_410) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_410,U_412),U_411))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_410,U_411),U_412))
| ~ class_Orderings_Olinorder(U_410) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x_2),V_y_2)) ) )
| hBOOL(hAPP(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_147_2,plain,
! [U_415,U_414,U_413] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_413,U_414),U_415))
| U_414 != U_415 )
& ( U_414 = U_415
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_413,U_414),U_415)) ) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_413,U_414),U_415))
| ~ class_Orderings_Olinorder(U_413) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( U_414 = U_415
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_413,U_414),U_415))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_413,U_414),U_415))
| ~ class_Orderings_Olinorder(U_413) ),
inference(clausify,[status(thm)],[f_147_2]) ).
cnf(f_147_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_413,U_414),U_415))
| U_414 != U_415
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_413,U_414),U_415))
| ~ class_Orderings_Olinorder(U_413) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans]) ).
fof(f_148_2,plain,
! [U_418,U_417,U_416] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_416,U_417),U_418))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_416,U_417),U_418))
| U_417 = U_418
| ~ class_Orderings_Oorder(U_416) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_416,U_417),U_418))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_416,U_417),U_418))
| U_417 = U_418
| ~ class_Orderings_Oorder(U_416) ),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I12_J]) ).
fof(f_149_2,plain,
! [U_421,U_420,U_419] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_419,U_421),U_420))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_419,U_421),U_420))
| U_420 = U_421
| ~ class_Orderings_Oorder(U_419) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_419,U_421),U_420))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_419,U_421),U_420))
| U_420 = U_421
| ~ class_Orderings_Oorder(U_419) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [V_x,V_y,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leD]) ).
fof(f_150_2,plain,
! [U_424,U_423,U_422] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_422,U_424),U_423))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_422,U_423),U_424))
| ~ class_Orderings_Olinorder(U_422) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_422,U_424),U_423))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_422,U_423),U_424))
| ~ class_Orderings_Olinorder(U_422) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__le]) ).
fof(f_151_2,plain,
! [U_427,U_426,U_425] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_425,U_426),U_427))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_425,U_426),U_427))
| ~ class_Orderings_Opreorder(U_425) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_425,U_426),U_427))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_425,U_426),U_427))
| ~ class_Orderings_Opreorder(U_425) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ hBOOL(hAPP(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
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(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_152_2,plain,
! [U_430,U_429,U_428] :
( ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_428,U_429),U_430))
| U_429 != U_430 )
& ( U_429 = U_430
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_428,U_429),U_430)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_428,U_429),U_430))
| ~ class_Orderings_Olinorder(U_428) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( U_429 = U_430
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_428,U_429),U_430))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_428,U_429),U_430))
| ~ class_Orderings_Olinorder(U_428) ),
inference(clausify,[status(thm)],[f_152_2]) ).
cnf(f_152_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_428,U_429),U_430))
| U_429 != U_430
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_428,U_429),U_430))
| ~ class_Orderings_Olinorder(U_428) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq]) ).
fof(f_153_2,plain,
! [U_433,U_432,U_431] :
( U_432 = U_433
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_431,U_432),U_433))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_431,U_432),U_433))
| ~ class_Orderings_Oorder(U_431) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( U_432 = U_433
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_431,U_432),U_433))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_431,U_432),U_433))
| ~ class_Orderings_Oorder(U_431) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| V_a = V_b
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans]) ).
fof(f_154_2,plain,
! [U_436,U_435,U_434] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_434,U_435),U_436))
| U_435 = U_436
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_434,U_435),U_436))
| ~ class_Orderings_Oorder(U_434) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_434,U_435),U_436))
| U_435 = U_436
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_434,U_435),U_436))
| ~ class_Orderings_Oorder(U_434) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_1,plain,
! [V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
| V_a = V_b
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I11_J]) ).
fof(f_155_2,plain,
! [U_439,U_438,U_437] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_437,U_438),U_439))
| U_439 = U_438
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_437,U_438),U_439))
| ~ class_Orderings_Oorder(U_437) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_437,U_438),U_439))
| U_439 = U_438
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_437,U_438),U_439))
| ~ class_Orderings_Oorder(U_437) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le__trans]) ).
fof(f_156_2,plain,
! [U_443,U_442,U_441,U_440] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_440,U_441),U_443))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_440,U_442),U_443))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_440,U_441),U_442))
| ~ class_Orderings_Opreorder(U_440) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_440,U_441),U_443))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_440,U_442),U_443))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_440,U_441),U_442))
| ~ class_Orderings_Opreorder(U_440) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_z),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I7_J]) ).
fof(f_157_2,plain,
! [U_447,U_446,U_445,U_444] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_444,U_447),U_446))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_444,U_447),U_445))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_444,U_445),U_446))
| ~ class_Orderings_Oorder(U_444) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_444,U_447),U_446))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_444,U_447),U_445))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_444,U_445),U_446))
| ~ class_Orderings_Oorder(U_444) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_y))
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less__trans]) ).
fof(f_158_2,plain,
! [U_451,U_450,U_449,U_448] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_448,U_449),U_451))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_448,U_450),U_451))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_448,U_449),U_450))
| ~ class_Orderings_Opreorder(U_448) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_448,U_449),U_451))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_448,U_450),U_451))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_448,U_449),U_450))
| ~ class_Orderings_Opreorder(U_448) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
! [V_z,V_x,V_y,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_z),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_x))
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I8_J]) ).
fof(f_159_2,plain,
! [U_455,U_454,U_453,U_452] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_452,U_455),U_454))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_452,U_455),U_453))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_452,U_453),U_454))
| ~ class_Orderings_Oorder(U_452) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_452,U_455),U_454))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_452,U_455),U_453))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_452,U_453),U_454))
| ~ class_Orderings_Oorder(U_452) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [V_a_2,T_a] :
( ( ( hAPP(hAPP(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)
| hAPP(hAPP(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_160_2,plain,
! [U_457,U_456] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_456),U_457),U_457) = c_Groups_Ozero__class_Ozero(U_456)
| U_457 != c_Groups_Ozero__class_Ozero(U_456) )
& ( U_457 = c_Groups_Ozero__class_Ozero(U_456)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_456),U_457),U_457) != c_Groups_Ozero__class_Ozero(U_456) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_456) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( U_457 = c_Groups_Ozero__class_Ozero(U_456)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_456),U_457),U_457) != c_Groups_Ozero__class_Ozero(U_456)
| ~ class_Groups_Olinordered__ab__group__add(U_456) ),
inference(clausify,[status(thm)],[f_160_2]) ).
cnf(f_160_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_456),U_457),U_457) = c_Groups_Ozero__class_Ozero(U_456)
| U_457 != c_Groups_Ozero__class_Ozero(U_456)
| ~ class_Groups_Olinordered__ab__group__add(U_456) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_Im_Ozero]) ).
cnf(f_161_2,plain,
hAPP(c_Complex_OIm,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_161_1]) ).
fof(f_162_1,plain,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_complex__Im__one]) ).
cnf(f_162_2,plain,
hAPP(c_Complex_OIm,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_162_1]) ).
fof(f_163_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_163_2,plain,
! [U_459,U_458] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_458,U_459)) = c_RealVector_Onorm__class_Onorm(U_458,U_459)
| ~ class_RealVector_Oreal__normed__vector(U_458) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_458,U_459)) = c_RealVector_Onorm__class_Onorm(U_458,U_459)
| ~ class_RealVector_Oreal__normed__vector(U_458) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_1,plain,
! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y)),
inference(fof_nnf,[status(thm)],[fact_Im_Oadd]) ).
fof(f_164_2,plain,
! [U_461,U_460] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_460),U_461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_460)),hAPP(c_Complex_OIm,U_461)),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_460),U_461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_460)),hAPP(c_Complex_OIm,U_461)),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
inference(fof_nnf,[status(thm)],[fact_le0]) ).
fof(f_165_2,plain,
! [U_462] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_462)),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_462)),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_1,plain,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_less__zeroE]) ).
fof(f_166_2,plain,
! [U_463] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_463),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_463),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_167_2,plain,
! [U_465,U_464] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_464),c_Groups_Ozero__class_Ozero(U_464)),U_465) = U_465
| ~ class_Rings_Ocomm__semiring__1(U_464) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_464),c_Groups_Ozero__class_Ozero(U_464)),U_465) = U_465
| ~ class_Rings_Ocomm__semiring__1(U_464) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_168_2,plain,
! [U_467,U_466] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_466),U_467),c_Groups_Ozero__class_Ozero(U_466)) = U_467
| ~ class_Rings_Ocomm__semiring__1(U_466) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_466),U_467),c_Groups_Ozero__class_Ozero(U_466)) = U_467
| ~ class_Rings_Ocomm__semiring__1(U_466) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( V_b_2 = hAPP(hAPP(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 != hAPP(hAPP(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_169_2,plain,
! [U_470,U_469,U_468] :
( ( ( U_469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_468),U_469),U_470)
| U_470 != c_Groups_Ozero__class_Ozero(U_468) )
& ( U_470 = c_Groups_Ozero__class_Ozero(U_468)
| U_469 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_468),U_469),U_470) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_468) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( U_470 = c_Groups_Ozero__class_Ozero(U_468)
| U_469 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_468),U_469),U_470)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_468) ),
inference(clausify,[status(thm)],[f_169_2]) ).
cnf(f_169_4,plain,
( U_469 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_468),U_469),U_470)
| U_470 != c_Groups_Ozero__class_Ozero(U_468)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_468) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_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_170_2,plain,
! [U_472,U_471] :
( ( ( c_RealVector_Onorm__class_Onorm(U_471,c_Groups_Osgn__class_Osgn(U_471,U_472)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_472 = c_Groups_Ozero__class_Ozero(U_471) )
& ( c_RealVector_Onorm__class_Onorm(U_471,c_Groups_Osgn__class_Osgn(U_471,U_472)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_472 != c_Groups_Ozero__class_Ozero(U_471) ) )
| ~ class_RealVector_Oreal__normed__vector(U_471) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( c_RealVector_Onorm__class_Onorm(U_471,c_Groups_Osgn__class_Osgn(U_471,U_472)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_472 != c_Groups_Ozero__class_Ozero(U_471)
| ~ class_RealVector_Oreal__normed__vector(U_471) ),
inference(clausify,[status(thm)],[f_170_2]) ).
cnf(f_170_4,plain,
( c_RealVector_Onorm__class_Onorm(U_471,c_Groups_Osgn__class_Osgn(U_471,U_472)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_472 = c_Groups_Ozero__class_Ozero(U_471)
| ~ class_RealVector_Oreal__normed__vector(U_471) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [V_p_2,T_a] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_p_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_p_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff]) ).
fof(f_171_2,plain,
! [U_474,U_473] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_473,U_474) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_474 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_473)) )
& ( U_474 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_473))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_473,U_474) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(U_473) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( U_474 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_473))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_473,U_474) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(U_473) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_4,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_473,U_474) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_474 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_473))
| ~ class_Groups_Ozero(U_473) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_y),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x),V_a))
| ~ class_Rings_Olinordered__semiring__1__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__lt]) ).
fof(f_172_2,plain,
! [U_480,U_479,U_478,U_477,U_476,U_475] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_475,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),U_479),U_476)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),U_480),U_478))),U_477))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_475),U_479),U_480) != c_Groups_Oone__class_Oone(U_475)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_475,c_Groups_Ozero__class_Ozero(U_475)),U_480))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_475,c_Groups_Ozero__class_Ozero(U_475)),U_479))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_475,U_478),U_477))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_475,U_476),U_477))
| ~ class_Rings_Olinordered__semiring__1__strict(U_475) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_475,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),U_479),U_476)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),U_480),U_478))),U_477))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_475),U_479),U_480) != c_Groups_Oone__class_Oone(U_475)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_475,c_Groups_Ozero__class_Ozero(U_475)),U_480))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_475,c_Groups_Ozero__class_Ozero(U_475)),U_479))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_475,U_478),U_477))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_475,U_476),U_477))
| ~ class_Rings_Olinordered__semiring__1__strict(U_475) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(fof_nnf,[status(thm)],[fact_g_I2_J]) ).
cnf(f_173_2,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)))),
inference(clausify,[status(thm)],[f_173_1]) ).
fof(f_174_1,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(fof_nnf,[status(thm)],[fact_f_I2_J]) ).
cnf(f_174_2,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(clausify,[status(thm)],[f_174_1]) ).
fof(f_175_1,plain,
! [V_j,V_i] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)),
inference(fof_nnf,[status(thm)],[fact_not__add__less1]) ).
fof(f_175_2,plain,
! [U_482,U_481] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_481),U_482)),U_481)),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_481),U_482)),U_481)),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [V_i,V_j] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
inference(fof_nnf,[status(thm)],[fact_not__add__less2]) ).
fof(f_176_2,plain,
! [U_484,U_483] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_483),U_484)),U_484)),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_483),U_484)),U_484)),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_1,plain,
! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
inference(fof_nnf,[status(thm)],[fact_le__add2]) ).
fof(f_177_2,plain,
! [U_486,U_485] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_486),U_485))),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_486),U_485))),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_1,plain,
! [V_m,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))),
inference(fof_nnf,[status(thm)],[fact_le__add1]) ).
fof(f_178_2,plain,
! [U_488,U_487] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_487),U_488))),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_487),U_488))),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_491,U_490,U_489] :
( c_RealVector_Onorm__class_Onorm(U_489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_489),U_490),U_491)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_489,U_490)),c_RealVector_Onorm__class_Onorm(U_489,U_491))
| ~ class_RealVector_Oreal__normed__div__algebra(U_489) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( c_RealVector_Onorm__class_Onorm(U_489,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_489),U_490),U_491)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_489,U_490)),c_RealVector_Onorm__class_Onorm(U_489,U_491))
| ~ class_RealVector_Oreal__normed__div__algebra(U_489) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ! [B_k] : V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) )
& ( ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).
fof(f_180_2,plain,
! [U_495,U_494] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_494),U_495))
| ! [U_493] : U_495 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_494),U_493) )
& ( ? [U_492] : U_495 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_494),U_492)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_494),U_495)) ) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
( ! [U_499,U_497] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_497),U_499))
| ! [U_493] : U_499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_497),U_493) )
& ! [U_498,U_496] :
( ? [U_492] : U_498 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_496),U_492)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_496),U_498)) ) ),
inference(miniscope,[status(thm)],[f_180_2]) ).
fof(f_180_4,plain,
( ! [U_499,U_497] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_497),U_499))
| ! [U_493] : U_499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_497),U_493) )
& ! [U_498,U_496] :
( U_498 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_496),sK3(U_498,U_496))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_496),U_498)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_492,sK3(U_498,U_496))],[f_180_3]) ).
cnf(f_180_5,plain,
( U_498 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_496),sK3(U_498,U_496))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_496),U_498)) ),
inference(clausify,[status(thm)],[f_180_4]) ).
cnf(f_180_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_497),U_499))
| U_499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_497),U_493) ),
inference(clausify,[status(thm)],[f_180_4]) ).
fof(f_181_1,plain,
! [V_gb_2,V_fa_2,T_a,T_b] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_gb_2),V_fa_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) )
& ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_gb_2),V_fa_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_fa_2),V_gb_2)) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_181_2,plain,
! [U_503,U_502,U_501,U_500] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_501,U_500),U_502),U_503))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_503),U_502))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_502),U_503)) )
& ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_503),U_502))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_502),U_503)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_501,U_500),U_502),U_503)) ) )
| ~ class_Orderings_Oord(U_500) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_502),U_503))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_501,U_500),U_502),U_503))
| ~ class_Orderings_Oord(U_500) ),
inference(clausify,[status(thm)],[f_181_2]) ).
cnf(f_181_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_503),U_502))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_501,U_500),U_502),U_503))
| ~ class_Orderings_Oord(U_500) ),
inference(clausify,[status(thm)],[f_181_2]) ).
cnf(f_181_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_501,U_500),U_502),U_503))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_503),U_502))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_501,U_500),U_502),U_503))
| ~ class_Orderings_Oord(U_500) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).
fof(f_182_2,plain,
! [U_506,U_505,U_504] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_504),U_505)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_504),U_506)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_505),U_506)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_505),U_506))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_504),U_505)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_504),U_506))) ) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
( ! [U_512,U_510] :
( ! [U_508] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_508),U_510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_508),U_512)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_510),U_512)) )
& ! [U_511,U_509] :
( ! [U_507] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_507),U_509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_507),U_511)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_509),U_511)) ) ),
inference(miniscope,[status(thm)],[f_182_2]) ).
cnf(f_182_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_507),U_509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_507),U_511)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_509),U_511)) ),
inference(clausify,[status(thm)],[f_182_3]) ).
cnf(f_182_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_508),U_510)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_508),U_512)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_510),U_512)) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).
fof(f_183_2,plain,
! [U_515,U_514,U_513] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_513),U_514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_513),U_515)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_514),U_515)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_514),U_515))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_513),U_514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_513),U_515))) ) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
( ! [U_521,U_519] :
( ! [U_517] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_517),U_519)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_517),U_521)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_519),U_521)) )
& ! [U_520,U_518] :
( ! [U_516] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_516),U_518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_516),U_520)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_518),U_520)) ) ),
inference(miniscope,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_516),U_518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_516),U_520)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_518),U_520)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_517),U_519)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_517),U_521)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_519),U_521)) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).
fof(f_184_2,plain,
! [U_524,U_523,U_522] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_523),U_524)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_522),U_523)) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_523),U_524)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_522),U_523)) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_1,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).
fof(f_185_2,plain,
! [U_527,U_526,U_525] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_527),U_526)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_525),U_526)) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_525),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_527),U_526)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_525),U_526)) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_1,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).
fof(f_186_2,plain,
! [U_530,U_529,U_528] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_529),U_530)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_528),U_529)) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_529),U_530)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_528),U_529)) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [V_m,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).
fof(f_187_2,plain,
! [U_533,U_532,U_531] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_531),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_533),U_532)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_531),U_532)) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_531),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_533),U_532)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_531),U_532)) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).
fof(f_188_2,plain,
! [U_536,U_535,U_534] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_534),U_536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_535),U_536)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_534),U_535)) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_534),U_536)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_535),U_536)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_534),U_535)) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).
fof(f_189_2,plain,
! [U_539,U_538,U_537] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_537),U_539)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_538),U_539)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_537),U_538)) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_537),U_539)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_538),U_539)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_537),U_538)) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).
fof(f_190_2,plain,
! [U_543,U_542,U_541,U_540] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_540),U_542)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_541),U_543)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_542),U_543))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_540),U_541)) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_540),U_542)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_541),U_543)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_542),U_543))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_540),U_541)) ),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).
fof(f_191_2,plain,
! [U_547,U_546,U_545,U_544] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_544),U_546)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_545),U_547)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_546),U_547))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_544),U_545)) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_544),U_546)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_545),U_547)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_546),U_547))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_544),U_545)) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [V_n,V_m,V_l,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k),V_l)) ),
inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).
fof(f_192_2,plain,
! [U_551,U_550,U_549,U_548] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_550),U_551))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_550),U_549) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_548),U_551)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_548),U_549)) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_550),U_551))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_550),U_549) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_548),U_551)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_548),U_549)) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).
fof(f_193_2,plain,
! [U_554,U_553,U_552] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_552),U_554))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_552),U_553)),U_554)) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_552),U_554))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_552),U_553)),U_554)) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_1,plain,
! [V_n,V_k,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).
fof(f_194_2,plain,
! [U_557,U_556,U_555] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_556),U_557))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_555),U_556)),U_557)) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
! [U_557,U_556] :
( ! [U_555] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_555),U_556)),U_557))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_556),U_557)) ),
inference(miniscope,[status(thm)],[f_194_2]) ).
cnf(f_194_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_555),U_556)),U_557))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_556),U_557)) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [V_n,V_k,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).
fof(f_195_2,plain,
! [U_560,U_559,U_558] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_558),U_560))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_558),U_559)),U_560)) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_558),U_560))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_558),U_559)),U_560)) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_1,plain,
! [V_n,V_k,V_m] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_add__leE]) ).
fof(f_196_2,plain,
! [U_563,U_562,U_561] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_562),U_563))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_561),U_563)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_561),U_562)),U_563)) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_561),U_563))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_561),U_562)),U_563)) ),
inference(clausify,[status(thm)],[f_196_2]) ).
cnf(f_196_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_562),U_563))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_561),U_562)),U_563)) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_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_197_2,plain,
! [U_566,U_565,U_564] :
( c_Groups_Osgn__class_Osgn(U_564,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_564),U_565),U_566)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_564),c_Groups_Osgn__class_Osgn(U_564,U_565)),c_Groups_Osgn__class_Osgn(U_564,U_566))
| ~ class_RealVector_Oreal__normed__div__algebra(U_564) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( c_Groups_Osgn__class_Osgn(U_564,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_564),U_565),U_566)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_564),c_Groups_Osgn__class_Osgn(U_564,U_565)),c_Groups_Osgn__class_Osgn(U_564,U_566))
| ~ class_RealVector_Oreal__normed__div__algebra(U_564) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_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_198_2,plain,
! [U_569,U_568,U_567] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_567),U_568),U_569) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_567),U_569),U_568)
| ~ class_Rings_Ocomm__semiring__1(U_567) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_567),U_568),U_569) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_567),U_569),U_568)
| ~ class_Rings_Ocomm__semiring__1(U_567) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_573,U_572,U_571,U_570] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_572),U_573)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_571),U_573))
| ~ class_Rings_Ocomm__semiring__1(U_570) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_572),U_573)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_570),U_571),U_573))
| ~ class_Rings_Ocomm__semiring__1(U_570) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_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_200_2,plain,
! [U_577,U_576,U_575,U_574] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),U_575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),U_576),U_577)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),U_575),U_576)),U_577)
| ~ class_Rings_Ocomm__semiring__1(U_574) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),U_575),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),U_576),U_577)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_574),U_575),U_576)),U_577)
| ~ class_Rings_Ocomm__semiring__1(U_574) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_581,U_580,U_579,U_578] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),U_579),U_580)),U_581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),U_579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),U_580),U_581))
| ~ class_Rings_Ocomm__semiring__1(U_578) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),U_579),U_580)),U_581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),U_579),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_578),U_580),U_581))
| ~ class_Rings_Ocomm__semiring__1(U_578) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_585,U_584,U_583,U_582] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),U_583),U_584)),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),U_583),U_585)),U_584)
| ~ class_Rings_Ocomm__semiring__1(U_582) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),U_583),U_584)),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_582),U_583),U_585)),U_584)
| ~ class_Rings_Ocomm__semiring__1(U_582) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_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_203_2,plain,
! [U_590,U_589,U_588,U_587,U_586] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_587),U_588)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_589),U_590)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_589),U_590)))
| ~ class_Rings_Ocomm__semiring__1(U_586) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_587),U_588)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_589),U_590)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_587),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_588),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_586),U_589),U_590)))
| ~ class_Rings_Ocomm__semiring__1(U_586) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_204_2,plain,
! [U_595,U_594,U_593,U_592,U_591] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_592),U_593)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_594),U_595)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_592),U_593)),U_595))
| ~ class_Rings_Ocomm__semiring__1(U_591) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_592),U_593)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_594),U_595)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_591),U_592),U_593)),U_595))
| ~ class_Rings_Ocomm__semiring__1(U_591) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_600,U_599,U_598,U_597,U_596] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_597),U_598)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_599),U_600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_597),U_599)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_598),U_600))
| ~ class_Rings_Ocomm__semiring__1(U_596) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_597),U_598)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_599),U_600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_597),U_599)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_596),U_598),U_600))
| ~ class_Rings_Ocomm__semiring__1(U_596) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
! [V_P_2,V_n_2,V_m_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& V_m_2 = V_n_2 )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_206_2,plain,
! [U_603,U_602,U_601] :
( hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| ( ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602),U_601)) )
| ( ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
& U_601 = U_602 )
| ( ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_601),U_602)) ) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| U_601 = U_602
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_601),U_602)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_4,plain,
( ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| U_601 = U_602
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_601),U_602)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_601),U_602)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_6,plain,
( ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_601),U_602)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_7,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| U_601 = U_602
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_8,plain,
( ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| U_601 = U_602
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_9,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_10,plain,
( ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601))
| ~ hBOOL(hAPP(hAPP(U_603,U_602),U_601)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ( V_m != V_n
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le]) ).
fof(f_207_2,plain,
! [U_605,U_604] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_604),U_605))
| ( U_604 != U_605
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_604),U_605)) ) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_604),U_605))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_604),U_605)) ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( U_604 != U_605
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_604),U_605)) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [V_l,V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_l))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono]) ).
fof(f_208_2,plain,
! [U_609,U_608,U_607,U_606] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_606),U_608)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_607),U_609)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_608),U_609))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_606),U_607)) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_606),U_608)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_607),U_609)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_608),U_609))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_606),U_607)) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).
fof(f_209_2,plain,
! [U_611,U_610] :
( U_610 = U_611
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_611),U_610))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_610),U_611)) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( U_610 = U_611
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_611),U_610))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_610),U_611)) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_le__trans]) ).
fof(f_210_2,plain,
! [U_614,U_613,U_612] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_612),U_614))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_613),U_614))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_612),U_613)) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_612),U_614))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_613),U_614))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_612),U_613)) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| V_m = V_n
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less]) ).
fof(f_211_2,plain,
! [U_616,U_615] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_615),U_616))
| U_615 = U_616
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_615),U_616)) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_615),U_616))
| U_615 = U_616
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_615),U_616)) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).
fof(f_212_2,plain,
! [U_619,U_618,U_617] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_619),U_617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_619),U_618)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_617),U_618)) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_619),U_617)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_619),U_618)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_617),U_618)) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono1]) ).
fof(f_213_2,plain,
! [U_622,U_621,U_620] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_620),U_622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_621),U_622)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_620),U_621)) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_620),U_622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_621),U_622)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_620),U_621)) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).
fof(f_214_2,plain,
! [U_624,U_623] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_623),U_624))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_623),U_624)) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_623),U_624))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_623),U_624)) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| V_m != V_n ),
inference(fof_nnf,[status(thm)],[fact_eq__imp__le]) ).
fof(f_215_2,plain,
! [U_626,U_625] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_625),U_626))
| U_625 != U_626 ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_625),U_626))
| U_625 != U_626 ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_1,plain,
! [V_t,V_s] :
( V_s != V_t
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s),V_t)) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).
fof(f_216_2,plain,
! [U_628,U_627] :
( U_627 != U_628
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_627),U_628)) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( U_627 != U_628
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_627),U_628)) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_1,plain,
! [V_m,V_n] :
( V_m != V_n
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).
fof(f_217_2,plain,
! [U_630,U_629] :
( U_630 != U_629
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_629),U_630)) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( U_630 != U_629
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_629),U_630)) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)),
inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).
fof(f_218_2,plain,
! [U_631] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_631),U_631)),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_631),U_631)),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y),V_x))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y))
| V_x = V_y ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(f_219_2,plain,
! [U_633,U_632] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_633),U_632))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_632),U_633))
| U_632 = U_633 ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_633),U_632))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_632),U_633))
| U_632 = U_633 ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_637,U_636,U_635,U_634] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636)),U_637) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_636),U_637))
| ~ class_Groups_Oab__semigroup__mult(U_634) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636)),U_637) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_636),U_637))
| ~ class_Groups_Oab__semigroup__mult(U_634) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ( V_m_2 != V_n_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) )
& ( V_m_2 = V_n_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).
fof(f_221_2,plain,
! [U_639,U_638] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_638),U_639))
| ( U_638 != U_639
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_638),U_639)) ) )
& ( U_638 = U_639
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_638),U_639))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_638),U_639)) ) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
( ! [U_643,U_641] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_641),U_643))
| ( U_641 != U_643
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_641),U_643)) ) )
& ! [U_642,U_640] :
( U_640 = U_642
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_640),U_642))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_640),U_642)) ) ),
inference(miniscope,[status(thm)],[f_221_2]) ).
cnf(f_221_4,plain,
( U_640 = U_642
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_640),U_642))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_640),U_642)) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_641),U_643))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_641),U_643)) ),
inference(clausify,[status(thm)],[f_221_3]) ).
cnf(f_221_6,plain,
( U_641 != U_643
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_641),U_643)) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| V_m_2 = V_n_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( ( V_m_2 != V_n_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).
fof(f_222_2,plain,
! [U_645,U_644] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_644),U_645))
| U_644 = U_645
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_644),U_645)) )
& ( ( U_644 != U_645
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_644),U_645)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_644),U_645)) ) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
( ! [U_649,U_647] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_647),U_649))
| U_647 = U_649
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_647),U_649)) )
& ! [U_648,U_646] :
( ( U_646 != U_648
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_646),U_648)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_646),U_648)) ) ),
inference(miniscope,[status(thm)],[f_222_2]) ).
cnf(f_222_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_646),U_648))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_646),U_648)) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_5,plain,
( U_646 != U_648
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_646),U_648)) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_647),U_649))
| U_647 = U_649
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_647),U_649)) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).
fof(f_223_2,plain,
! [U_651,U_650] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_651),U_650))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_650),U_651)) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_651),U_650))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_650),U_651)) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_1,plain,
! [V_n_2,V_m_2] :
( ( V_m_2 != V_n_2
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| V_m_2 = V_n_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).
fof(f_224_2,plain,
! [U_653,U_652] :
( ( U_652 != U_653
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_653),U_652))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_652),U_653)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_653),U_652))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_652),U_653))
| U_652 = U_653 ) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
( ! [U_657,U_655] :
( U_655 != U_657
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_657),U_655))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_655),U_657)) ) )
& ! [U_656,U_654] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_656),U_654))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_654),U_656))
| U_654 = U_656 ) ),
inference(miniscope,[status(thm)],[f_224_2]) ).
cnf(f_224_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_656),U_654))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_654),U_656))
| U_654 = U_656 ),
inference(clausify,[status(thm)],[f_224_3]) ).
cnf(f_224_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_655),U_657))
| U_655 != U_657 ),
inference(clausify,[status(thm)],[f_224_3]) ).
cnf(f_224_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_657),U_655))
| U_655 != U_657 ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_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_225_2,plain,
! [U_660,U_659,U_658] :
( c_Groups_Osgn__class_Osgn(U_658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_658),U_659),U_660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_658),c_Groups_Osgn__class_Osgn(U_658,U_659)),c_Groups_Osgn__class_Osgn(U_658,U_660))
| ~ class_Rings_Olinordered__idom(U_658) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( c_Groups_Osgn__class_Osgn(U_658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_658),U_659),U_660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_658),c_Groups_Osgn__class_Osgn(U_658,U_659)),c_Groups_Osgn__class_Osgn(U_658,U_660))
| ~ class_Rings_Olinordered__idom(U_658) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_662,U_661] :
( c_Groups_Osgn__class_Osgn(U_661,c_Groups_Osgn__class_Osgn(U_661,U_662)) = c_Groups_Osgn__class_Osgn(U_661,U_662)
| ~ class_Rings_Olinordered__idom(U_661) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( c_Groups_Osgn__class_Osgn(U_661,c_Groups_Osgn__class_Osgn(U_661,U_662)) = c_Groups_Osgn__class_Osgn(U_661,U_662)
| ~ class_Rings_Olinordered__idom(U_661) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_1,plain,
! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))),
inference(fof_nnf,[status(thm)],[fact_le__cube]) ).
fof(f_227_2,plain,
! [U_663] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_663),U_663)))),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_663),U_663)))),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [V_m] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
inference(fof_nnf,[status(thm)],[fact_le__square]) ).
fof(f_228_2,plain,
! [U_664] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_664),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_664),U_664))),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_664),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_664),U_664))),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_1,plain,
! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_n)),
inference(fof_nnf,[status(thm)],[fact_le__refl]) ).
fof(f_229_2,plain,
! [U_665] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_665),U_665)),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_665),U_665)),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_1,plain,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_n)),
inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).
fof(f_230_2,plain,
! [U_666] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_666),U_666)),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_666),U_666)),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_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_231_2,plain,
! [U_668,U_667] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_668),c_Groups_Ozero__class_Ozero(U_667)) = c_Groups_Ozero__class_Ozero(U_667)
| ~ class_Rings_Ocomm__semiring__1(U_667) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_668),c_Groups_Ozero__class_Ozero(U_667)) = c_Groups_Ozero__class_Ozero(U_667)
| ~ class_Rings_Ocomm__semiring__1(U_667) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_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_232_2,plain,
! [U_670,U_669] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),c_Groups_Ozero__class_Ozero(U_669)),U_670) = c_Groups_Ozero__class_Ozero(U_669)
| ~ class_Rings_Ocomm__semiring__1(U_669) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),c_Groups_Ozero__class_Ozero(U_669)),U_670) = c_Groups_Ozero__class_Ozero(U_669)
| ~ class_Rings_Ocomm__semiring__1(U_669) ),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_1,plain,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
( ( ( hAPP(hAPP(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)) = hAPP(hAPP(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
| hAPP(hAPP(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)) != hAPP(hAPP(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_233_2,plain,
! [U_675,U_674,U_673,U_672,U_671] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_673)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_675)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673))
| ( U_673 != U_675
& U_672 != U_674 ) )
& ( U_673 = U_675
| U_672 = U_674
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_673)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_675)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_671) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( U_673 = U_675
| U_672 = U_674
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_673)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_675)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_671) ),
inference(clausify,[status(thm)],[f_233_2]) ).
cnf(f_233_4,plain,
( U_672 != U_674
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_673)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_675)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_671) ),
inference(clausify,[status(thm)],[f_233_2]) ).
cnf(f_233_5,plain,
( U_673 != U_675
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_673)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_675)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_672),U_675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_671) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [V_b,V_m,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_234_2,plain,
! [U_679,U_678,U_677,U_676] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_679),U_678)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_676),U_677),U_679)),U_678)
| ~ class_Rings_Ocomm__semiring__1(U_676) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_679),U_678)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_676),U_677),U_679)),U_678)
| ~ class_Rings_Ocomm__semiring__1(U_676) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_235_2,plain,
! [U_683,U_682,U_681,U_680] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_680),U_681),U_682)),U_683) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_683)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_682),U_683))
| ~ class_Rings_Ocomm__semiring__1(U_680) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_680),U_681),U_682)),U_683) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_683)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_682),U_683))
| ~ class_Rings_Ocomm__semiring__1(U_680) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) = hAPP(hAPP(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_c_2)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(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_c_2))
| V_c_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_236_2,plain,
! [U_688,U_687,U_686,U_685,U_684] :
( ( ( ( U_687 != U_688
& U_685 != U_686 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_688)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_687)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_688)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_688)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_687))
| U_687 = U_688
| U_685 = U_686 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_684) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_688)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_688)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_687))
| U_687 = U_688
| U_685 = U_686
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_684) ),
inference(clausify,[status(thm)],[f_236_2]) ).
cnf(f_236_4,plain,
( U_685 != U_686
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_688)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_687))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_684) ),
inference(clausify,[status(thm)],[f_236_2]) ).
cnf(f_236_5,plain,
( U_687 != U_688
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_684),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_685),U_688)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_684),U_686),U_687))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_684) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_1,plain,
! [V_z,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_237_2,plain,
! [U_692,U_691,U_690,U_689] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_689),U_691),U_692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692))
| ~ class_Rings_Ocomm__semiring__1(U_689) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_689),U_691),U_692)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692))
| ~ class_Rings_Ocomm__semiring__1(U_689) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_694,U_693] :
( c_Groups_Oabs__class_Oabs(U_693,U_694) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),c_Groups_Osgn__class_Osgn(U_693,U_694))
| ~ class_Rings_Olinordered__idom(U_693) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( c_Groups_Oabs__class_Oabs(U_693,U_694) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),c_Groups_Osgn__class_Osgn(U_693,U_694))
| ~ class_Rings_Olinordered__idom(U_693) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_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_239_2,plain,
! [U_696,U_695] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),c_Groups_Osgn__class_Osgn(U_695,U_696)),c_Groups_Oabs__class_Oabs(U_695,U_696)) = U_696
| ~ class_Rings_Olinordered__idom(U_695) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),c_Groups_Osgn__class_Osgn(U_695,U_696)),c_Groups_Oabs__class_Oabs(U_695,U_696)) = U_696
| ~ class_Rings_Olinordered__idom(U_695) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_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_240_2,plain,
! [U_698,U_697] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),c_Groups_Oone__class_Oone(U_697)) = U_698
| ~ class_Rings_Ocomm__semiring__1(U_697) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),c_Groups_Oone__class_Oone(U_697)) = U_698
| ~ class_Rings_Ocomm__semiring__1(U_697) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_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_241_2,plain,
! [U_700,U_699] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_699),c_Groups_Oone__class_Oone(U_699)),U_700) = U_700
| ~ class_Rings_Ocomm__semiring__1(U_699) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_699),c_Groups_Oone__class_Oone(U_699)),U_700) = U_700
| ~ class_Rings_Ocomm__semiring__1(U_699) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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_242_2,plain,
! [U_702,U_701] :
( U_701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_702 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_701 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_701),U_702) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( U_701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_702 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_701 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_701),U_702) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).
fof(f_243_2,plain,
! [U_705,U_704,U_703] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_705),U_703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_705),U_704)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_705))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_703),U_704)) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_705),U_703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_705),U_704)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_705))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_703),U_704)) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).
fof(f_244_2,plain,
! [U_708,U_707,U_706] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_706),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_707),U_708)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_708))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_706),U_707)) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
cnf(f_244_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_706),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_707),U_708)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_708))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_706),U_707)) ),
inference(clausify,[status(thm)],[f_244_2]) ).
fof(f_245_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).
fof(f_245_2,plain,
! [U_711,U_710,U_709] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_709),U_710) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_711),U_710)
| ( U_710 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_709 != U_711 ) )
& ( U_710 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_709 = U_711
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_709),U_710) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_711),U_710) ) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
( ! [U_717,U_715,U_713] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_713),U_715) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_717),U_715)
| ( U_715 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_713 != U_717 ) )
& ! [U_716,U_714,U_712] :
( U_714 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_712 = U_716
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_712),U_714) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_716),U_714) ) ),
inference(miniscope,[status(thm)],[f_245_2]) ).
cnf(f_245_4,plain,
( U_714 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_712 = U_716
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_712),U_714) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_716),U_714) ),
inference(clausify,[status(thm)],[f_245_3]) ).
cnf(f_245_5,plain,
( U_713 != U_717
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_713),U_715) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_717),U_715) ),
inference(clausify,[status(thm)],[f_245_3]) ).
cnf(f_245_6,plain,
( U_715 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_713),U_715) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_717),U_715) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).
fof(f_246_2,plain,
! [U_720,U_719,U_718] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_718),U_719) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_718),U_720)
| ( U_718 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_719 != U_720 ) )
& ( U_718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_719 = U_720
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_718),U_719) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_718),U_720) ) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
( ! [U_726,U_724,U_722] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_722),U_724) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_722),U_726)
| ( U_722 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_724 != U_726 ) )
& ! [U_725,U_723,U_721] :
( U_721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_723 = U_725
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_721),U_723) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_721),U_725) ) ),
inference(miniscope,[status(thm)],[f_246_2]) ).
cnf(f_246_4,plain,
( U_721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_723 = U_725
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_721),U_723) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_721),U_725) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_5,plain,
( U_724 != U_726
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_722),U_724) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_722),U_726) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_6,plain,
( U_722 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_722),U_724) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_722),U_726) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).
fof(f_247_2,plain,
! [U_729,U_728,U_727] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_727),U_728)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_729),U_728)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_727),U_729))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_728)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_727),U_729))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_728))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_727),U_728)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_729),U_728))) ) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
( ! [U_735,U_733,U_731] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_731),U_733)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_735),U_733)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_731),U_735))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_733)) ) )
& ! [U_734,U_732,U_730] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_730),U_734))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_732))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_730),U_732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_734),U_732))) ) ),
inference(miniscope,[status(thm)],[f_247_2]) ).
cnf(f_247_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_730),U_734))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_732))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_730),U_732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_734),U_732))) ),
inference(clausify,[status(thm)],[f_247_3]) ).
cnf(f_247_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_733))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_731),U_733)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_735),U_733))) ),
inference(clausify,[status(thm)],[f_247_3]) ).
cnf(f_247_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_731),U_735))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_731),U_733)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_735),U_733))) ),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).
fof(f_248_2,plain,
! [U_738,U_737,U_736] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_736),U_737)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_736),U_738)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_737),U_738))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_736)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_737),U_738))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_736))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_736),U_737)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_736),U_738))) ) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
( ! [U_744,U_742,U_740] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_740),U_742)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_740),U_744)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_742),U_744))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_740)) ) )
& ! [U_743,U_741,U_739] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_741),U_743))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_739))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_739),U_741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_739),U_743))) ) ),
inference(miniscope,[status(thm)],[f_248_2]) ).
cnf(f_248_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_741),U_743))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_739))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_739),U_741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_739),U_743))) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_740))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_740),U_742)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_740),U_744))) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_742),U_744))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_740),U_742)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_740),U_744))) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).
fof(f_249_2,plain,
! [U_747,U_746,U_745] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_745),U_746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_747),U_746)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_745),U_747))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_746)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_745),U_747))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_746)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_745),U_746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_747),U_746))) ) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
( ! [U_753,U_751,U_749] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_749),U_751)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_753),U_751)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_749),U_753))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_751)) )
& ! [U_752,U_750,U_748] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_748),U_752))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_750)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_748),U_750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_752),U_750))) ) ),
inference(miniscope,[status(thm)],[f_249_2]) ).
cnf(f_249_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_750))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_748),U_750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_752),U_750))) ),
inference(clausify,[status(thm)],[f_249_3]) ).
cnf(f_249_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_748),U_752))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_748),U_750)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_752),U_750))) ),
inference(clausify,[status(thm)],[f_249_3]) ).
cnf(f_249_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_749),U_751)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_753),U_751)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_749),U_753))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_751)) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).
fof(f_250_2,plain,
! [U_756,U_755,U_754] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_754),U_755)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_754),U_756)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_755),U_756))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_754)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_755),U_756))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_754)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_754),U_755)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_754),U_756))) ) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
( ! [U_762,U_760,U_758] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_758),U_760)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_758),U_762)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_760),U_762))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_758)) )
& ! [U_761,U_759,U_757] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_759),U_761))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_757)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_761))) ) ),
inference(miniscope,[status(thm)],[f_250_2]) ).
cnf(f_250_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_757))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_761))) ),
inference(clausify,[status(thm)],[f_250_3]) ).
cnf(f_250_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_759),U_761))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_761))) ),
inference(clausify,[status(thm)],[f_250_3]) ).
cnf(f_250_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_758),U_760)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_758),U_762)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_760),U_762))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_758)) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).
fof(f_251_2,plain,
! [U_764,U_763] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_763),U_764) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_764 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_763 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_763 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_763),U_764) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_768,U_766] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_766),U_768) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_766 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_767,U_765] :
( U_767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_765),U_767) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_251_2]) ).
cnf(f_251_4,plain,
( U_767 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_765),U_767) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
( U_766 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_766),U_768) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_6,plain,
( U_768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_766),U_768) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_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_252_2,plain,
! [U_769] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_769),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_769),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).
fof(f_253_2,plain,
! [U_771,U_770] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_770),U_771)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_771))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_770)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_771))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_770)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_770),U_771))) ) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
( ! [U_775,U_773] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_773),U_775)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_775))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_773)) )
& ! [U_774,U_772] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_774))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_772)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_772),U_774))) ) ),
inference(miniscope,[status(thm)],[f_253_2]) ).
cnf(f_253_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_772))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_772),U_774))) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_774))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_772),U_774))) ),
inference(clausify,[status(thm)],[f_253_3]) ).
cnf(f_253_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_773),U_775)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_775))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_773)) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_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_254_2,plain,
! [U_776] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_776) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(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_255_2,plain,
! [U_779,U_778,U_777] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_777,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_777),U_778),U_779))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_777,U_778)),c_RealVector_Onorm__class_Onorm(U_777,U_779))))
| ~ class_RealVector_Oreal__normed__algebra(U_777) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_777,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_777),U_778),U_779))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_777,U_778)),c_RealVector_Onorm__class_Onorm(U_777,U_779))))
| ~ class_RealVector_Oreal__normed__algebra(U_777) ),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_1,plain,
! [V_s,V_y,V_r,V_x,T_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y)),V_s))
| ~ hBOOL(hAPP(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_256_2,plain,
! [U_784,U_783,U_782,U_781,U_780] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),U_783))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_782),U_784)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,U_783)),U_784))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,U_781)),U_782))
| ~ class_RealVector_Oreal__normed__algebra(U_780) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),U_783))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_782),U_784)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,U_783)),U_784))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,U_781)),U_782))
| ~ class_RealVector_Oreal__normed__algebra(U_780) ),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_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_257_2,plain,
! [U_787,U_786,U_785] :
( U_787 = c_Groups_Ozero__class_Ozero(U_785)
| U_786 = c_Groups_Ozero__class_Ozero(U_785)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_785),U_786),U_787) != c_Groups_Ozero__class_Ozero(U_785)
| ~ class_Rings_Ono__zero__divisors(U_785) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( U_787 = c_Groups_Ozero__class_Ozero(U_785)
| U_786 = c_Groups_Ozero__class_Ozero(U_785)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_785),U_786),U_787) != c_Groups_Ozero__class_Ozero(U_785)
| ~ class_Rings_Ono__zero__divisors(U_785) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_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_258_2,plain,
! [U_790,U_789,U_788] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_789),U_790) != c_Groups_Ozero__class_Ozero(U_788)
| U_790 = c_Groups_Ozero__class_Ozero(U_788)
| U_789 = c_Groups_Ozero__class_Ozero(U_788)
| ~ class_Rings_Ono__zero__divisors(U_788) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
cnf(f_258_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_788),U_789),U_790) != c_Groups_Ozero__class_Ozero(U_788)
| U_790 = c_Groups_Ozero__class_Ozero(U_788)
| U_789 = c_Groups_Ozero__class_Ozero(U_788)
| ~ class_Rings_Ono__zero__divisors(U_788) ),
inference(clausify,[status(thm)],[f_258_2]) ).
fof(f_259_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_259_2,plain,
! [U_793,U_792,U_791] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_791),U_792),U_793) = c_Groups_Ozero__class_Ozero(U_791)
| ( U_793 != c_Groups_Ozero__class_Ozero(U_791)
& U_792 != c_Groups_Ozero__class_Ozero(U_791) ) )
& ( U_793 = c_Groups_Ozero__class_Ozero(U_791)
| U_792 = c_Groups_Ozero__class_Ozero(U_791)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_791),U_792),U_793) != c_Groups_Ozero__class_Ozero(U_791) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_791) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
( U_793 = c_Groups_Ozero__class_Ozero(U_791)
| U_792 = c_Groups_Ozero__class_Ozero(U_791)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_791),U_792),U_793) != c_Groups_Ozero__class_Ozero(U_791)
| ~ class_Rings_Oring__no__zero__divisors(U_791) ),
inference(clausify,[status(thm)],[f_259_2]) ).
cnf(f_259_4,plain,
( U_792 != c_Groups_Ozero__class_Ozero(U_791)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_791),U_792),U_793) = c_Groups_Ozero__class_Ozero(U_791)
| ~ class_Rings_Oring__no__zero__divisors(U_791) ),
inference(clausify,[status(thm)],[f_259_2]) ).
cnf(f_259_5,plain,
( U_793 != c_Groups_Ozero__class_Ozero(U_791)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_791),U_792),U_793) = c_Groups_Ozero__class_Ozero(U_791)
| ~ class_Rings_Oring__no__zero__divisors(U_791) ),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_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_260_2,plain,
! [U_795,U_794] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_794),U_795),c_Groups_Ozero__class_Ozero(U_794)) = c_Groups_Ozero__class_Ozero(U_794)
| ~ class_Rings_Omult__zero(U_794) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_794),U_795),c_Groups_Ozero__class_Ozero(U_794)) = c_Groups_Ozero__class_Ozero(U_794)
| ~ class_Rings_Omult__zero(U_794) ),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_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_261_2,plain,
! [U_797,U_796] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),c_Groups_Ozero__class_Ozero(U_796)),U_797) = c_Groups_Ozero__class_Ozero(U_796)
| ~ class_Rings_Omult__zero(U_796) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),c_Groups_Ozero__class_Ozero(U_796)),U_797) = c_Groups_Ozero__class_Ozero(U_796)
| ~ class_Rings_Omult__zero(U_796) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_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_262_2,plain,
! [U_799,U_798] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_798),U_799),c_Groups_Ozero__class_Ozero(U_798)) = c_Groups_Ozero__class_Ozero(U_798)
| ~ class_RealVector_Oreal__normed__algebra(U_798) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_798),U_799),c_Groups_Ozero__class_Ozero(U_798)) = c_Groups_Ozero__class_Ozero(U_798)
| ~ class_RealVector_Oreal__normed__algebra(U_798) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_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_263_2,plain,
! [U_801,U_800] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_800),U_801),c_Groups_Ozero__class_Ozero(U_800)) = c_Groups_Ozero__class_Ozero(U_800)
| ~ class_RealVector_Oreal__normed__algebra(U_800) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_800),U_801),c_Groups_Ozero__class_Ozero(U_800)) = c_Groups_Ozero__class_Ozero(U_800)
| ~ class_RealVector_Oreal__normed__algebra(U_800) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_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_264_2,plain,
! [U_803,U_802] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),c_Groups_Ozero__class_Ozero(U_802)),U_803) = c_Groups_Ozero__class_Ozero(U_802)
| ~ class_RealVector_Oreal__normed__algebra(U_802) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),c_Groups_Ozero__class_Ozero(U_802)),U_803) = c_Groups_Ozero__class_Ozero(U_802)
| ~ class_RealVector_Oreal__normed__algebra(U_802) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_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_265_2,plain,
! [U_805,U_804] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ozero__class_Ozero(U_804)),U_805) = c_Groups_Ozero__class_Ozero(U_804)
| ~ class_RealVector_Oreal__normed__algebra(U_804) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ozero__class_Ozero(U_804)),U_805) = c_Groups_Ozero__class_Ozero(U_804)
| ~ class_RealVector_Oreal__normed__algebra(U_804) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_1,plain,
! [V_c,V_b,V_e,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c)
| ~ class_Rings_Osemiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_combine__common__factor]) ).
fof(f_266_2,plain,
! [U_810,U_809,U_808,U_807,U_806] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_808)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_809),U_808)),U_810)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),U_807),U_809)),U_808)),U_810)
| ~ class_Rings_Osemiring(U_806) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_808)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_809),U_808)),U_810)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_806),U_807),U_809)),U_808)),U_810)
| ~ class_Rings_Osemiring(U_806) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Ocomm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib]) ).
fof(f_267_2,plain,
! [U_814,U_813,U_812,U_811] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_811),U_812),U_813)),U_814) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_811),U_812),U_814)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_811),U_813),U_814))
| ~ class_Rings_Ocomm__semiring(U_811) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_811),U_812),U_813)),U_814) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_811),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_811),U_812),U_814)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_811),U_813),U_814))
| ~ class_Rings_Ocomm__semiring(U_811) ),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(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_268_2,plain,
! [U_818,U_817,U_816,U_815] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_815),U_816),U_817)),U_818) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),U_816),U_818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),U_817),U_818))
| ~ class_RealVector_Oreal__normed__algebra(U_815) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_815),U_816),U_817)),U_818) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_815),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),U_816),U_818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),U_817),U_818))
| ~ class_RealVector_Oreal__normed__algebra(U_815) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_a_H)),V_b) = hAPP(hAPP(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_269_2,plain,
! [U_822,U_821,U_820,U_819] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_819),U_820),U_821)),U_822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),U_820),U_822)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),U_821),U_822))
| ~ class_RealVector_Oreal__normed__algebra(U_819) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_819),U_820),U_821)),U_822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),U_820),U_822)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),U_821),U_822))
| ~ class_RealVector_Oreal__normed__algebra(U_819) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
! [V_y,V_x,V_xa,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)) = hAPP(hAPP(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_270_2,plain,
! [U_826,U_825,U_824,U_823] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_823),U_824),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_823),U_825),U_826)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_823),U_824),U_825)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_823),U_824),U_826))
| ~ class_RealVector_Oreal__normed__algebra(U_823) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_823),U_824),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_823),U_825),U_826)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_823),U_824),U_825)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_823),U_824),U_826))
| ~ class_RealVector_Oreal__normed__algebra(U_823) ),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_b_H)) = hAPP(hAPP(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_271_2,plain,
! [U_830,U_829,U_828,U_827] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_827),U_829),U_830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),U_829)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),U_830))
| ~ class_RealVector_Oreal__normed__algebra(U_827) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_827),U_829),U_830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),U_829)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),U_830))
| ~ class_RealVector_Oreal__normed__algebra(U_827) ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_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_272_2,plain,
! [U_832,U_831] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_831),U_832),c_Groups_Oone__class_Oone(U_831)) = U_832
| ~ class_Groups_Ocomm__monoid__mult(U_831) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_831),U_832),c_Groups_Oone__class_Oone(U_831)) = U_832
| ~ class_Groups_Ocomm__monoid__mult(U_831) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_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_273_2,plain,
! [U_834,U_833] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),c_Groups_Oone__class_Oone(U_833)) = U_834
| ~ class_Groups_Omonoid__mult(U_833) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),c_Groups_Oone__class_Oone(U_833)) = U_834
| ~ class_Groups_Omonoid__mult(U_833) ),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_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_274_2,plain,
! [U_836,U_835] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_835),c_Groups_Oone__class_Oone(U_835)),U_836) = U_836
| ~ class_Groups_Ocomm__monoid__mult(U_835) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_835),c_Groups_Oone__class_Oone(U_835)),U_836) = U_836
| ~ class_Groups_Ocomm__monoid__mult(U_835) ),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_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_275_2,plain,
! [U_838,U_837] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_837),c_Groups_Oone__class_Oone(U_837)),U_838) = U_838
| ~ class_Groups_Omonoid__mult(U_837) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
cnf(f_275_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_837),c_Groups_Oone__class_Oone(U_837)),U_838) = U_838
| ~ class_Groups_Omonoid__mult(U_837) ),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_1,plain,
! [V_b_2,V_a_2,V_c_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_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_c_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_b_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel]) ).
fof(f_276_2,plain,
! [U_841,U_840,U_839] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_840) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_841)
| U_840 != U_841 )
& ( U_840 = U_841
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_840) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_841) ) )
| U_839 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( U_840 = U_841
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_840) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_841)
| U_839 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_276_2]) ).
cnf(f_276_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_840) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_841)
| U_840 != U_841
| U_839 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_1,plain,
! [V_b_2,V_a_2,V_c_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_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_c_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_c_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel]) ).
fof(f_277_2,plain,
! [U_844,U_843,U_842] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_843),U_842) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_844),U_842)
| U_843 != U_844 )
& ( U_843 = U_844
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_843),U_842) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_844),U_842) ) )
| U_842 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( U_843 = U_844
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_843),U_842) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_844),U_842)
| U_842 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_277_2]) ).
cnf(f_277_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_843),U_842) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_844),U_842)
| U_843 != U_844
| U_842 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_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_278_2,plain,
! [U_846,U_845] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_845),c_Groups_Oabs__class_Oabs(U_845,U_846)),c_Groups_Oabs__class_Oabs(U_845,U_846)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_845),U_846),U_846)
| ~ class_Rings_Olinordered__idom(U_845) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_845),c_Groups_Oabs__class_Oabs(U_845,U_846)),c_Groups_Oabs__class_Oabs(U_845,U_846)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_845),U_846),U_846)
| ~ class_Rings_Olinordered__idom(U_845) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_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_279_2,plain,
! [U_849,U_848,U_847] :
( c_Groups_Oabs__class_Oabs(U_847,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_847),U_848),U_849)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_847),c_Groups_Oabs__class_Oabs(U_847,U_848)),c_Groups_Oabs__class_Oabs(U_847,U_849))
| ~ class_Rings_Olinordered__idom(U_847) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
( c_Groups_Oabs__class_Oabs(U_847,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_847),U_848),U_849)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_847),c_Groups_Oabs__class_Oabs(U_847,U_848)),c_Groups_Oabs__class_Oabs(U_847,U_849))
| ~ class_Rings_Olinordered__idom(U_847) ),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_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_280_2,plain,
! [U_850] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_850) = U_850,
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_850) = U_850,
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_z1),V_z2)),V_w) = hAPP(hAPP(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_281_2,plain,
! [U_853,U_852,U_851] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_851),U_852)),U_853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_851),U_853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_852),U_853)),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_851),U_852)),U_853) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_851),U_853)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_852),U_853)),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))
| V_c = V_d
| V_a != V_b
| V_r = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq]) ).
fof(f_282_2,plain,
! [U_859,U_858,U_857,U_856,U_855,U_854] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_854),U_856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_854),U_855),U_858)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_854),U_857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_854),U_855),U_859))
| U_858 = U_859
| U_856 != U_857
| U_855 = c_Groups_Ozero__class_Ozero(U_854)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_854) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_854),U_856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_854),U_855),U_858)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_854),U_857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_854),U_855),U_859))
| U_858 = U_859
| U_856 != U_857
| U_855 = c_Groups_Ozero__class_Ozero(U_854)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_854) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [V_m,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_283_2,plain,
! [U_862,U_861,U_860] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_860),U_861),U_862)),U_862) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_860),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_860),U_861),c_Groups_Oone__class_Oone(U_860))),U_862)
| ~ class_Rings_Ocomm__semiring__1(U_860) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_860),U_861),U_862)),U_862) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_860),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_860),U_861),c_Groups_Oone__class_Oone(U_860))),U_862)
| ~ class_Rings_Ocomm__semiring__1(U_860) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [V_a,V_m,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_284_2,plain,
! [U_865,U_864,U_863] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_863),U_865),U_864)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_863),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_865),c_Groups_Oone__class_Oone(U_863))),U_864)
| ~ class_Rings_Ocomm__semiring__1(U_863) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_863),U_865),U_864)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_863),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_863),U_865),c_Groups_Oone__class_Oone(U_863))),U_864)
| ~ class_Rings_Ocomm__semiring__1(U_863) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [V_m,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_285_2,plain,
! [U_867,U_866] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_866),U_867),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_866),c_Groups_Oone__class_Oone(U_866)),c_Groups_Oone__class_Oone(U_866))),U_867)
| ~ class_Rings_Ocomm__semiring__1(U_866) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
cnf(f_285_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_866),U_867),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_866),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_866),c_Groups_Oone__class_Oone(U_866)),c_Groups_Oone__class_Oone(U_866))),U_867)
| ~ class_Rings_Ocomm__semiring__1(U_866) ),
inference(clausify,[status(thm)],[f_285_2]) ).
fof(f_286_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_286_2,plain,
! [U_869,U_868] :
( ( ( c_Groups_Osgn__class_Osgn(U_868,U_869) = c_Groups_Ozero__class_Ozero(U_868)
| U_869 != c_Groups_Ozero__class_Ozero(U_868) )
& ( U_869 = c_Groups_Ozero__class_Ozero(U_868)
| c_Groups_Osgn__class_Osgn(U_868,U_869) != c_Groups_Ozero__class_Ozero(U_868) ) )
| ~ class_Rings_Olinordered__idom(U_868) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( U_869 = c_Groups_Ozero__class_Ozero(U_868)
| c_Groups_Osgn__class_Osgn(U_868,U_869) != c_Groups_Ozero__class_Ozero(U_868)
| ~ class_Rings_Olinordered__idom(U_868) ),
inference(clausify,[status(thm)],[f_286_2]) ).
cnf(f_286_4,plain,
( c_Groups_Osgn__class_Osgn(U_868,U_869) = c_Groups_Ozero__class_Ozero(U_868)
| U_869 != c_Groups_Ozero__class_Ozero(U_868)
| ~ class_Rings_Olinordered__idom(U_868) ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_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_287_2,plain,
! [U_870] :
( c_Groups_Osgn__class_Osgn(U_870,c_Groups_Ozero__class_Ozero(U_870)) = c_Groups_Ozero__class_Ozero(U_870)
| ~ class_Groups_Osgn__if(U_870) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( c_Groups_Osgn__class_Osgn(U_870,c_Groups_Ozero__class_Ozero(U_870)) = c_Groups_Ozero__class_Ozero(U_870)
| ~ class_Groups_Osgn__if(U_870) ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_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_288_2,plain,
! [U_872,U_871] :
( ( ( c_Groups_Osgn__class_Osgn(U_871,U_872) = c_Groups_Ozero__class_Ozero(U_871)
| U_872 != c_Groups_Ozero__class_Ozero(U_871) )
& ( U_872 = c_Groups_Ozero__class_Ozero(U_871)
| c_Groups_Osgn__class_Osgn(U_871,U_872) != c_Groups_Ozero__class_Ozero(U_871) ) )
| ~ class_RealVector_Oreal__normed__vector(U_871) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( U_872 = c_Groups_Ozero__class_Ozero(U_871)
| c_Groups_Osgn__class_Osgn(U_871,U_872) != c_Groups_Ozero__class_Ozero(U_871)
| ~ class_RealVector_Oreal__normed__vector(U_871) ),
inference(clausify,[status(thm)],[f_288_2]) ).
cnf(f_288_4,plain,
( c_Groups_Osgn__class_Osgn(U_871,U_872) = c_Groups_Ozero__class_Ozero(U_871)
| U_872 != c_Groups_Ozero__class_Ozero(U_871)
| ~ class_RealVector_Oreal__normed__vector(U_871) ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_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_289_2,plain,
! [U_873] :
( c_Groups_Osgn__class_Osgn(U_873,c_Groups_Ozero__class_Ozero(U_873)) = c_Groups_Ozero__class_Ozero(U_873)
| ~ class_RealVector_Oreal__normed__vector(U_873) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( c_Groups_Osgn__class_Osgn(U_873,c_Groups_Ozero__class_Ozero(U_873)) = c_Groups_Ozero__class_Ozero(U_873)
| ~ class_RealVector_Oreal__normed__vector(U_873) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_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_290_2,plain,
! [U_874] :
( c_Groups_Osgn__class_Osgn(U_874,c_Groups_Oone__class_Oone(U_874)) = c_Groups_Oone__class_Oone(U_874)
| ~ class_RealVector_Oreal__normed__algebra__1(U_874) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( c_Groups_Osgn__class_Osgn(U_874,c_Groups_Oone__class_Oone(U_874)) = c_Groups_Oone__class_Oone(U_874)
| ~ class_RealVector_Oreal__normed__algebra__1(U_874) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le]) ).
fof(f_291_2,plain,
! [U_877,U_876,U_875] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_875),U_876),U_877)),c_Groups_Ozero__class_Ozero(U_875)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,c_Groups_Ozero__class_Ozero(U_875)),U_877))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,U_876),c_Groups_Ozero__class_Ozero(U_875))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,U_877),c_Groups_Ozero__class_Ozero(U_875)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,c_Groups_Ozero__class_Ozero(U_875)),U_876)) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_875) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,U_877),c_Groups_Ozero__class_Ozero(U_875)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,c_Groups_Ozero__class_Ozero(U_875)),U_876))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_875),U_876),U_877)),c_Groups_Ozero__class_Ozero(U_875)))
| ~ class_Rings_Oordered__cancel__semiring(U_875) ),
inference(clausify,[status(thm)],[f_291_2]) ).
cnf(f_291_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,c_Groups_Ozero__class_Ozero(U_875)),U_877))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,U_876),c_Groups_Ozero__class_Ozero(U_875)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_875),U_876),U_877)),c_Groups_Ozero__class_Ozero(U_875)))
| ~ class_Rings_Oordered__cancel__semiring(U_875) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le]) ).
fof(f_292_2,plain,
! [U_880,U_879,U_878] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,c_Groups_Ozero__class_Ozero(U_878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_878),U_879),U_880)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,U_880),c_Groups_Ozero__class_Ozero(U_878)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,U_879),c_Groups_Ozero__class_Ozero(U_878))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,c_Groups_Ozero__class_Ozero(U_878)),U_880))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,c_Groups_Ozero__class_Ozero(U_878)),U_879)) ) )
| ~ class_Rings_Oordered__ring(U_878) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,c_Groups_Ozero__class_Ozero(U_878)),U_880))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,c_Groups_Ozero__class_Ozero(U_878)),U_879))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,c_Groups_Ozero__class_Ozero(U_878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_878),U_879),U_880)))
| ~ class_Rings_Oordered__ring(U_878) ),
inference(clausify,[status(thm)],[f_292_2]) ).
cnf(f_292_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,U_880),c_Groups_Ozero__class_Ozero(U_878)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,U_879),c_Groups_Ozero__class_Ozero(U_878)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_878,c_Groups_Ozero__class_Ozero(U_878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_878),U_879),U_880)))
| ~ class_Rings_Oordered__ring(U_878) ),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono]) ).
fof(f_293_2,plain,
! [U_885,U_884,U_883,U_882,U_881] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_881),U_882),U_884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_881),U_883),U_885)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,c_Groups_Ozero__class_Ozero(U_881)),U_884))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,c_Groups_Ozero__class_Ozero(U_881)),U_883))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,U_884),U_885))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,U_882),U_883))
| ~ class_Rings_Oordered__semiring(U_881) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_881),U_882),U_884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_881),U_883),U_885)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,c_Groups_Ozero__class_Ozero(U_881)),U_884))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,c_Groups_Ozero__class_Ozero(U_881)),U_883))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,U_884),U_885))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_881,U_882),U_883))
| ~ class_Rings_Oordered__semiring(U_881) ),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono_H]) ).
fof(f_294_2,plain,
! [U_890,U_889,U_888,U_887,U_886] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_886),U_887),U_889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_886),U_888),U_890)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,c_Groups_Ozero__class_Ozero(U_886)),U_889))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,c_Groups_Ozero__class_Ozero(U_886)),U_887))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,U_889),U_890))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,U_887),U_888))
| ~ class_Rings_Oordered__semiring(U_886) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_886),U_887),U_889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_886),U_888),U_890)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,c_Groups_Ozero__class_Ozero(U_886)),U_889))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,c_Groups_Ozero__class_Ozero(U_886)),U_887))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,U_889),U_890))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_886,U_887),U_888))
| ~ class_Rings_Oordered__semiring(U_886) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg]) ).
fof(f_295_2,plain,
! [U_894,U_893,U_892,U_891] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_894),U_893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_894),U_892)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_891,U_894),c_Groups_Ozero__class_Ozero(U_891)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_891,U_892),U_893))
| ~ class_Rings_Oordered__ring(U_891) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_894),U_893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_894),U_892)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_891,U_894),c_Groups_Ozero__class_Ozero(U_891)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_891,U_892),U_893))
| ~ class_Rings_Oordered__ring(U_891) ),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg]) ).
fof(f_296_2,plain,
! [U_898,U_897,U_896,U_895] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_895,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_895),U_897),U_898)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_895),U_896),U_898)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_895,U_898),c_Groups_Ozero__class_Ozero(U_895)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_895,U_896),U_897))
| ~ class_Rings_Oordered__ring(U_895) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_895,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_895),U_897),U_898)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_895),U_896),U_898)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_895,U_898),c_Groups_Ozero__class_Ozero(U_895)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_895,U_896),U_897))
| ~ class_Rings_Oordered__ring(U_895) ),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Rings_Oordered__comm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono]) ).
fof(f_297_2,plain,
! [U_902,U_901,U_900,U_899] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_899,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_902),U_900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_902),U_901)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_899,c_Groups_Ozero__class_Ozero(U_899)),U_902))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_899,U_900),U_901))
| ~ class_Rings_Oordered__comm__semiring(U_899) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_899,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_902),U_900)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_902),U_901)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_899,c_Groups_Ozero__class_Ozero(U_899)),U_902))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_899,U_900),U_901))
| ~ class_Rings_Oordered__comm__semiring(U_899) ),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono]) ).
fof(f_298_2,plain,
! [U_906,U_905,U_904,U_903] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_903,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_903),U_906),U_904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_903),U_906),U_905)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_903,c_Groups_Ozero__class_Ozero(U_903)),U_906))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_903,U_904),U_905))
| ~ class_Rings_Oordered__semiring(U_903) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_903,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_903),U_906),U_904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_903),U_906),U_905)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_903,c_Groups_Ozero__class_Ozero(U_903)),U_906))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_903,U_904),U_905))
| ~ class_Rings_Oordered__semiring(U_903) ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono]) ).
fof(f_299_2,plain,
! [U_910,U_909,U_908,U_907] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_907),U_908),U_910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_907),U_909),U_910)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_907,c_Groups_Ozero__class_Ozero(U_907)),U_910))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_907,U_908),U_909))
| ~ class_Rings_Oordered__semiring(U_907) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_907),U_908),U_910)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_907),U_909),U_910)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_907,c_Groups_Ozero__class_Ozero(U_907)),U_910))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_907,U_908),U_909))
| ~ class_Rings_Oordered__semiring(U_907) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos]) ).
fof(f_300_2,plain,
! [U_913,U_912,U_911] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_911,c_Groups_Ozero__class_Ozero(U_911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_911),U_912),U_913)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_911,U_913),c_Groups_Ozero__class_Ozero(U_911)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_911,U_912),c_Groups_Ozero__class_Ozero(U_911)))
| ~ class_Rings_Oordered__ring(U_911) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_911,c_Groups_Ozero__class_Ozero(U_911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_911),U_912),U_913)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_911,U_913),c_Groups_Ozero__class_Ozero(U_911)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_911,U_912),c_Groups_Ozero__class_Ozero(U_911)))
| ~ class_Rings_Oordered__ring(U_911) ),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg]) ).
fof(f_301_2,plain,
! [U_916,U_915,U_914] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_914,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_914),U_915),U_916)),c_Groups_Ozero__class_Ozero(U_914)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_914,c_Groups_Ozero__class_Ozero(U_914)),U_916))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_914,U_915),c_Groups_Ozero__class_Ozero(U_914)))
| ~ class_Rings_Oordered__cancel__semiring(U_914) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_914,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_914),U_915),U_916)),c_Groups_Ozero__class_Ozero(U_914)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_914,c_Groups_Ozero__class_Ozero(U_914)),U_916))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_914,U_915),c_Groups_Ozero__class_Ozero(U_914)))
| ~ class_Rings_Oordered__cancel__semiring(U_914) ),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2]) ).
fof(f_302_2,plain,
! [U_919,U_918,U_917] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_917),U_919),U_918)),c_Groups_Ozero__class_Ozero(U_917)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_917,U_919),c_Groups_Ozero__class_Ozero(U_917)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_917,c_Groups_Ozero__class_Ozero(U_917)),U_918))
| ~ class_Rings_Oordered__cancel__semiring(U_917) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_917),U_919),U_918)),c_Groups_Ozero__class_Ozero(U_917)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_917,U_919),c_Groups_Ozero__class_Ozero(U_917)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_917,c_Groups_Ozero__class_Ozero(U_917)),U_918))
| ~ class_Rings_Oordered__cancel__semiring(U_917) ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos]) ).
fof(f_303_2,plain,
! [U_922,U_921,U_920] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_920,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_922)),c_Groups_Ozero__class_Ozero(U_920)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_920,U_922),c_Groups_Ozero__class_Ozero(U_920)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_920,c_Groups_Ozero__class_Ozero(U_920)),U_921))
| ~ class_Rings_Oordered__cancel__semiring(U_920) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_920,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_922)),c_Groups_Ozero__class_Ozero(U_920)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_920,U_922),c_Groups_Ozero__class_Ozero(U_920)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_920,c_Groups_Ozero__class_Ozero(U_920)),U_921))
| ~ class_Rings_Oordered__cancel__semiring(U_920) ),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg]) ).
fof(f_304_2,plain,
! [U_925,U_924,U_923] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_923),U_924),U_925)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923)),U_925))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923)),U_924))
| ~ class_Rings_Oordered__cancel__semiring(U_923) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
cnf(f_304_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_923),U_924),U_925)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923)),U_925))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923)),U_924))
| ~ class_Rings_Oordered__cancel__semiring(U_923) ),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(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)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
| ~ hBOOL(hAPP(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_305_2,plain,
! [U_928,U_927,U_926] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_928))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_927),c_Groups_Ozero__class_Ozero(U_926))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_928),c_Groups_Ozero__class_Ozero(U_926)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_927)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_928))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_927),c_Groups_Ozero__class_Ozero(U_926))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_928),c_Groups_Ozero__class_Ozero(U_926)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_927)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_926) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_927),c_Groups_Ozero__class_Ozero(U_926)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_927))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926)))
| ~ class_Rings_Olinordered__ring__strict(U_926) ),
inference(clausify,[status(thm)],[f_305_2]) ).
cnf(f_305_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_928))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_927))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926)))
| ~ class_Rings_Olinordered__ring__strict(U_926) ),
inference(clausify,[status(thm)],[f_305_2]) ).
cnf(f_305_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_927),c_Groups_Ozero__class_Ozero(U_926)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_928),c_Groups_Ozero__class_Ozero(U_926)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926)))
| ~ class_Rings_Olinordered__ring__strict(U_926) ),
inference(clausify,[status(thm)],[f_305_2]) ).
cnf(f_305_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_928))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_928),c_Groups_Ozero__class_Ozero(U_926)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926)))
| ~ class_Rings_Olinordered__ring__strict(U_926) ),
inference(clausify,[status(thm)],[f_305_2]) ).
cnf(f_305_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_928),c_Groups_Ozero__class_Ozero(U_926)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_927))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926)))
| ~ class_Rings_Olinordered__ring__strict(U_926) ),
inference(clausify,[status(thm)],[f_305_2]) ).
cnf(f_305_8,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926)),U_928))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,U_927),c_Groups_Ozero__class_Ozero(U_926)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_928)),c_Groups_Ozero__class_Ozero(U_926)))
| ~ class_Rings_Olinordered__ring__strict(U_926) ),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).
fof(f_306_2,plain,
! [U_931,U_930,U_929] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_931),c_Groups_Ozero__class_Ozero(U_929)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_930),c_Groups_Ozero__class_Ozero(U_929))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_931))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_930)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_931),c_Groups_Ozero__class_Ozero(U_929)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_930),c_Groups_Ozero__class_Ozero(U_929))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_931))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_930)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_929) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_930),c_Groups_Ozero__class_Ozero(U_929)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_930))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931)))
| ~ class_Rings_Olinordered__ring__strict(U_929) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_931),c_Groups_Ozero__class_Ozero(U_929)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_930))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931)))
| ~ class_Rings_Olinordered__ring__strict(U_929) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_930),c_Groups_Ozero__class_Ozero(U_929)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_931))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931)))
| ~ class_Rings_Olinordered__ring__strict(U_929) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_931),c_Groups_Ozero__class_Ozero(U_929)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_931))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931)))
| ~ class_Rings_Olinordered__ring__strict(U_929) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_931))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),U_930))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931)))
| ~ class_Rings_Olinordered__ring__strict(U_929) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_8,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_931),c_Groups_Ozero__class_Ozero(U_929)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,U_930),c_Groups_Ozero__class_Ozero(U_929)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_929,c_Groups_Ozero__class_Ozero(U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_929),U_930),U_931)))
| ~ class_Rings_Olinordered__ring__strict(U_929) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__square]) ).
fof(f_307_2,plain,
! [U_933,U_932] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_932,c_Groups_Ozero__class_Ozero(U_932)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_932),U_933),U_933)))
| ~ class_Rings_Olinordered__ring(U_932) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_932,c_Groups_Ozero__class_Ozero(U_932)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_932),U_933),U_933)))
| ~ class_Rings_Olinordered__ring(U_932) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg]) ).
fof(f_308_2,plain,
! [U_937,U_936,U_935,U_934] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_934,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_937),U_936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_937),U_935)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_934,U_937),c_Groups_Ozero__class_Ozero(U_934)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_934,U_935),U_936))
| ~ class_Rings_Olinordered__ring__strict(U_934) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_934,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_937),U_936)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_934),U_937),U_935)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_934,U_937),c_Groups_Ozero__class_Ozero(U_934)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_934,U_935),U_936))
| ~ class_Rings_Olinordered__ring__strict(U_934) ),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),V_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg]) ).
fof(f_309_2,plain,
! [U_941,U_940,U_939,U_938] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_940),U_941)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_939),U_941)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_938,U_941),c_Groups_Ozero__class_Ozero(U_938)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_938,U_939),U_940))
| ~ class_Rings_Olinordered__ring__strict(U_938) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_940),U_941)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_938),U_939),U_941)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_938,U_941),c_Groups_Ozero__class_Ozero(U_938)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_938,U_939),U_940))
| ~ class_Rings_Olinordered__ring__strict(U_938) ),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__comm__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono]) ).
fof(f_310_2,plain,
! [U_945,U_944,U_943,U_942] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_942,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_942),U_945),U_943)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_942),U_945),U_944)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_942,c_Groups_Ozero__class_Ozero(U_942)),U_945))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_942,U_943),U_944))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_942) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_942,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_942),U_945),U_943)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_942),U_945),U_944)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_942,c_Groups_Ozero__class_Ozero(U_942)),U_945))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_942,U_943),U_944))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_942) ),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono]) ).
fof(f_311_2,plain,
! [U_949,U_948,U_947,U_946] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_949),U_947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_949),U_948)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_946,c_Groups_Ozero__class_Ozero(U_946)),U_949))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_946,U_947),U_948))
| ~ class_Rings_Olinordered__semiring__strict(U_946) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_949),U_947)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_949),U_948)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_946,c_Groups_Ozero__class_Ozero(U_946)),U_949))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_946,U_947),U_948))
| ~ class_Rings_Olinordered__semiring__strict(U_946) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono]) ).
fof(f_312_2,plain,
! [U_953,U_952,U_951,U_950] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_951),U_953)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_952),U_953)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_950,c_Groups_Ozero__class_Ozero(U_950)),U_953))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_950,U_951),U_952))
| ~ class_Rings_Olinordered__semiring__strict(U_950) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
cnf(f_312_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_950,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_951),U_953)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_950),U_952),U_953)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_950,c_Groups_Ozero__class_Ozero(U_950)),U_953))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_950,U_951),U_952))
| ~ class_Rings_Olinordered__semiring__strict(U_950) ),
inference(clausify,[status(thm)],[f_312_2]) ).
fof(f_313_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__neg]) ).
fof(f_313_2,plain,
! [U_956,U_955,U_954] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_954,c_Groups_Ozero__class_Ozero(U_954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_954),U_955),U_956)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_954,U_956),c_Groups_Ozero__class_Ozero(U_954)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_954,U_955),c_Groups_Ozero__class_Ozero(U_954)))
| ~ class_Rings_Olinordered__ring__strict(U_954) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_954,c_Groups_Ozero__class_Ozero(U_954)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_954),U_955),U_956)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_954,U_956),c_Groups_Ozero__class_Ozero(U_954)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_954,U_955),c_Groups_Ozero__class_Ozero(U_954)))
| ~ class_Rings_Olinordered__ring__strict(U_954) ),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__pos]) ).
fof(f_314_2,plain,
! [U_959,U_958,U_957] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_957,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),U_959)),c_Groups_Ozero__class_Ozero(U_957)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_957,c_Groups_Ozero__class_Ozero(U_957)),U_959))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_957,U_958),c_Groups_Ozero__class_Ozero(U_957)))
| ~ class_Rings_Olinordered__semiring__strict(U_957) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_957,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),U_959)),c_Groups_Ozero__class_Ozero(U_957)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_957,c_Groups_Ozero__class_Ozero(U_957)),U_959))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_957,U_958),c_Groups_Ozero__class_Ozero(U_957)))
| ~ class_Rings_Olinordered__semiring__strict(U_957) ),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_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_315_2,plain,
! [U_963,U_962,U_961,U_960] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_963)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,U_963),U_962)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,U_963),U_962))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_963))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,U_961),c_Groups_Ozero__class_Ozero(U_960)))
| ~ class_Rings_Olinordered__ring__strict(U_960) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,U_963),U_962))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_963)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,U_961),c_Groups_Ozero__class_Ozero(U_960)))
| ~ class_Rings_Olinordered__ring__strict(U_960) ),
inference(clausify,[status(thm)],[f_315_2]) ).
cnf(f_315_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_962)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_963)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,U_963),U_962))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_960,U_961),c_Groups_Ozero__class_Ozero(U_960)))
| ~ class_Rings_Olinordered__ring__strict(U_960) ),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_1,plain,
! [V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2]) ).
fof(f_316_2,plain,
! [U_966,U_965,U_964] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_964,c_Groups_Ozero__class_Ozero(U_964)),U_965))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_964,c_Groups_Ozero__class_Ozero(U_964)),U_966))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_964,c_Groups_Ozero__class_Ozero(U_964)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_964),U_965),U_966)))
| ~ class_Rings_Olinordered__semiring__strict(U_964) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_964,c_Groups_Ozero__class_Ozero(U_964)),U_965))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_964,c_Groups_Ozero__class_Ozero(U_964)),U_966))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_964,c_Groups_Ozero__class_Ozero(U_964)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_964),U_965),U_966)))
| ~ class_Rings_Olinordered__semiring__strict(U_964) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos]) ).
fof(f_317_2,plain,
! [U_969,U_968,U_967] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_967,c_Groups_Ozero__class_Ozero(U_967)),U_969))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_967,c_Groups_Ozero__class_Ozero(U_967)),U_968))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_967,c_Groups_Ozero__class_Ozero(U_967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_967),U_968),U_969)))
| ~ class_Rings_Olinordered__semiring__strict(U_967) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_967,c_Groups_Ozero__class_Ozero(U_967)),U_969))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_967,c_Groups_Ozero__class_Ozero(U_967)),U_968))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_967,c_Groups_Ozero__class_Ozero(U_967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_967),U_968),U_969)))
| ~ class_Rings_Olinordered__semiring__strict(U_967) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2]) ).
fof(f_318_2,plain,
! [U_972,U_971,U_970] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_972),U_971)),c_Groups_Ozero__class_Ozero(U_970)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_970,U_972),c_Groups_Ozero__class_Ozero(U_970)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_970,c_Groups_Ozero__class_Ozero(U_970)),U_971))
| ~ class_Rings_Olinordered__semiring__strict(U_970) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
cnf(f_318_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_970,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_972),U_971)),c_Groups_Ozero__class_Ozero(U_970)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_970,U_972),c_Groups_Ozero__class_Ozero(U_970)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_970,c_Groups_Ozero__class_Ozero(U_970)),U_971))
| ~ class_Rings_Olinordered__semiring__strict(U_970) ),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg]) ).
fof(f_319_2,plain,
! [U_975,U_974,U_973] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_973,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_973),U_974),U_975)),c_Groups_Ozero__class_Ozero(U_973)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_973,U_975),c_Groups_Ozero__class_Ozero(U_973)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_973,c_Groups_Ozero__class_Ozero(U_973)),U_974))
| ~ class_Rings_Olinordered__semiring__strict(U_973) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
cnf(f_319_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_973,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_973),U_974),U_975)),c_Groups_Ozero__class_Ozero(U_973)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_973,U_975),c_Groups_Ozero__class_Ozero(U_973)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_973,c_Groups_Ozero__class_Ozero(U_973)),U_974))
| ~ class_Rings_Olinordered__semiring__strict(U_973) ),
inference(clausify,[status(thm)],[f_319_2]) ).
fof(f_320_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__pos]) ).
fof(f_320_2,plain,
! [U_978,U_977,U_976] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_976,c_Groups_Ozero__class_Ozero(U_976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_976),U_977),U_978)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_976,c_Groups_Ozero__class_Ozero(U_976)),U_978))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_976,c_Groups_Ozero__class_Ozero(U_976)),U_977))
| ~ class_Rings_Olinordered__semiring__strict(U_976) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_976,c_Groups_Ozero__class_Ozero(U_976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_976),U_977),U_978)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_976,c_Groups_Ozero__class_Ozero(U_976)),U_978))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_976,c_Groups_Ozero__class_Ozero(U_976)),U_977))
| ~ class_Rings_Olinordered__semiring__strict(U_976) ),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_321_2,plain,
! [U_982,U_981,U_980,U_979] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_982)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,U_981),U_982)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,U_981),U_982))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_982))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,c_Groups_Ozero__class_Ozero(U_979)),U_980))
| ~ class_Rings_Olinordered__ring__strict(U_979) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,U_981),U_982))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_982)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,c_Groups_Ozero__class_Ozero(U_979)),U_980))
| ~ class_Rings_Olinordered__ring__strict(U_979) ),
inference(clausify,[status(thm)],[f_321_2]) ).
cnf(f_321_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_982)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,U_981),U_982))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_979,c_Groups_Ozero__class_Ozero(U_979)),U_980))
| ~ class_Rings_Olinordered__ring__strict(U_979) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_322_2,plain,
! [U_986,U_985,U_984,U_983] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_986),U_985))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_984),c_Groups_Ozero__class_Ozero(U_983))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_985),U_986))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,c_Groups_Ozero__class_Ozero(U_983)),U_984)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_986),U_985))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_984),c_Groups_Ozero__class_Ozero(U_983))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_985),U_986))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,c_Groups_Ozero__class_Ozero(U_983)),U_984)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_983) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_984),c_Groups_Ozero__class_Ozero(U_983)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,c_Groups_Ozero__class_Ozero(U_983)),U_984))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986)))
| ~ class_Rings_Olinordered__ring__strict(U_983) ),
inference(clausify,[status(thm)],[f_322_2]) ).
cnf(f_322_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_986),U_985))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,c_Groups_Ozero__class_Ozero(U_983)),U_984))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986)))
| ~ class_Rings_Olinordered__ring__strict(U_983) ),
inference(clausify,[status(thm)],[f_322_2]) ).
cnf(f_322_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_984),c_Groups_Ozero__class_Ozero(U_983)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_985),U_986))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986)))
| ~ class_Rings_Olinordered__ring__strict(U_983) ),
inference(clausify,[status(thm)],[f_322_2]) ).
cnf(f_322_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_986),U_985))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_985),U_986))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986)))
| ~ class_Rings_Olinordered__ring__strict(U_983) ),
inference(clausify,[status(thm)],[f_322_2]) ).
cnf(f_322_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_985),U_986))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,c_Groups_Ozero__class_Ozero(U_983)),U_984))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986)))
| ~ class_Rings_Olinordered__ring__strict(U_983) ),
inference(clausify,[status(thm)],[f_322_2]) ).
cnf(f_322_8,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_986),U_985))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,U_984),c_Groups_Ozero__class_Ozero(U_983)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_983,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_985)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_983),U_984),U_986)))
| ~ class_Rings_Olinordered__ring__strict(U_983) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_1,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_b_2),V_a_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),c_Groups_Ozero__class_Ozero(T_a))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_323_2,plain,
! [U_990,U_989,U_988,U_987] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989)))
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_990),U_988))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_989),c_Groups_Ozero__class_Ozero(U_987))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_988),U_990))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,c_Groups_Ozero__class_Ozero(U_987)),U_989)) ) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_990),U_988))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_989),c_Groups_Ozero__class_Ozero(U_987))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_988),U_990))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,c_Groups_Ozero__class_Ozero(U_987)),U_989)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_987) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_989),c_Groups_Ozero__class_Ozero(U_987)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,c_Groups_Ozero__class_Ozero(U_987)),U_989))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989)))
| ~ class_Rings_Olinordered__ring__strict(U_987) ),
inference(clausify,[status(thm)],[f_323_2]) ).
cnf(f_323_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_990),U_988))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,c_Groups_Ozero__class_Ozero(U_987)),U_989))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989)))
| ~ class_Rings_Olinordered__ring__strict(U_987) ),
inference(clausify,[status(thm)],[f_323_2]) ).
cnf(f_323_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_989),c_Groups_Ozero__class_Ozero(U_987)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_988),U_990))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989)))
| ~ class_Rings_Olinordered__ring__strict(U_987) ),
inference(clausify,[status(thm)],[f_323_2]) ).
cnf(f_323_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_990),U_988))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_988),U_990))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989)))
| ~ class_Rings_Olinordered__ring__strict(U_987) ),
inference(clausify,[status(thm)],[f_323_2]) ).
cnf(f_323_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_988),U_990))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,c_Groups_Ozero__class_Ozero(U_987)),U_989))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989)))
| ~ class_Rings_Olinordered__ring__strict(U_987) ),
inference(clausify,[status(thm)],[f_323_2]) ).
cnf(f_323_8,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_990),U_988))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,U_989),c_Groups_Ozero__class_Ozero(U_987)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_987,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_988),U_989)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_987),U_990),U_989)))
| ~ class_Rings_Olinordered__ring__strict(U_987) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_1,plain,
! [V_a,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__square__less__zero]) ).
fof(f_324_2,plain,
! [U_992,U_991] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_991,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_991),U_992),U_992)),c_Groups_Ozero__class_Ozero(U_991)))
| ~ class_Rings_Olinordered__ring(U_991) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
cnf(f_324_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_991,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_991),U_992),U_992)),c_Groups_Ozero__class_Ozero(U_991)))
| ~ class_Rings_Olinordered__ring(U_991) ),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_1,plain,
! [V_n,V_m,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_m))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__1__mult]) ).
fof(f_325_2,plain,
! [U_995,U_994,U_993] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_993,c_Groups_Oone__class_Oone(U_993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_993),U_994),U_995)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_993,c_Groups_Oone__class_Oone(U_993)),U_995))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_993,c_Groups_Oone__class_Oone(U_993)),U_994))
| ~ class_Rings_Olinordered__semidom(U_993) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_993,c_Groups_Oone__class_Oone(U_993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_993),U_994),U_995)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_993,c_Groups_Oone__class_Oone(U_993)),U_995))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_993,c_Groups_Oone__class_Oone(U_993)),U_994))
| ~ class_Rings_Olinordered__semidom(U_993) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b)),V_d))
| ~ hBOOL(hAPP(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_326_2,plain,
! [U_1000,U_999,U_998,U_997,U_996] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_996,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_996),c_Groups_Oabs__class_Oabs(U_996,U_997)),c_Groups_Oabs__class_Oabs(U_996,U_999))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_996),U_998),U_1000)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_996,c_Groups_Oabs__class_Oabs(U_996,U_999)),U_1000))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_996,c_Groups_Oabs__class_Oabs(U_996,U_997)),U_998))
| ~ class_Rings_Olinordered__idom(U_996) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_996,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_996),c_Groups_Oabs__class_Oabs(U_996,U_997)),c_Groups_Oabs__class_Oabs(U_996,U_999))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_996),U_998),U_1000)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_996,c_Groups_Oabs__class_Oabs(U_996,U_999)),U_1000))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_996,c_Groups_Oabs__class_Oabs(U_996,U_997)),U_998))
| ~ class_Rings_Olinordered__idom(U_996) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_1,plain,
! [V_y,V_x,V_z] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_y))
| ~ hBOOL(hAPP(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_327_2,plain,
! [U_1003,U_1002,U_1001] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1001),U_1002)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1001),U_1003)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1002),U_1003))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1001)) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1001),U_1002)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1001),U_1003)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1002),U_1003))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1001)) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
| ~ hBOOL(hAPP(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_328_2,plain,
! [U_1005,U_1004] :
( hBOOL(hAPP(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_1004),U_1005)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1005))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1004)) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( hBOOL(hAPP(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_1004),U_1005)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1005))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1004)) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(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_329_2,plain,
! [U_1008,U_1007,U_1006] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1007),U_1006)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1008),U_1006)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1007),U_1008)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1007),U_1008))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1007),U_1006)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1008),U_1006))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1006)) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1007),U_1008))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1007),U_1006)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1008),U_1006)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1006)) ),
inference(clausify,[status(thm)],[f_329_2]) ).
cnf(f_329_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1007),U_1006)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1008),U_1006)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1007),U_1008))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1006)) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_1,plain,
! [V_y_2,V_x_2] :
( ( hAPP(hAPP(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) )
| hAPP(hAPP(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_330_2,plain,
! [U_1010,U_1009] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1009),U_1009)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1010),U_1010)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1010 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1009 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_1010 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_1009 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1009),U_1009)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1010),U_1010)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
( ! [U_1014,U_1012] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1012),U_1012)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1014),U_1014)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1014 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1012 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1013,U_1011] :
( ( U_1013 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_1011 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1011),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1013),U_1013)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_330_2]) ).
cnf(f_330_4,plain,
( U_1011 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1011),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1013),U_1013)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_5,plain,
( U_1013 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1011),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1013),U_1013)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1012),U_1012)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1014),U_1014)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1014 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1012 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2)),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(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_331_2,plain,
! [U_1016,U_1015] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,c_Groups_Osgn__class_Osgn(U_1015,U_1016)),c_Groups_Ozero__class_Ozero(U_1015)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,U_1016),c_Groups_Ozero__class_Ozero(U_1015))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,U_1016),c_Groups_Ozero__class_Ozero(U_1015)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,c_Groups_Osgn__class_Osgn(U_1015,U_1016)),c_Groups_Ozero__class_Ozero(U_1015))) ) )
| ~ class_Rings_Olinordered__idom(U_1015) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,U_1016),c_Groups_Ozero__class_Ozero(U_1015)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,c_Groups_Osgn__class_Osgn(U_1015,U_1016)),c_Groups_Ozero__class_Ozero(U_1015)))
| ~ class_Rings_Olinordered__idom(U_1015) ),
inference(clausify,[status(thm)],[f_331_2]) ).
cnf(f_331_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,c_Groups_Osgn__class_Osgn(U_1015,U_1016)),c_Groups_Ozero__class_Ozero(U_1015)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1015,U_1016),c_Groups_Ozero__class_Ozero(U_1015)))
| ~ class_Rings_Olinordered__idom(U_1015) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_1,plain,
! [V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Osgn__class_Osgn(T_a,V_a_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2))
| ~ hBOOL(hAPP(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_332_2,plain,
! [U_1018,U_1017] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),c_Groups_Osgn__class_Osgn(U_1017,U_1018)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),U_1018)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),U_1018))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),c_Groups_Osgn__class_Osgn(U_1017,U_1018))) ) )
| ~ class_Rings_Olinordered__idom(U_1017) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),U_1018))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),c_Groups_Osgn__class_Osgn(U_1017,U_1018)))
| ~ class_Rings_Olinordered__idom(U_1017) ),
inference(clausify,[status(thm)],[f_332_2]) ).
cnf(f_332_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),c_Groups_Osgn__class_Osgn(U_1017,U_1018)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1017,c_Groups_Ozero__class_Ozero(U_1017)),U_1018))
| ~ class_Rings_Olinordered__idom(U_1017) ),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le]) ).
fof(f_333_2,plain,
! [U_1022,U_1021,U_1020,U_1019] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1019,U_1021),U_1022))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1019,c_Groups_Ozero__class_Ozero(U_1019)),U_1020))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1019,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1019),U_1020),U_1021)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1019),U_1020),U_1022)))
| ~ class_Rings_Olinordered__semiring__strict(U_1019) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1019,U_1021),U_1022))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1019,c_Groups_Ozero__class_Ozero(U_1019)),U_1020))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1019,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1019),U_1020),U_1021)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1019),U_1020),U_1022)))
| ~ class_Rings_Olinordered__semiring__strict(U_1019) ),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le]) ).
fof(f_334_2,plain,
! [U_1026,U_1025,U_1024,U_1023] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1023,U_1024),U_1026))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1023,c_Groups_Ozero__class_Ozero(U_1023)),U_1025))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1023,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1023),U_1024),U_1025)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1023),U_1026),U_1025)))
| ~ class_Rings_Olinordered__semiring__strict(U_1023) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
cnf(f_334_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1023,U_1024),U_1026))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1023,c_Groups_Ozero__class_Ozero(U_1023)),U_1025))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1023,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1023),U_1024),U_1025)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1023),U_1026),U_1025)))
| ~ class_Rings_Olinordered__semiring__strict(U_1023) ),
inference(clausify,[status(thm)],[f_334_2]) ).
fof(f_335_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left]) ).
fof(f_335_2,plain,
! [U_1030,U_1029,U_1028,U_1027] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1027,U_1029),U_1030))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1027,c_Groups_Ozero__class_Ozero(U_1027)),U_1028))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1027,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1027),U_1028),U_1029)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1027),U_1028),U_1030)))
| ~ class_Rings_Olinordered__semiring__strict(U_1027) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1027,U_1029),U_1030))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1027,c_Groups_Ozero__class_Ozero(U_1027)),U_1028))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1027,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1027),U_1028),U_1029)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1027),U_1028),U_1030)))
| ~ class_Rings_Olinordered__semiring__strict(U_1027) ),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_1,plain,
! [V_b,V_a,V_c,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less]) ).
fof(f_336_2,plain,
! [U_1034,U_1033,U_1032,U_1031] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1031,U_1033),U_1034))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Ozero__class_Ozero(U_1031)),U_1032))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1031),U_1032),U_1033)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1031),U_1032),U_1034)))
| ~ class_Rings_Olinordered__semiring(U_1031) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1031,U_1033),U_1034))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Ozero__class_Ozero(U_1031)),U_1032))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1031),U_1032),U_1033)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1031),U_1032),U_1034)))
| ~ class_Rings_Olinordered__semiring(U_1031) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right]) ).
fof(f_337_2,plain,
! [U_1038,U_1037,U_1036,U_1035] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1035,U_1036),U_1038))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1035,c_Groups_Ozero__class_Ozero(U_1035)),U_1037))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1035,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1035),U_1036),U_1037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1035),U_1038),U_1037)))
| ~ class_Rings_Olinordered__semiring__strict(U_1035) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1035,U_1036),U_1038))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1035,c_Groups_Ozero__class_Ozero(U_1035)),U_1037))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1035,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1035),U_1036),U_1037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1035),U_1038),U_1037)))
| ~ class_Rings_Olinordered__semiring__strict(U_1035) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less]) ).
fof(f_338_2,plain,
! [U_1042,U_1041,U_1040,U_1039] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1039,U_1040),U_1042))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1039,c_Groups_Ozero__class_Ozero(U_1039)),U_1041))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1040),U_1041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1042),U_1041)))
| ~ class_Rings_Olinordered__semiring(U_1039) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1039,U_1040),U_1042))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1039,c_Groups_Ozero__class_Ozero(U_1039)),U_1041))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1040),U_1041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1042),U_1041)))
| ~ class_Rings_Olinordered__semiring(U_1039) ),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less]) ).
fof(f_339_2,plain,
! [U_1047,U_1046,U_1045,U_1044,U_1043] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1043,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1043),U_1044),U_1046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1043),U_1045),U_1047)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043)),U_1046))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1043,c_Groups_Ozero__class_Ozero(U_1043)),U_1044))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1043,U_1046),U_1047))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043,U_1044),U_1045))
| ~ class_Rings_Olinordered__semiring__strict(U_1043) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1043,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1043),U_1044),U_1046)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1043),U_1045),U_1047)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043,c_Groups_Ozero__class_Ozero(U_1043)),U_1046))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1043,c_Groups_Ozero__class_Ozero(U_1043)),U_1044))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1043,U_1046),U_1047))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043,U_1044),U_1045))
| ~ class_Rings_Olinordered__semiring__strict(U_1043) ),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less]) ).
fof(f_340_2,plain,
! [U_1052,U_1051,U_1050,U_1049,U_1048] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1048),U_1049),U_1051)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1048),U_1050),U_1052)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1048,c_Groups_Ozero__class_Ozero(U_1048)),U_1051))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1048,c_Groups_Ozero__class_Ozero(U_1048)),U_1049))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1048,U_1051),U_1052))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1048,U_1049),U_1050))
| ~ class_Rings_Olinordered__semiring__strict(U_1048) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1048,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1048),U_1049),U_1051)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1048),U_1050),U_1052)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1048,c_Groups_Ozero__class_Ozero(U_1048)),U_1051))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1048,c_Groups_Ozero__class_Ozero(U_1048)),U_1049))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1048,U_1051),U_1052))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1048,U_1049),U_1050))
| ~ class_Rings_Olinordered__semiring__strict(U_1048) ),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H]) ).
fof(f_341_2,plain,
! [U_1057,U_1056,U_1055,U_1054,U_1053] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1053,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1053),U_1054),U_1056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1053),U_1055),U_1057)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1053,c_Groups_Ozero__class_Ozero(U_1053)),U_1056))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1053,c_Groups_Ozero__class_Ozero(U_1053)),U_1054))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1053,U_1056),U_1057))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1053,U_1054),U_1055))
| ~ class_Rings_Olinordered__semiring__strict(U_1053) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1053,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1053),U_1054),U_1056)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1053),U_1055),U_1057)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1053,c_Groups_Ozero__class_Ozero(U_1053)),U_1056))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1053,c_Groups_Ozero__class_Ozero(U_1053)),U_1054))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1053,U_1056),U_1057))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1053,U_1054),U_1055))
| ~ class_Rings_Olinordered__semiring__strict(U_1053) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c),V_d))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__mono]) ).
fof(f_342_2,plain,
! [U_1062,U_1061,U_1060,U_1059,U_1058] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1059),U_1061)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1060),U_1062)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1058,c_Groups_Ozero__class_Ozero(U_1058)),U_1061))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,c_Groups_Ozero__class_Ozero(U_1058)),U_1060))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,U_1061),U_1062))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,U_1059),U_1060))
| ~ class_Rings_Olinordered__semiring__strict(U_1058) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1059),U_1061)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1060),U_1062)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1058,c_Groups_Ozero__class_Ozero(U_1058)),U_1061))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,c_Groups_Ozero__class_Ozero(U_1058)),U_1060))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,U_1061),U_1062))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1058,U_1059),U_1060))
| ~ class_Rings_Olinordered__semiring__strict(U_1058) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),V_a_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b_2),V_a_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_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_343_2,plain,
! [U_1066,U_1065,U_1064,U_1063] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1065)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1066)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,U_1066),U_1065)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,U_1066),U_1065))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1065)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1066))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1063,U_1064),c_Groups_Ozero__class_Ozero(U_1063)))
| ~ class_Rings_Olinordered__ring__strict(U_1063) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,U_1066),U_1065))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1065)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1066)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1063,U_1064),c_Groups_Ozero__class_Ozero(U_1063)))
| ~ class_Rings_Olinordered__ring__strict(U_1063) ),
inference(clausify,[status(thm)],[f_343_2]) ).
cnf(f_343_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1065)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1063),U_1064),U_1066)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1063,U_1066),U_1065))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1063,U_1064),c_Groups_Ozero__class_Ozero(U_1063)))
| ~ class_Rings_Olinordered__ring__strict(U_1063) ),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).
fof(f_344_2,plain,
! [U_1070,U_1069,U_1068,U_1067] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1070)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,U_1069),U_1070)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,U_1069),U_1070))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1070))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1067,c_Groups_Ozero__class_Ozero(U_1067)),U_1068))
| ~ class_Rings_Olinordered__ring__strict(U_1067) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,U_1069),U_1070))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1070)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1067,c_Groups_Ozero__class_Ozero(U_1067)),U_1068))
| ~ class_Rings_Olinordered__ring__strict(U_1067) ),
inference(clausify,[status(thm)],[f_344_2]) ).
cnf(f_344_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),U_1068),U_1070)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1067,U_1069),U_1070))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1067,c_Groups_Ozero__class_Ozero(U_1067)),U_1068))
| ~ class_Rings_Olinordered__ring__strict(U_1067) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le]) ).
fof(f_345_2,plain,
! [U_1073,U_1072,U_1071] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1071),U_1073),U_1072)),U_1072))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,U_1073),c_Groups_Oone__class_Oone(U_1071)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,c_Groups_Ozero__class_Ozero(U_1071)),U_1073))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,c_Groups_Ozero__class_Ozero(U_1071)),U_1072))
| ~ class_Rings_Olinordered__idom(U_1071) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1071),U_1073),U_1072)),U_1072))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,U_1073),c_Groups_Oone__class_Oone(U_1071)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,c_Groups_Ozero__class_Ozero(U_1071)),U_1073))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1071,c_Groups_Ozero__class_Ozero(U_1071)),U_1072))
| ~ class_Rings_Olinordered__idom(U_1071) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le]) ).
fof(f_346_2,plain,
! [U_1076,U_1075,U_1074] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1074),U_1075),U_1076)),U_1075))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,U_1076),c_Groups_Oone__class_Oone(U_1074)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,c_Groups_Ozero__class_Ozero(U_1074)),U_1076))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,c_Groups_Ozero__class_Ozero(U_1074)),U_1075))
| ~ class_Rings_Olinordered__idom(U_1074) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1074),U_1075),U_1076)),U_1075))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,U_1076),c_Groups_Oone__class_Oone(U_1074)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,c_Groups_Ozero__class_Ozero(U_1074)),U_1076))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1074,c_Groups_Ozero__class_Ozero(U_1074)),U_1075))
| ~ class_Rings_Olinordered__idom(U_1074) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_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))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
| ~ class_Rings_Oordered__ring__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__mult]) ).
fof(f_347_2,plain,
! [U_1079,U_1078,U_1077] :
( c_Groups_Oabs__class_Oabs(U_1077,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),c_Groups_Oabs__class_Oabs(U_1077,U_1078)),c_Groups_Oabs__class_Oabs(U_1077,U_1079))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,U_1079),c_Groups_Ozero__class_Ozero(U_1077)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,c_Groups_Ozero__class_Ozero(U_1077)),U_1079)) )
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,U_1078),c_Groups_Ozero__class_Ozero(U_1077)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,c_Groups_Ozero__class_Ozero(U_1077)),U_1078)) )
| ~ class_Rings_Oordered__ring__abs(U_1077) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,c_Groups_Ozero__class_Ozero(U_1077)),U_1079))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,c_Groups_Ozero__class_Ozero(U_1077)),U_1078))
| c_Groups_Oabs__class_Oabs(U_1077,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),c_Groups_Oabs__class_Oabs(U_1077,U_1078)),c_Groups_Oabs__class_Oabs(U_1077,U_1079))
| ~ class_Rings_Oordered__ring__abs(U_1077) ),
inference(clausify,[status(thm)],[f_347_2]) ).
cnf(f_347_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,U_1079),c_Groups_Ozero__class_Ozero(U_1077)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,c_Groups_Ozero__class_Ozero(U_1077)),U_1078))
| c_Groups_Oabs__class_Oabs(U_1077,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),c_Groups_Oabs__class_Oabs(U_1077,U_1078)),c_Groups_Oabs__class_Oabs(U_1077,U_1079))
| ~ class_Rings_Oordered__ring__abs(U_1077) ),
inference(clausify,[status(thm)],[f_347_2]) ).
cnf(f_347_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,c_Groups_Ozero__class_Ozero(U_1077)),U_1079))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,U_1078),c_Groups_Ozero__class_Ozero(U_1077)))
| c_Groups_Oabs__class_Oabs(U_1077,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),c_Groups_Oabs__class_Oabs(U_1077,U_1078)),c_Groups_Oabs__class_Oabs(U_1077,U_1079))
| ~ class_Rings_Oordered__ring__abs(U_1077) ),
inference(clausify,[status(thm)],[f_347_2]) ).
cnf(f_347_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,U_1079),c_Groups_Ozero__class_Ozero(U_1077)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1077,U_1078),c_Groups_Ozero__class_Ozero(U_1077)))
| c_Groups_Oabs__class_Oabs(U_1077,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),c_Groups_Oabs__class_Oabs(U_1077,U_1078)),c_Groups_Oabs__class_Oabs(U_1077,U_1079))
| ~ class_Rings_Oordered__ring__abs(U_1077) ),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_x))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult__pos]) ).
fof(f_348_2,plain,
! [U_1082,U_1081,U_1080] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1080),c_Groups_Oabs__class_Oabs(U_1080,U_1082)),U_1081) = c_Groups_Oabs__class_Oabs(U_1080,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1080),U_1082),U_1081))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080,c_Groups_Ozero__class_Ozero(U_1080)),U_1081))
| ~ class_Rings_Olinordered__idom(U_1080) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
cnf(f_348_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1080),c_Groups_Oabs__class_Oabs(U_1080,U_1082)),U_1081) = c_Groups_Oabs__class_Oabs(U_1080,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1080),U_1082),U_1081))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080,c_Groups_Ozero__class_Ozero(U_1080)),U_1081))
| ~ class_Rings_Olinordered__idom(U_1080) ),
inference(clausify,[status(thm)],[f_348_2]) ).
fof(f_349_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(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_349_2,plain,
! [U_1085,U_1084,U_1083] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1085)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1084),U_1085)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1084),U_1085))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1085))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1083)) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1084),U_1085))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1085)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1083)) ),
inference(clausify,[status(thm)],[f_349_2]) ).
cnf(f_349_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1083),U_1085)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1084),U_1085))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1083)) ),
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(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_350_2,plain,
! [U_1088,U_1087,U_1086] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1087),U_1086)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1088),U_1086)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1087),U_1088)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1087),U_1088))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1087),U_1086)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1088),U_1086))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1086)) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
cnf(f_350_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1087),U_1088))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1087),U_1086)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1088),U_1086)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1086)) ),
inference(clausify,[status(thm)],[f_350_2]) ).
cnf(f_350_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1087),U_1086)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1088),U_1086)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1087),U_1088))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1086)) ),
inference(clausify,[status(thm)],[f_350_2]) ).
fof(f_351_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_351_2,plain,
! [U_1093,U_1092,U_1091,U_1090,U_1089] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1090),U_1091)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1092),U_1093)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1090),U_1092)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1091),U_1093))
| ~ class_Rings_Ocomm__semiring__1(U_1089) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
cnf(f_351_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1090),U_1091)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1092),U_1093)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1090),U_1092)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1089),U_1091),U_1093))
| ~ class_Rings_Ocomm__semiring__1(U_1089) ),
inference(clausify,[status(thm)],[f_351_2]) ).
fof(f_352_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_352_2,plain,
! [U_1097,U_1096,U_1095,U_1094] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),U_1095),U_1096)),U_1097) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),U_1095),U_1097)),U_1096)
| ~ class_Rings_Ocomm__semiring__1(U_1094) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),U_1095),U_1096)),U_1097) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1094),U_1095),U_1097)),U_1096)
| ~ class_Rings_Ocomm__semiring__1(U_1094) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_353_2,plain,
! [U_1101,U_1100,U_1099,U_1098] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),U_1099),U_1100)),U_1101) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),U_1099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),U_1100),U_1101))
| ~ class_Rings_Ocomm__semiring__1(U_1098) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),U_1099),U_1100)),U_1101) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),U_1099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1098),U_1100),U_1101))
| ~ class_Rings_Ocomm__semiring__1(U_1098) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_1,plain,
! [V_d,V_c,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_354_2,plain,
! [U_1105,U_1104,U_1103,U_1102] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),U_1103),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),U_1104),U_1105)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),U_1103),U_1104)),U_1105)
| ~ class_Rings_Ocomm__semiring__1(U_1102) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),U_1103),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),U_1104),U_1105)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1102),U_1103),U_1104)),U_1105)
| ~ class_Rings_Ocomm__semiring__1(U_1102) ),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_1,plain,
! [V_d,V_c,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_355_2,plain,
! [U_1109,U_1108,U_1107,U_1106] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1107),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1108),U_1109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1108),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1107),U_1109))
| ~ class_Rings_Ocomm__semiring__1(U_1106) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1107),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1108),U_1109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1108),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1106),U_1107),U_1109))
| ~ class_Rings_Ocomm__semiring__1(U_1106) ),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_1,plain,
! [V_c,V_a,T_a] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_356_2,plain,
! [U_1112,U_1111,U_1110] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1110),U_1111),U_1112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1110),U_1112),U_1111)
| ~ class_Rings_Ocomm__semiring__1(U_1110) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1110),U_1111),U_1112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1110),U_1112),U_1111)
| ~ class_Rings_Ocomm__semiring__1(U_1110) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_1,plain,
! [V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_gr0I]) ).
fof(f_357_2,plain,
! [U_1113] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1113))
| U_1113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1113))
| U_1113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_1,plain,
! [V_n,V_m] :
( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) != V_m ),
inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero]) ).
fof(f_358_2,plain,
! [U_1115,U_1114] :
( U_1115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1114),U_1115) != U_1114 ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_1115] :
( ! [U_1114] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1114),U_1115) != U_1114
| U_1115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_358_2]) ).
cnf(f_358_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1114),U_1115) != U_1114
| U_1115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_1,plain,
! [V_n,V_m] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).
fof(f_359_2,plain,
! [U_1117,U_1116] :
( U_1117 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116),U_1117))
| U_1117 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_359_2]) ).
cnf(f_359_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116),U_1117))
| U_1117 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).
fof(f_360_2,plain,
! [U_1119,U_1118] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1118),U_1119) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1119 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1118 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_1119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1118 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1118),U_1119) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
( ! [U_1123,U_1121] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1121),U_1123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1123 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1122,U_1120] :
( ( U_1122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1120),U_1122) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_360_2]) ).
cnf(f_360_4,plain,
( U_1120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1120),U_1122) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_360_3]) ).
cnf(f_360_5,plain,
( U_1122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1120),U_1122) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_360_3]) ).
cnf(f_360_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1121),U_1123) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1123 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1121 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_n_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_361_2,plain,
! [U_1124] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1124),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1124 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1124),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
( ! [U_1126] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1126),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1126 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1125] :
( U_1125 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1125),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_361_2]) ).
cnf(f_361_4,plain,
( U_1125 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1125),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_361_3]) ).
cnf(f_361_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1126),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1126 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
inference(fof_nnf,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(f_362_2,plain,
! [U_1127] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1127),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1127,
inference(variable_rename,[status(thm)],[f_362_1]) ).
cnf(f_362_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1127),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1127,
inference(clausify,[status(thm)],[f_362_2]) ).
fof(f_363_1,plain,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_less__nat__zero__code]) ).
fof(f_363_2,plain,
! [U_1128] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).
fof(f_364_2,plain,
! [U_1130,U_1129] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1129),U_1130)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1130))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1129)) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1130))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1129),U_1130))) ) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
( ! [U_1134,U_1132] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1132),U_1134)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1134))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1132)) ) )
& ! [U_1133,U_1131] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1133))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1131))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1131),U_1133))) ) ),
inference(miniscope,[status(thm)],[f_364_2]) ).
cnf(f_364_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1133))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1131))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1131),U_1133))) ),
inference(clausify,[status(thm)],[f_364_3]) ).
cnf(f_364_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1132))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1132),U_1134))) ),
inference(clausify,[status(thm)],[f_364_3]) ).
cnf(f_364_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1134))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1132),U_1134))) ),
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(f_365_2,plain,
! [U_1135] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1135) = U_1135,
inference(variable_rename,[status(thm)],[f_365_1]) ).
cnf(f_365_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1135) = U_1135,
inference(clausify,[status(thm)],[f_365_2]) ).
fof(f_366_1,plain,
! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(f_366_2,plain,
! [U_1136] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1136)),
inference(variable_rename,[status(thm)],[f_366_1]) ).
cnf(f_366_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1136)),
inference(clausify,[status(thm)],[f_366_2]) ).
fof(f_367_1,plain,
! [V_n_2] :
( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).
fof(f_367_2,plain,
! [U_1137] :
( ( U_1137 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1137)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1137))
| U_1137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
( ! [U_1139] :
( U_1139 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1139)) )
& ! [U_1138] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1138))
| U_1138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_367_2]) ).
cnf(f_367_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1138))
| U_1138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_367_3]) ).
cnf(f_367_5,plain,
( U_1139 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1139)) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [V_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_not__less0]) ).
fof(f_368_2,plain,
! [U_1140] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1140),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_368_1]) ).
cnf(f_368_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1140),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_368_2]) ).
fof(f_369_1,plain,
! [V_x] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(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_369_2,plain,
! [U_1141] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1141) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1141)) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1141) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1141)) ),
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__pos]) ).
fof(f_370_2,plain,
! [U_1143,U_1142] :
( c_Groups_Osgn__class_Osgn(U_1142,U_1143) = c_Groups_Oone__class_Oone(U_1142)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1142,c_Groups_Ozero__class_Ozero(U_1142)),U_1143))
| ~ class_Rings_Olinordered__idom(U_1142) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
( c_Groups_Osgn__class_Osgn(U_1142,U_1143) = c_Groups_Oone__class_Oone(U_1142)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1142,c_Groups_Ozero__class_Ozero(U_1142)),U_1143))
| ~ class_Rings_Olinordered__idom(U_1142) ),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) )
& ( hBOOL(hAPP(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_371_2,plain,
! [U_1145,U_1144] :
( ( ( c_Groups_Osgn__class_Osgn(U_1144,U_1145) = c_Groups_Oone__class_Oone(U_1144)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1144,c_Groups_Ozero__class_Ozero(U_1144)),U_1145)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1144,c_Groups_Ozero__class_Ozero(U_1144)),U_1145))
| c_Groups_Osgn__class_Osgn(U_1144,U_1145) != c_Groups_Oone__class_Oone(U_1144) ) )
| ~ class_Rings_Olinordered__idom(U_1144) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1144,c_Groups_Ozero__class_Ozero(U_1144)),U_1145))
| c_Groups_Osgn__class_Osgn(U_1144,U_1145) != c_Groups_Oone__class_Oone(U_1144)
| ~ class_Rings_Olinordered__idom(U_1144) ),
inference(clausify,[status(thm)],[f_371_2]) ).
cnf(f_371_4,plain,
( c_Groups_Osgn__class_Osgn(U_1144,U_1145) = c_Groups_Oone__class_Oone(U_1144)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1144,c_Groups_Ozero__class_Ozero(U_1144)),U_1145))
| ~ class_Rings_Olinordered__idom(U_1144) ),
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_v))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_u))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_y),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_x),V_a))
| ~ class_Rings_Olinordered__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__le]) ).
fof(f_372_2,plain,
! [U_1151,U_1150,U_1149,U_1148,U_1147,U_1146] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1146),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1146),U_1150),U_1147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1146),U_1151),U_1149))),U_1148))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1146),U_1150),U_1151) != c_Groups_Oone__class_Oone(U_1146)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,c_Groups_Ozero__class_Ozero(U_1146)),U_1151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,c_Groups_Ozero__class_Ozero(U_1146)),U_1150))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,U_1149),U_1148))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,U_1147),U_1148))
| ~ class_Rings_Olinordered__semiring__1(U_1146) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1146),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1146),U_1150),U_1147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1146),U_1151),U_1149))),U_1148))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1146),U_1150),U_1151) != c_Groups_Oone__class_Oone(U_1146)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,c_Groups_Ozero__class_Ozero(U_1146)),U_1151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,c_Groups_Ozero__class_Ozero(U_1146)),U_1150))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,U_1149),U_1148))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1146,U_1147),U_1148))
| ~ class_Rings_Olinordered__semiring__1(U_1146) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_1,plain,
? [B_g] :
( c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,B_g))))
& c_SEQ_Osubseq(B_g) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_Asubseq_Ag_059_Amonoseq_A_I_Fn_O_AIm_A_Is_A_If_A_Ig_An_J_J_J_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(f_373_2,plain,
? [U_1152] :
( c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,U_1152))))
& c_SEQ_Osubseq(U_1152) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
( c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,sK4))))
& c_SEQ_Osubseq(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_1152,sK4)],[f_373_2]) ).
cnf(f_373_4,plain,
c_SEQ_Osubseq(sK4),
inference(clausify,[status(thm)],[f_373_3]) ).
cnf(f_373_5,plain,
c_SEQ_Omonoseq(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,sK4)))),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_1,plain,
! [V_y,V_x,V_c,T_a] :
( V_x = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_374_2,plain,
! [U_1156,U_1155,U_1154,U_1153] :
( U_1155 = c_Groups_Ozero__class_Ozero(U_1153)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1153,U_1155)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1154),c_RealVector_Onorm__class_Onorm(U_1153,U_1156))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1154),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_RealVector_Oreal__normed__vector(U_1153) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
( U_1155 = c_Groups_Ozero__class_Ozero(U_1153)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1153,U_1155)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1154),c_RealVector_Onorm__class_Onorm(U_1153,U_1156))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1154),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ class_RealVector_Oreal__normed__vector(U_1153) ),
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_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_375_2,plain,
! [U_1159,U_1158,U_1157] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1157,c_Groups_Ozero__class_Ozero(U_1157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1158),U_1158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1159),U_1159))))
| ( U_1159 = c_Groups_Ozero__class_Ozero(U_1157)
& U_1158 = c_Groups_Ozero__class_Ozero(U_1157) ) )
& ( U_1159 != c_Groups_Ozero__class_Ozero(U_1157)
| U_1158 != c_Groups_Ozero__class_Ozero(U_1157)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1157,c_Groups_Ozero__class_Ozero(U_1157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1158),U_1158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1159),U_1159)))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1157) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
cnf(f_375_3,plain,
( U_1159 != c_Groups_Ozero__class_Ozero(U_1157)
| U_1158 != c_Groups_Ozero__class_Ozero(U_1157)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1157,c_Groups_Ozero__class_Ozero(U_1157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1158),U_1158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1159),U_1159))))
| ~ class_Rings_Olinordered__ring__strict(U_1157) ),
inference(clausify,[status(thm)],[f_375_2]) ).
cnf(f_375_4,plain,
( U_1158 = c_Groups_Ozero__class_Ozero(U_1157)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1157,c_Groups_Ozero__class_Ozero(U_1157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1158),U_1158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1159),U_1159))))
| ~ class_Rings_Olinordered__ring__strict(U_1157) ),
inference(clausify,[status(thm)],[f_375_2]) ).
cnf(f_375_5,plain,
( U_1159 = c_Groups_Ozero__class_Ozero(U_1157)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1157,c_Groups_Ozero__class_Ozero(U_1157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1158),U_1158)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1157),U_1159),U_1159))))
| ~ class_Rings_Olinordered__ring__strict(U_1157) ),
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_1,plain,
! [V_y,V_x,T_a] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(f_376_2,plain,
! [U_1162,U_1161,U_1160] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1160,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1160),U_1161),U_1161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1160),U_1162),U_1162))),c_Groups_Ozero__class_Ozero(U_1160)))
| ~ class_Rings_Olinordered__ring(U_1160) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1160,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1160),U_1161),U_1161)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1160),U_1162),U_1162))),c_Groups_Ozero__class_Ozero(U_1160)))
| ~ class_Rings_Olinordered__ring(U_1160) ),
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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_377_2,plain,
! [U_1165,U_1164,U_1163] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1163,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1164),U_1164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1165),U_1165))),c_Groups_Ozero__class_Ozero(U_1163)))
| U_1165 != c_Groups_Ozero__class_Ozero(U_1163)
| U_1164 != c_Groups_Ozero__class_Ozero(U_1163) )
& ( ( U_1165 = c_Groups_Ozero__class_Ozero(U_1163)
& U_1164 = c_Groups_Ozero__class_Ozero(U_1163) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1163,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1164),U_1164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1165),U_1165))),c_Groups_Ozero__class_Ozero(U_1163))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1163) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
( U_1164 = c_Groups_Ozero__class_Ozero(U_1163)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1163,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1164),U_1164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1165),U_1165))),c_Groups_Ozero__class_Ozero(U_1163)))
| ~ class_Rings_Olinordered__ring__strict(U_1163) ),
inference(clausify,[status(thm)],[f_377_2]) ).
cnf(f_377_4,plain,
( U_1165 = c_Groups_Ozero__class_Ozero(U_1163)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1163,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1164),U_1164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1165),U_1165))),c_Groups_Ozero__class_Ozero(U_1163)))
| ~ class_Rings_Olinordered__ring__strict(U_1163) ),
inference(clausify,[status(thm)],[f_377_2]) ).
cnf(f_377_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1163,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1164),U_1164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1163),U_1165),U_1165))),c_Groups_Ozero__class_Ozero(U_1163)))
| U_1165 != c_Groups_Ozero__class_Ozero(U_1163)
| U_1164 != c_Groups_Ozero__class_Ozero(U_1163)
| ~ class_Rings_Olinordered__ring__strict(U_1163) ),
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero]) ).
fof(f_378_2,plain,
! [U_1168,U_1167,U_1166] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1166,c_Groups_Ozero__class_Ozero(U_1166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1166),U_1167),U_1167)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1166),U_1168),U_1168))))
| ~ class_Rings_Olinordered__ring(U_1166) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1166,c_Groups_Ozero__class_Ozero(U_1166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1166),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1166),U_1167),U_1167)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1166),U_1168),U_1168))))
| ~ class_Rings_Olinordered__ring(U_1166) ),
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Omonoseq(T_a,V_X_2)
| ( ? [B_m,B_n] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) )
& ? [B_m,B_n] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) ) ) )
& ( ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) )
| ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) )
| ~ c_SEQ_Omonoseq(T_a,V_X_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_monoseq__def]) ).
fof(f_379_2,plain,
! [U_1178,U_1177] :
( ( ( c_SEQ_Omonoseq(U_1177,U_1178)
| ( ? [U_1176,U_1175] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1175)),hAPP(U_1178,U_1176)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1176),U_1175)) )
& ? [U_1174,U_1173] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1174)),hAPP(U_1178,U_1173)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1174),U_1173)) ) ) )
& ( ! [U_1172,U_1171] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1171)),hAPP(U_1178,U_1172)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172),U_1171)) )
| ! [U_1170,U_1169] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1170)),hAPP(U_1178,U_1169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170),U_1169)) )
| ~ c_SEQ_Omonoseq(U_1177,U_1178) ) )
| ~ class_Orderings_Oorder(U_1177) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_1178,U_1177] :
( ( ( c_SEQ_Omonoseq(U_1177,U_1178)
| ( ? [U_1176,U_1175] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1175)),hAPP(U_1178,U_1176)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1176),U_1175)) )
& ? [U_1173] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,sK5(U_1178,U_1177))),hAPP(U_1178,U_1173)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(U_1178,U_1177)),U_1173)) ) ) )
& ( ! [U_1172,U_1171] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1171)),hAPP(U_1178,U_1172)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172),U_1171)) )
| ! [U_1170,U_1169] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1170)),hAPP(U_1178,U_1169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170),U_1169)) )
| ~ c_SEQ_Omonoseq(U_1177,U_1178) ) )
| ~ class_Orderings_Oorder(U_1177) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_1174,sK5(U_1178,U_1177))],[f_379_2]) ).
fof(f_379_4,plain,
! [U_1178,U_1177] :
( ( ( c_SEQ_Omonoseq(U_1177,U_1178)
| ( ? [U_1176,U_1175] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1175)),hAPP(U_1178,U_1176)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1176),U_1175)) )
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,sK5(U_1178,U_1177))),hAPP(U_1178,sK6(U_1178,U_1177))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(U_1178,U_1177)),sK6(U_1178,U_1177))) ) )
& ( ! [U_1172,U_1171] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1171)),hAPP(U_1178,U_1172)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172),U_1171)) )
| ! [U_1170,U_1169] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1170)),hAPP(U_1178,U_1169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170),U_1169)) )
| ~ c_SEQ_Omonoseq(U_1177,U_1178) ) )
| ~ class_Orderings_Oorder(U_1177) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_1173,sK6(U_1178,U_1177))],[f_379_3]) ).
fof(f_379_5,plain,
! [U_1178,U_1177] :
( ( ( c_SEQ_Omonoseq(U_1177,U_1178)
| ( ? [U_1175] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1175)),hAPP(U_1178,sK7(U_1178,U_1177))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK7(U_1178,U_1177)),U_1175)) )
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,sK5(U_1178,U_1177))),hAPP(U_1178,sK6(U_1178,U_1177))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(U_1178,U_1177)),sK6(U_1178,U_1177))) ) )
& ( ! [U_1172,U_1171] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1171)),hAPP(U_1178,U_1172)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172),U_1171)) )
| ! [U_1170,U_1169] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1170)),hAPP(U_1178,U_1169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170),U_1169)) )
| ~ c_SEQ_Omonoseq(U_1177,U_1178) ) )
| ~ class_Orderings_Oorder(U_1177) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_1176,sK7(U_1178,U_1177))],[f_379_4]) ).
fof(f_379_6,plain,
! [U_1178,U_1177] :
( ( ( c_SEQ_Omonoseq(U_1177,U_1178)
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,sK8(U_1178,U_1177))),hAPP(U_1178,sK7(U_1178,U_1177))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK7(U_1178,U_1177)),sK8(U_1178,U_1177)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,sK5(U_1178,U_1177))),hAPP(U_1178,sK6(U_1178,U_1177))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(U_1178,U_1177)),sK6(U_1178,U_1177))) ) )
& ( ! [U_1172,U_1171] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1171)),hAPP(U_1178,U_1172)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172),U_1171)) )
| ! [U_1170,U_1169] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1170)),hAPP(U_1178,U_1169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170),U_1169)) )
| ~ c_SEQ_Omonoseq(U_1177,U_1178) ) )
| ~ class_Orderings_Oorder(U_1177) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_1175,sK8(U_1178,U_1177))],[f_379_5]) ).
cnf(f_379_7,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1171)),hAPP(U_1178,U_1172)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172),U_1171))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,U_1170)),hAPP(U_1178,U_1169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170),U_1169))
| ~ c_SEQ_Omonoseq(U_1177,U_1178)
| ~ class_Orderings_Oorder(U_1177) ),
inference(clausify,[status(thm)],[f_379_6]) ).
cnf(f_379_8,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK5(U_1178,U_1177)),sK6(U_1178,U_1177)))
| c_SEQ_Omonoseq(U_1177,U_1178)
| ~ class_Orderings_Oorder(U_1177) ),
inference(clausify,[status(thm)],[f_379_6]) ).
cnf(f_379_9,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,sK5(U_1178,U_1177))),hAPP(U_1178,sK6(U_1178,U_1177))))
| c_SEQ_Omonoseq(U_1177,U_1178)
| ~ class_Orderings_Oorder(U_1177) ),
inference(clausify,[status(thm)],[f_379_6]) ).
cnf(f_379_10,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK7(U_1178,U_1177)),sK8(U_1178,U_1177)))
| c_SEQ_Omonoseq(U_1177,U_1178)
| ~ class_Orderings_Oorder(U_1177) ),
inference(clausify,[status(thm)],[f_379_6]) ).
cnf(f_379_11,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1177,hAPP(U_1178,sK8(U_1178,U_1177))),hAPP(U_1178,sK7(U_1178,U_1177))))
| c_SEQ_Omonoseq(U_1177,U_1178)
| ~ class_Orderings_Oorder(U_1177) ),
inference(clausify,[status(thm)],[f_379_6]) ).
fof(f_380_1,plain,
! [V_y,V_x,V_c] :
( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(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_380_2,plain,
! [U_1181,U_1180,U_1179] :
( U_1180 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1179),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1181))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1179),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
( U_1180 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1179),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1181))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1179),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),
inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).
fof(f_381_2,plain,
! [U_1183,U_1182] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1182),U_1183) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1183),U_1182),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1182),U_1183) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1183),U_1182),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_1,plain,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).
fof(f_382_2,plain,
! [U_1186,U_1185,U_1184] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1185),U_1186)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1184),U_1186)),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1185),U_1186)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1184),U_1186)),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).
fof(f_383_2,plain,
! [U_1189,U_1188,U_1187] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1188),U_1189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1187),U_1188)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1187),U_1189)),
inference(variable_rename,[status(thm)],[f_383_1]) ).
cnf(f_383_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1188),U_1189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1187),U_1188)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1187),U_1189)),
inference(clausify,[status(thm)],[f_383_2]) ).
fof(f_384_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).
fof(f_384_2,plain,
! [U_1192,U_1191,U_1190] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1190),U_1191)),U_1192) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1191),U_1192)),
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1190),U_1191)),U_1192) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1191),U_1192)),
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).
fof(f_385_2,plain,
! [U_1195,U_1194,U_1193] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1193),U_1194)),U_1195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1193),U_1195)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1194),U_1195)),
inference(variable_rename,[status(thm)],[f_385_1]) ).
cnf(f_385_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1193),U_1194)),U_1195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1193),U_1195)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1194),U_1195)),
inference(clausify,[status(thm)],[f_385_2]) ).
fof(f_386_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).
fof(f_386_2,plain,
! [U_1198,U_1197,U_1196] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1196),U_1197) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1196),U_1198)
| U_1197 != U_1198 )
& ( U_1197 = U_1198
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1196),U_1197) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1196),U_1198) ) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
( ! [U_1204,U_1202] :
( ! [U_1200] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1200),U_1202) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1200),U_1204)
| U_1202 != U_1204 )
& ! [U_1203,U_1201] :
( ! [U_1199] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1199),U_1201) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1199),U_1203)
| U_1201 = U_1203 ) ),
inference(miniscope,[status(thm)],[f_386_2]) ).
cnf(f_386_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1199),U_1201) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1199),U_1203)
| U_1201 = U_1203 ),
inference(clausify,[status(thm)],[f_386_3]) ).
cnf(f_386_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1200),U_1202) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1200),U_1204)
| U_1202 != U_1204 ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).
fof(f_387_2,plain,
! [U_1207,U_1206,U_1205] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1205),U_1206) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1207),U_1206)
| U_1205 != U_1207 )
& ( U_1205 = U_1207
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1205),U_1206) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1207),U_1206) ) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
( ! [U_1213,U_1211,U_1209] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1209),U_1211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1213),U_1211)
| U_1209 != U_1213 )
& ! [U_1212,U_1210,U_1208] :
( U_1208 = U_1212
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1208),U_1210) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1212),U_1210) ) ),
inference(miniscope,[status(thm)],[f_387_2]) ).
cnf(f_387_4,plain,
( U_1208 = U_1212
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1208),U_1210) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1212),U_1210) ),
inference(clausify,[status(thm)],[f_387_3]) ).
cnf(f_387_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1209),U_1211) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1213),U_1211)
| U_1209 != U_1213 ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_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_388_2,plain,
! [U_1215,U_1214] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1214),U_1215) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1215),U_1214),
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1214),U_1215) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1215),U_1214),
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_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_389_2,plain,
! [U_1218,U_1217,U_1216] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1216),U_1217)),U_1218) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1217),U_1218)),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1216),U_1217)),U_1218) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1217),U_1218)),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_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_390_2,plain,
! [U_1221,U_1220,U_1219] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1219),U_1220)),U_1221) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1220),U_1221)),
inference(variable_rename,[status(thm)],[f_390_1]) ).
cnf(f_390_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1219),U_1220)),U_1221) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1220),U_1221)),
inference(clausify,[status(thm)],[f_390_2]) ).
fof(f_391_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).
fof(f_391_2,plain,
! [U_1223,U_1222] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1222),U_1223) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1223 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1222 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1223 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1222 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1222),U_1223) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
( ! [U_1227,U_1225] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1225),U_1227) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1227 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1225 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1226,U_1224] :
( ( U_1226 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1224 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1224),U_1226) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_391_2]) ).
cnf(f_391_4,plain,
( U_1224 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1224),U_1226) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_391_3]) ).
cnf(f_391_5,plain,
( U_1226 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1224),U_1226) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_391_3]) ).
cnf(f_391_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1225),U_1227) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1227 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1225 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_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_392_2,plain,
! [U_1229,U_1228] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1228),U_1229) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1229),U_1228),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1228),U_1229) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1229),U_1228),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_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_393_2,plain,
! [U_1230] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1230),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1230,
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1230),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1230,
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_1,plain,
! [V_n_2,V_m_2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).
fof(f_394_2,plain,
! [U_1232,U_1231] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1231),U_1232)
| U_1232 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1231 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1232 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1231 = 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_1231),U_1232) ) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
( ! [U_1236,U_1234] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),U_1236)
| U_1236 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1234 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1235,U_1233] :
( ( U_1235 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1233 = 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_1233),U_1235) ) ),
inference(miniscope,[status(thm)],[f_394_2]) ).
cnf(f_394_4,plain,
( U_1233 = 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_1233),U_1235) ),
inference(clausify,[status(thm)],[f_394_3]) ).
cnf(f_394_5,plain,
( U_1235 = 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_1233),U_1235) ),
inference(clausify,[status(thm)],[f_394_3]) ).
cnf(f_394_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1234),U_1236)
| U_1236 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1234 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_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_395_2,plain,
! [U_1237] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1237) = U_1237,
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1237) = U_1237,
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_1,plain,
! [V_y_2,V_x_2] :
( ( V_x_2 = V_y_2
| hAPP(c_Complex_OIm,V_x_2) != hAPP(c_Complex_OIm,V_y_2)
| hAPP(c_Complex_ORe,V_x_2) != hAPP(c_Complex_ORe,V_y_2) )
& ( ( hAPP(c_Complex_OIm,V_x_2) = hAPP(c_Complex_OIm,V_y_2)
& hAPP(c_Complex_ORe,V_x_2) = hAPP(c_Complex_ORe,V_y_2) )
| V_x_2 != V_y_2 ) ),
inference(fof_nnf,[status(thm)],[fact_expand__complex__eq]) ).
fof(f_396_2,plain,
! [U_1239,U_1238] :
( ( U_1238 = U_1239
| hAPP(c_Complex_OIm,U_1238) != hAPP(c_Complex_OIm,U_1239)
| hAPP(c_Complex_ORe,U_1238) != hAPP(c_Complex_ORe,U_1239) )
& ( ( hAPP(c_Complex_OIm,U_1238) = hAPP(c_Complex_OIm,U_1239)
& hAPP(c_Complex_ORe,U_1238) = hAPP(c_Complex_ORe,U_1239) )
| U_1238 != U_1239 ) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
( ! [U_1243,U_1241] :
( U_1241 = U_1243
| hAPP(c_Complex_OIm,U_1241) != hAPP(c_Complex_OIm,U_1243)
| hAPP(c_Complex_ORe,U_1241) != hAPP(c_Complex_ORe,U_1243) )
& ! [U_1242,U_1240] :
( ( hAPP(c_Complex_OIm,U_1240) = hAPP(c_Complex_OIm,U_1242)
& hAPP(c_Complex_ORe,U_1240) = hAPP(c_Complex_ORe,U_1242) )
| U_1240 != U_1242 ) ),
inference(miniscope,[status(thm)],[f_396_2]) ).
cnf(f_396_4,plain,
( hAPP(c_Complex_ORe,U_1240) = hAPP(c_Complex_ORe,U_1242)
| U_1240 != U_1242 ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_5,plain,
( hAPP(c_Complex_OIm,U_1240) = hAPP(c_Complex_OIm,U_1242)
| U_1240 != U_1242 ),
inference(clausify,[status(thm)],[f_396_3]) ).
cnf(f_396_6,plain,
( U_1241 = U_1243
| hAPP(c_Complex_OIm,U_1241) != hAPP(c_Complex_OIm,U_1243)
| hAPP(c_Complex_ORe,U_1241) != hAPP(c_Complex_ORe,U_1243) ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [V_y,V_x] :
( V_x = V_y
| hAPP(c_Complex_OIm,V_x) != hAPP(c_Complex_OIm,V_y)
| hAPP(c_Complex_ORe,V_x) != hAPP(c_Complex_ORe,V_y) ),
inference(fof_nnf,[status(thm)],[fact_complex__equality]) ).
fof(f_397_2,plain,
! [U_1245,U_1244] :
( U_1244 = U_1245
| hAPP(c_Complex_OIm,U_1244) != hAPP(c_Complex_OIm,U_1245)
| hAPP(c_Complex_ORe,U_1244) != hAPP(c_Complex_ORe,U_1245) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( U_1244 = U_1245
| hAPP(c_Complex_OIm,U_1244) != hAPP(c_Complex_OIm,U_1245)
| hAPP(c_Complex_ORe,U_1244) != hAPP(c_Complex_ORe,U_1245) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_1,plain,
! [V_y,V_x] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y))),
inference(fof_nnf,[status(thm)],[fact_complex__Im__mult]) ).
fof(f_398_2,plain,
! [U_1247,U_1246] : hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_1246),U_1247)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_1246)),hAPP(c_Complex_OIm,U_1247))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_1246)),hAPP(c_Complex_ORe,U_1247))),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
hAPP(c_Complex_OIm,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_1246),U_1247)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_1246)),hAPP(c_Complex_OIm,U_1247))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_1246)),hAPP(c_Complex_ORe,U_1247))),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
inference(fof_nnf,[status(thm)],[fact_complex__Re__le__cmod]) ).
fof(f_399_2,plain,
! [U_1248] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1248)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1248))),
inference(variable_rename,[status(thm)],[f_399_1]) ).
cnf(f_399_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1248)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1248))),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_1,plain,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_Re_Ozero]) ).
cnf(f_400_2,plain,
hAPP(c_Complex_ORe,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_400_1]) ).
fof(f_401_1,plain,
! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),
inference(fof_nnf,[status(thm)],[fact_Re_Oadd]) ).
fof(f_401_2,plain,
! [U_1250,U_1249] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_1249),U_1250)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_1249)),hAPP(c_Complex_ORe,U_1250)),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_1249),U_1250)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_1249)),hAPP(c_Complex_ORe,U_1250)),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_1,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_complex__Re__one]) ).
cnf(f_402_2,plain,
hAPP(c_Complex_ORe,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_402_1]) ).
fof(f_403_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x))),
inference(fof_nnf,[status(thm)],[fact_abs__Re__le__cmod]) ).
fof(f_403_2,plain,
! [U_1251] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1251))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1251))),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1251))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1251))),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_l_2))
| ! [B_n] : V_l_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n) )
& ( ? [B_n] : V_l_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),B_n)
| ~ hBOOL(hAPP(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_404_2,plain,
! [U_1255,U_1254] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1254),U_1255))
| ! [U_1253] : U_1255 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1254),U_1253) )
& ( ? [U_1252] : U_1255 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1254),U_1252)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1254),U_1255)) ) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
( ! [U_1259,U_1257] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1257),U_1259))
| ! [U_1253] : U_1259 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1257),U_1253) )
& ! [U_1258,U_1256] :
( ? [U_1252] : U_1258 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1256),U_1252)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1256),U_1258)) ) ),
inference(miniscope,[status(thm)],[f_404_2]) ).
fof(f_404_4,plain,
( ! [U_1259,U_1257] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1257),U_1259))
| ! [U_1253] : U_1259 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1257),U_1253) )
& ! [U_1258,U_1256] :
( U_1258 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1256),sK9(U_1258,U_1256))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1256),U_1258)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_1252,sK9(U_1258,U_1256))],[f_404_3]) ).
cnf(f_404_5,plain,
( U_1258 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1256),sK9(U_1258,U_1256))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1256),U_1258)) ),
inference(clausify,[status(thm)],[f_404_4]) ).
cnf(f_404_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1257),U_1259))
| U_1259 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1257),U_1253) ),
inference(clausify,[status(thm)],[f_404_4]) ).
fof(f_405_1,plain,
! [V_fa_2] :
( ( c_SEQ_Osubseq(V_fa_2)
| ? [B_m,B_n] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n)) ) )
& ( ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_m)),hAPP(V_fa_2,B_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m),B_n)) )
| ~ c_SEQ_Osubseq(V_fa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_subseq__def]) ).
fof(f_405_2,plain,
! [U_1264] :
( ( c_SEQ_Osubseq(U_1264)
| ? [U_1263,U_1262] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1264,U_1263)),hAPP(U_1264,U_1262)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1263),U_1262)) ) )
& ( ! [U_1261,U_1260] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1264,U_1261)),hAPP(U_1264,U_1260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1261),U_1260)) )
| ~ c_SEQ_Osubseq(U_1264) ) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
( ! [U_1266] :
( c_SEQ_Osubseq(U_1266)
| ? [U_1263,U_1262] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1266,U_1263)),hAPP(U_1266,U_1262)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1263),U_1262)) ) )
& ! [U_1265] :
( ! [U_1261,U_1260] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1265,U_1261)),hAPP(U_1265,U_1260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1261),U_1260)) )
| ~ c_SEQ_Osubseq(U_1265) ) ),
inference(miniscope,[status(thm)],[f_405_2]) ).
fof(f_405_4,plain,
( ! [U_1266] :
( c_SEQ_Osubseq(U_1266)
| ? [U_1262] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1266,sK10(U_1266))),hAPP(U_1266,U_1262)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK10(U_1266)),U_1262)) ) )
& ! [U_1265] :
( ! [U_1261,U_1260] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1265,U_1261)),hAPP(U_1265,U_1260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1261),U_1260)) )
| ~ c_SEQ_Osubseq(U_1265) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_1263,sK10(U_1266))],[f_405_3]) ).
fof(f_405_5,plain,
( ! [U_1266] :
( c_SEQ_Osubseq(U_1266)
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1266,sK10(U_1266))),hAPP(U_1266,sK11(U_1266))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK10(U_1266)),sK11(U_1266))) ) )
& ! [U_1265] :
( ! [U_1261,U_1260] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1265,U_1261)),hAPP(U_1265,U_1260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1261),U_1260)) )
| ~ c_SEQ_Osubseq(U_1265) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_1262,sK11(U_1266))],[f_405_4]) ).
cnf(f_405_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1265,U_1261)),hAPP(U_1265,U_1260)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1261),U_1260))
| ~ c_SEQ_Osubseq(U_1265) ),
inference(clausify,[status(thm)],[f_405_5]) ).
cnf(f_405_7,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK10(U_1266)),sK11(U_1266)))
| c_SEQ_Osubseq(U_1266) ),
inference(clausify,[status(thm)],[f_405_5]) ).
cnf(f_405_8,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1266,sK10(U_1266))),hAPP(U_1266,sK11(U_1266))))
| c_SEQ_Osubseq(U_1266) ),
inference(clausify,[status(thm)],[f_405_5]) ).
fof(f_406_1,plain,
! [V_n_2,V_fa_2] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),hAPP(V_fa_2,V_n_2)))
| ~ c_SEQ_Osubseq(V_fa_2) ),
inference(fof_nnf,[status(thm)],[fact_seq__suble]) ).
fof(f_406_2,plain,
! [U_1268,U_1267] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1268),hAPP(U_1267,U_1268)))
| ~ c_SEQ_Osubseq(U_1267) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1268),hAPP(U_1267,U_1268)))
| ~ c_SEQ_Osubseq(U_1267) ),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hAPP(hAPP(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) )
| hAPP(hAPP(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_407_2,plain,
! [U_1271,U_1270,U_1269] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1270),U_1270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1271),U_1271)) = c_Groups_Ozero__class_Ozero(U_1269)
| U_1271 != c_Groups_Ozero__class_Ozero(U_1269)
| U_1270 != c_Groups_Ozero__class_Ozero(U_1269) )
& ( ( U_1271 = c_Groups_Ozero__class_Ozero(U_1269)
& U_1270 = c_Groups_Ozero__class_Ozero(U_1269) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1270),U_1270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1271),U_1271)) != c_Groups_Ozero__class_Ozero(U_1269) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1269) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
cnf(f_407_3,plain,
( U_1270 = c_Groups_Ozero__class_Ozero(U_1269)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1270),U_1270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1271),U_1271)) != c_Groups_Ozero__class_Ozero(U_1269)
| ~ class_Rings_Olinordered__ring__strict(U_1269) ),
inference(clausify,[status(thm)],[f_407_2]) ).
cnf(f_407_4,plain,
( U_1271 = c_Groups_Ozero__class_Ozero(U_1269)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1270),U_1270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1271),U_1271)) != c_Groups_Ozero__class_Ozero(U_1269)
| ~ class_Rings_Olinordered__ring__strict(U_1269) ),
inference(clausify,[status(thm)],[f_407_2]) ).
cnf(f_407_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1269),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1270),U_1270)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1269),U_1271),U_1271)) = c_Groups_Ozero__class_Ozero(U_1269)
| U_1271 != c_Groups_Ozero__class_Ozero(U_1269)
| U_1270 != c_Groups_Ozero__class_Ozero(U_1269)
| ~ class_Rings_Olinordered__ring__strict(U_1269) ),
inference(clausify,[status(thm)],[f_407_2]) ).
fof(f_408_1,plain,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(fof_nnf,[status(thm)],[fact_conv1]) ).
cnf(f_408_2,plain,
c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,c_COMBB(tc_Nat_Onat,tc_Complex_Ocomplex,tc_Nat_Onat,v_s,v_f____))),
inference(clausify,[status(thm)],[f_408_1]) ).
fof(f_409_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) )
| ~ hBOOL(hAPP(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_409_2,plain,
! [U_1274,U_1273,U_1272] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1274)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1273),U_1274)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1273),U_1274))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1274))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1272)) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1273),U_1274))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1274)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1272)) ),
inference(clausify,[status(thm)],[f_409_2]) ).
cnf(f_409_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1272),U_1274)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1273),U_1274))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1272)) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_1,plain,
! [V_x_2] :
( ( ~ hBOOL(hAPP(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)
| hBOOL(hAPP(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_410_2,plain,
! [U_1275] :
( ( ~ hBOOL(hAPP(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_1275),U_1275)))
| U_1275 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_1275 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(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_1275),U_1275))) ) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
( ! [U_1277] :
( ~ hBOOL(hAPP(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_1277),U_1277)))
| U_1277 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1276] :
( U_1276 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(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_1276),U_1276))) ) ),
inference(miniscope,[status(thm)],[f_410_2]) ).
cnf(f_410_4,plain,
( U_1276 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hBOOL(hAPP(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_1276),U_1276))) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_5,plain,
( ~ hBOOL(hAPP(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_1277),U_1277)))
| U_1277 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) )
| ~ hBOOL(hAPP(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_411_2,plain,
! [U_1280,U_1279,U_1278] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1280)
| U_1279 != U_1280 )
& ( U_1279 = U_1280
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1279) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1280) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1278)) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( U_1279 = U_1280
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1279) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1280)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1278)) ),
inference(clausify,[status(thm)],[f_411_2]) ).
cnf(f_411_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1278),U_1280)
| U_1279 != U_1280
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1278)) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) )
| ~ hBOOL(hAPP(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_412_2,plain,
! [U_1283,U_1282,U_1281] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1283)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1282),U_1283)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1282),U_1283))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1283))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1281)) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1282),U_1283))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1283)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1281)) ),
inference(clausify,[status(thm)],[f_412_2]) ).
cnf(f_412_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1282)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1281),U_1283)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1282),U_1283))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1281)) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_1,plain,
! [V_c_2,T_a] :
( c_SEQ_Oconvergent(T_a,c_COMBK(T_a,tc_Nat_Onat,V_c_2))
| ~ class_RealVector_Ometric__space(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convergent__const]) ).
fof(f_413_2,plain,
! [U_1285,U_1284] :
( c_SEQ_Oconvergent(U_1284,c_COMBK(U_1284,tc_Nat_Onat,U_1285))
| ~ class_RealVector_Ometric__space(U_1284) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
cnf(f_413_3,plain,
( c_SEQ_Oconvergent(U_1284,c_COMBK(U_1284,tc_Nat_Onat,U_1285))
| ~ class_RealVector_Ometric__space(U_1284) ),
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_1,plain,
! [V_x_2,V_X_2,T_a] :
( c_SEQ_Oconvergent(T_a,c_COMBB(T_a,T_a,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_X_2))
| ~ c_SEQ_Oconvergent(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Oconvergent]) ).
fof(f_414_2,plain,
! [U_1288,U_1287,U_1286] :
( c_SEQ_Oconvergent(U_1286,c_COMBB(U_1286,U_1286,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1288),U_1287))
| ~ c_SEQ_Oconvergent(U_1286,U_1287)
| ~ class_RealVector_Oreal__normed__algebra(U_1286) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( c_SEQ_Oconvergent(U_1286,c_COMBB(U_1286,U_1286,tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1288),U_1287))
| ~ c_SEQ_Oconvergent(U_1286,U_1287)
| ~ class_RealVector_Oreal__normed__algebra(U_1286) ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_1,plain,
! [V_y_2,V_X_2,T_a] :
( c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_y_2))
| ~ c_SEQ_Oconvergent(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Oconvergent]) ).
fof(f_415_2,plain,
! [U_1291,U_1290,U_1289] :
( c_SEQ_Oconvergent(U_1289,c_COMBC(tc_Nat_Onat,U_1289,U_1289,c_COMBB(U_1289,tc_fun(U_1289,U_1289),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(U_1289),U_1290),U_1291))
| ~ c_SEQ_Oconvergent(U_1289,U_1290)
| ~ class_RealVector_Oreal__normed__algebra(U_1289) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( c_SEQ_Oconvergent(U_1289,c_COMBC(tc_Nat_Onat,U_1289,U_1289,c_COMBB(U_1289,tc_fun(U_1289,U_1289),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(U_1289),U_1290),U_1291))
| ~ c_SEQ_Oconvergent(U_1289,U_1290)
| ~ class_RealVector_Oreal__normed__algebra(U_1289) ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_1,plain,
! [V_Y_2,V_X_2,T_a] :
( c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(T_a),V_X_2),V_Y_2))
| ~ c_SEQ_Oconvergent(T_a,V_Y_2)
| ~ c_SEQ_Oconvergent(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oconvergent]) ).
fof(f_416_2,plain,
! [U_1294,U_1293,U_1292] :
( c_SEQ_Oconvergent(U_1292,c_COMBS(tc_Nat_Onat,U_1292,U_1292,c_COMBB(U_1292,tc_fun(U_1292,U_1292),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(U_1292),U_1293),U_1294))
| ~ c_SEQ_Oconvergent(U_1292,U_1294)
| ~ c_SEQ_Oconvergent(U_1292,U_1293)
| ~ class_RealVector_Oreal__normed__algebra(U_1292) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
( c_SEQ_Oconvergent(U_1292,c_COMBS(tc_Nat_Onat,U_1292,U_1292,c_COMBB(U_1292,tc_fun(U_1292,U_1292),tc_Nat_Onat,c_Groups_Otimes__class_Otimes(U_1292),U_1293),U_1294))
| ~ c_SEQ_Oconvergent(U_1292,U_1294)
| ~ c_SEQ_Oconvergent(U_1292,U_1293)
| ~ class_RealVector_Oreal__normed__algebra(U_1292) ),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_1,plain,
! [V_Y_2,V_X_2,T_a] :
( c_SEQ_Oconvergent(T_a,c_COMBS(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(T_a),V_X_2),V_Y_2))
| ~ c_SEQ_Oconvergent(T_a,V_Y_2)
| ~ c_SEQ_Oconvergent(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convergent__add]) ).
fof(f_417_2,plain,
! [U_1297,U_1296,U_1295] :
( c_SEQ_Oconvergent(U_1295,c_COMBS(tc_Nat_Onat,U_1295,U_1295,c_COMBB(U_1295,tc_fun(U_1295,U_1295),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(U_1295),U_1296),U_1297))
| ~ c_SEQ_Oconvergent(U_1295,U_1297)
| ~ c_SEQ_Oconvergent(U_1295,U_1296)
| ~ class_RealVector_Oreal__normed__vector(U_1295) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
cnf(f_417_3,plain,
( c_SEQ_Oconvergent(U_1295,c_COMBS(tc_Nat_Onat,U_1295,U_1295,c_COMBB(U_1295,tc_fun(U_1295,U_1295),tc_Nat_Onat,c_Groups_Oplus__class_Oplus(U_1295),U_1296),U_1297))
| ~ c_SEQ_Oconvergent(U_1295,U_1297)
| ~ c_SEQ_Oconvergent(U_1295,U_1296)
| ~ class_RealVector_Oreal__normed__vector(U_1295) ),
inference(clausify,[status(thm)],[f_417_2]) ).
fof(f_418_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| ( V_m_2 != V_n_2
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_m_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).
fof(f_418_2,plain,
! [U_1300,U_1299,U_1298] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1298),U_1299) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1298),U_1300)
| ( U_1299 != U_1300
& U_1298 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1299 = U_1300
| U_1298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1298),U_1299) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1298),U_1300) ) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
( ! [U_1306,U_1304,U_1302] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1302),U_1304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1302),U_1306)
| ( U_1304 != U_1306
& U_1302 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1305,U_1303,U_1301] :
( U_1303 = U_1305
| U_1301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1301),U_1303) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1301),U_1305) ) ),
inference(miniscope,[status(thm)],[f_418_2]) ).
cnf(f_418_4,plain,
( U_1303 = U_1305
| U_1301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1301),U_1303) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1301),U_1305) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_5,plain,
( U_1302 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1302),U_1304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1302),U_1306) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_6,plain,
( U_1304 != U_1306
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1302),U_1304) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1302),U_1306) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_1,plain,
! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k),
inference(fof_nnf,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(f_419_2,plain,
! [U_1310,U_1309,U_1308,U_1307] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1307),U_1308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1309),U_1308)),U_1310)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1307),U_1309)),U_1308)),U_1310),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1307),U_1308)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1309),U_1308)),U_1310)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1307),U_1309)),U_1308)),U_1310),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_1,plain,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
inference(fof_nnf,[status(thm)],[fact_Im_Opos__bounded]) ).
fof(f_420_2,plain,
? [U_1312] :
( ! [U_1311] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1311))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1311)),U_1312)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1312)) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
( ! [U_1311] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1311))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1311)),sK12)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_1312,sK12)],[f_420_2]) ).
cnf(f_420_4,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK12)),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_5,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1311))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1311)),sK12))),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_1,plain,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
inference(fof_nnf,[status(thm)],[fact_Re_Opos__bounded]) ).
fof(f_421_2,plain,
? [U_1314] :
( ! [U_1313] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1313))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1313)),U_1314)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1314)) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
( ! [U_1313] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1313))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1313)),sK13)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK13)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_1314,sK13)],[f_421_2]) ).
cnf(f_421_4,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK13)),
inference(clausify,[status(thm)],[f_421_3]) ).
cnf(f_421_5,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1313))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1313)),sK13))),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_1,plain,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
inference(fof_nnf,[status(thm)],[fact_Im_Ononneg__bounded]) ).
fof(f_422_2,plain,
? [U_1316] :
( ! [U_1315] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1315))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1315)),U_1316)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1316)) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
( ! [U_1315] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1315))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1315)),sK14)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_1316,sK14)],[f_422_2]) ).
cnf(f_422_4,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK14)),
inference(clausify,[status(thm)],[f_422_3]) ).
cnf(f_422_5,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1315))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1315)),sK14))),
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_1,plain,
? [B_K] :
( ! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ),
inference(fof_nnf,[status(thm)],[fact_Re_Ononneg__bounded]) ).
fof(f_423_2,plain,
? [U_1318] :
( ! [U_1317] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1317))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1317)),U_1318)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1318)) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
( ! [U_1317] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1317))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1317)),sK15)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK15)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1318,sK15)],[f_423_2]) ).
cnf(f_423_4,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK15)),
inference(clausify,[status(thm)],[f_423_3]) ).
cnf(f_423_5,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1317))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1317)),sK15))),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_1,plain,
! [V_y,T_a] :
( ? [B_K] :
( ! [B_x] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_424_2,plain,
! [U_1322,U_1321] :
( ? [U_1320] :
( ! [U_1319] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1319),U_1322))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1321,U_1319)),U_1320)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1320)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1321) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
! [U_1322,U_1321] :
( ( ! [U_1319] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1319),U_1322))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1321,U_1319)),sK16(U_1322,U_1321))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK16(U_1322,U_1321))) )
| ~ class_RealVector_Oreal__normed__algebra(U_1321) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_1320,sK16(U_1322,U_1321))],[f_424_2]) ).
cnf(f_424_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK16(U_1322,U_1321)))
| ~ class_RealVector_Oreal__normed__algebra(U_1321) ),
inference(clausify,[status(thm)],[f_424_3]) ).
cnf(f_424_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1319),U_1322))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1321,U_1319)),sK16(U_1322,U_1321))))
| ~ class_RealVector_Oreal__normed__algebra(U_1321) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_1,plain,
! [V_X_2] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,V_X_2))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2) ),
inference(fof_nnf,[status(thm)],[fact_Re_Oconvergent]) ).
fof(f_425_2,plain,
! [U_1323] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,U_1323))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,U_1323) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_ORe,U_1323))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,U_1323) ),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_1,plain,
! [V_X_2] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,V_X_2))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,V_X_2) ),
inference(fof_nnf,[status(thm)],[fact_Im_Oconvergent]) ).
fof(f_426_2,plain,
! [U_1324] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,U_1324))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,U_1324) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,c_COMBB(tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_Nat_Onat,c_Complex_OIm,U_1324))
| ~ c_SEQ_Oconvergent(tc_Complex_Ocomplex,U_1324) ),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_1,plain,
! [T_a] :
( ? [B_K] :
( ! [B_a,B_b] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_427_2,plain,
! [U_1328] :
( ? [U_1327] :
( ! [U_1326,U_1325] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1328,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1328),U_1326),U_1325))),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_1328,U_1326)),c_RealVector_Onorm__class_Onorm(U_1328,U_1325))),U_1327)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1327)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1328) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
! [U_1328] :
( ( ! [U_1326,U_1325] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1328,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1328),U_1326),U_1325))),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_1328,U_1326)),c_RealVector_Onorm__class_Onorm(U_1328,U_1325))),sK17(U_1328))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK17(U_1328))) )
| ~ class_RealVector_Oreal__normed__algebra(U_1328) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_1327,sK17(U_1328))],[f_427_2]) ).
cnf(f_427_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK17(U_1328)))
| ~ class_RealVector_Oreal__normed__algebra(U_1328) ),
inference(clausify,[status(thm)],[f_427_3]) ).
cnf(f_427_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1328,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1328),U_1326),U_1325))),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_1328,U_1326)),c_RealVector_Onorm__class_Onorm(U_1328,U_1325))),sK17(U_1328))))
| ~ class_RealVector_Oreal__normed__algebra(U_1328) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_1,plain,
! [V_x,T_a] :
( ? [B_K] :
( ! [B_x] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_428_2,plain,
! [U_1332,U_1331] :
( ? [U_1330] :
( ! [U_1329] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1331,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1331),U_1332),U_1329))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1331,U_1329)),U_1330)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1330)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1331) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_1332,U_1331] :
( ( ! [U_1329] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1331,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1331),U_1332),U_1329))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1331,U_1329)),sK18(U_1332,U_1331))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK18(U_1332,U_1331))) )
| ~ class_RealVector_Oreal__normed__algebra(U_1331) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_1330,sK18(U_1332,U_1331))],[f_428_2]) ).
cnf(f_428_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK18(U_1332,U_1331)))
| ~ class_RealVector_Oreal__normed__algebra(U_1331) ),
inference(clausify,[status(thm)],[f_428_3]) ).
cnf(f_428_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1331,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1331),U_1332),U_1329))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1331,U_1329)),sK18(U_1332,U_1331))))
| ~ class_RealVector_Oreal__normed__algebra(U_1331) ),
inference(clausify,[status(thm)],[f_428_3]) ).
fof(f_429_1,plain,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
| ~ hBOOL(hAPP(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_429_2,plain,
! [U_1335,U_1334,U_1333] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1335),U_1334)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333),U_1334)) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1335),U_1334)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333),U_1334)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_1,plain,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
| ~ hBOOL(hAPP(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_430_2,plain,
! [U_1338,U_1337,U_1336] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1336),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1337),U_1338)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1336),U_1337)) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1336),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1337),U_1338)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1336),U_1337)) ),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).
fof(f_431_2,plain,
! [U_1340,U_1339] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1339),U_1340))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1339),U_1340)) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1339),U_1340))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1339),U_1340)) ),
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_1,plain,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
| ~ hBOOL(hAPP(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_432_2,plain,
! [U_1343,U_1342,U_1341] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1341),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1342),U_1343)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1341),U_1342)) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1341),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1342),U_1343)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1341),U_1342)) ),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_1,plain,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
| ~ hBOOL(hAPP(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_433_2,plain,
! [U_1346,U_1345,U_1344] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1346),U_1345)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344),U_1345)) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1346),U_1345)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344),U_1345)) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_1,plain,
? [B_K] :
! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))),
inference(fof_nnf,[status(thm)],[fact_Im_Obounded]) ).
fof(f_434_2,plain,
? [U_1348] :
! [U_1347] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1347))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1347)),U_1348))),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1347] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1347))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1347)),sK19))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1348,sK19)],[f_434_2]) ).
cnf(f_434_4,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_1347))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1347)),sK19))),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_1,plain,
? [B_K] :
! [B_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,B_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_x)),B_K))),
inference(fof_nnf,[status(thm)],[fact_Re_Obounded]) ).
fof(f_435_2,plain,
? [U_1350] :
! [U_1349] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1349))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1349)),U_1350))),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
! [U_1349] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1349))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1349)),sK20))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1350,sK20)],[f_435_2]) ).
cnf(f_435_4,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_1349))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1349)),sK20))),
inference(clausify,[status(thm)],[f_435_3]) ).
fof(f_436_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Odecseq(T_a,V_X_2)
| ? [B_m,B_n] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) ) )
& ( ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,B_m)))
| ~ hBOOL(hAPP(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_436_2,plain,
! [U_1356,U_1355] :
( ( ( c_SEQ_Odecseq(U_1355,U_1356)
| ? [U_1354,U_1353] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,U_1353)),hAPP(U_1356,U_1354)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1354),U_1353)) ) )
& ( ! [U_1352,U_1351] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,U_1351)),hAPP(U_1356,U_1352)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1352),U_1351)) )
| ~ c_SEQ_Odecseq(U_1355,U_1356) ) )
| ~ class_Orderings_Oorder(U_1355) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
! [U_1356,U_1355] :
( ( ( c_SEQ_Odecseq(U_1355,U_1356)
| ? [U_1353] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,U_1353)),hAPP(U_1356,sK21(U_1356,U_1355))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21(U_1356,U_1355)),U_1353)) ) )
& ( ! [U_1352,U_1351] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,U_1351)),hAPP(U_1356,U_1352)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1352),U_1351)) )
| ~ c_SEQ_Odecseq(U_1355,U_1356) ) )
| ~ class_Orderings_Oorder(U_1355) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1354,sK21(U_1356,U_1355))],[f_436_2]) ).
fof(f_436_4,plain,
! [U_1356,U_1355] :
( ( ( c_SEQ_Odecseq(U_1355,U_1356)
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,sK22(U_1356,U_1355))),hAPP(U_1356,sK21(U_1356,U_1355))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21(U_1356,U_1355)),sK22(U_1356,U_1355))) ) )
& ( ! [U_1352,U_1351] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,U_1351)),hAPP(U_1356,U_1352)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1352),U_1351)) )
| ~ c_SEQ_Odecseq(U_1355,U_1356) ) )
| ~ class_Orderings_Oorder(U_1355) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1353,sK22(U_1356,U_1355))],[f_436_3]) ).
cnf(f_436_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,U_1351)),hAPP(U_1356,U_1352)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1352),U_1351))
| ~ c_SEQ_Odecseq(U_1355,U_1356)
| ~ class_Orderings_Oorder(U_1355) ),
inference(clausify,[status(thm)],[f_436_4]) ).
cnf(f_436_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK21(U_1356,U_1355)),sK22(U_1356,U_1355)))
| c_SEQ_Odecseq(U_1355,U_1356)
| ~ class_Orderings_Oorder(U_1355) ),
inference(clausify,[status(thm)],[f_436_4]) ).
cnf(f_436_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1355,hAPP(U_1356,sK22(U_1356,U_1355))),hAPP(U_1356,sK21(U_1356,U_1355))))
| c_SEQ_Odecseq(U_1355,U_1356)
| ~ class_Orderings_Oorder(U_1355) ),
inference(clausify,[status(thm)],[f_436_4]) ).
fof(f_437_1,plain,
! [V_n_2,V_P_2] :
( ? [B_k] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i),B_k)) )
& hBOOL(hAPP(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_437_2,plain,
! [U_1360,U_1359] :
( ? [U_1358] :
( hBOOL(hAPP(U_1359,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1358),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_1357] :
( ~ hBOOL(hAPP(U_1359,U_1357))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357),U_1358)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1358),U_1360)) )
| ~ hBOOL(hAPP(U_1359,U_1360))
| hBOOL(hAPP(U_1359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
! [U_1360,U_1359] :
( ( hBOOL(hAPP(U_1359,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK23(U_1360,U_1359)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_1357] :
( ~ hBOOL(hAPP(U_1359,U_1357))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357),sK23(U_1360,U_1359))) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23(U_1360,U_1359)),U_1360)) )
| ~ hBOOL(hAPP(U_1359,U_1360))
| hBOOL(hAPP(U_1359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1358,sK23(U_1360,U_1359))],[f_437_2]) ).
cnf(f_437_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK23(U_1360,U_1359)),U_1360))
| ~ hBOOL(hAPP(U_1359,U_1360))
| hBOOL(hAPP(U_1359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_437_3]) ).
cnf(f_437_5,plain,
( ~ hBOOL(hAPP(U_1359,U_1357))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357),sK23(U_1360,U_1359)))
| ~ hBOOL(hAPP(U_1359,U_1360))
| hBOOL(hAPP(U_1359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_437_3]) ).
cnf(f_437_6,plain,
( hBOOL(hAPP(U_1359,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK23(U_1360,U_1359)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(U_1359,U_1360))
| hBOOL(hAPP(U_1359,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_437_3]) ).
fof(f_438_1,plain,
! [T_a] :
( ? [B_K] :
( ! [B_a,B_b] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_438_2,plain,
! [U_1364] :
( ? [U_1363] :
( ! [U_1362,U_1361] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1364),U_1362),U_1361))),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_1364,U_1362)),c_RealVector_Onorm__class_Onorm(U_1364,U_1361))),U_1363)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1363)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1364) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
! [U_1364] :
( ( ! [U_1362,U_1361] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1364),U_1362),U_1361))),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_1364,U_1362)),c_RealVector_Onorm__class_Onorm(U_1364,U_1361))),sK24(U_1364))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK24(U_1364))) )
| ~ class_RealVector_Oreal__normed__algebra(U_1364) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1363,sK24(U_1364))],[f_438_2]) ).
cnf(f_438_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK24(U_1364)))
| ~ class_RealVector_Oreal__normed__algebra(U_1364) ),
inference(clausify,[status(thm)],[f_438_3]) ).
cnf(f_438_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1364),U_1362),U_1361))),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_1364,U_1362)),c_RealVector_Onorm__class_Onorm(U_1364,U_1361))),sK24(U_1364))))
| ~ class_RealVector_Oreal__normed__algebra(U_1364) ),
inference(clausify,[status(thm)],[f_438_3]) ).
fof(f_439_1,plain,
! [V_X_2,T_a] :
( c_SEQ_Omonoseq(T_a,V_X_2)
| ~ c_SEQ_Odecseq(T_a,V_X_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_decseq__imp__monoseq]) ).
fof(f_439_2,plain,
! [U_1366,U_1365] :
( c_SEQ_Omonoseq(U_1365,U_1366)
| ~ c_SEQ_Odecseq(U_1365,U_1366)
| ~ class_Orderings_Oorder(U_1365) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( c_SEQ_Omonoseq(U_1365,U_1366)
| ~ c_SEQ_Odecseq(U_1365,U_1366)
| ~ class_Orderings_Oorder(U_1365) ),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_1,plain,
! [V_y,T_a] :
( ? [B_K] :
( ! [B_x] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_440_2,plain,
! [U_1370,U_1369] :
( ? [U_1368] :
( ! [U_1367] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1369,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1369),U_1367),U_1370))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1369,U_1367)),U_1368)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1368)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1369) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
! [U_1370,U_1369] :
( ( ! [U_1367] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1369,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1369),U_1367),U_1370))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1369,U_1367)),sK25(U_1370,U_1369))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK25(U_1370,U_1369))) )
| ~ class_RealVector_Oreal__normed__algebra(U_1369) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1368,sK25(U_1370,U_1369))],[f_440_2]) ).
cnf(f_440_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK25(U_1370,U_1369)))
| ~ class_RealVector_Oreal__normed__algebra(U_1369) ),
inference(clausify,[status(thm)],[f_440_3]) ).
cnf(f_440_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1369,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1369),U_1367),U_1370))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1369,U_1367)),sK25(U_1370,U_1369))))
| ~ class_RealVector_Oreal__normed__algebra(U_1369) ),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_1,plain,
! [V_x,T_a] :
( ? [B_K] :
( ! [B_x] : hBOOL(hAPP(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)))
& hBOOL(hAPP(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_441_2,plain,
! [U_1374,U_1373] :
( ? [U_1372] :
( ! [U_1371] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1373,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),U_1371))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1373,U_1371)),U_1372)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1372)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1373) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
! [U_1374,U_1373] :
( ( ! [U_1371] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1373,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),U_1371))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1373,U_1371)),sK26(U_1374,U_1373))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK26(U_1374,U_1373))) )
| ~ class_RealVector_Oreal__normed__algebra(U_1373) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1372,sK26(U_1374,U_1373))],[f_441_2]) ).
cnf(f_441_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK26(U_1374,U_1373)))
| ~ class_RealVector_Oreal__normed__algebra(U_1373) ),
inference(clausify,[status(thm)],[f_441_3]) ).
cnf(f_441_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1373,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1373),U_1374),U_1371))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1373,U_1371)),sK26(U_1374,U_1373))))
| ~ class_RealVector_Oreal__normed__algebra(U_1373) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_K] :
( ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) ) )
& ( ? [B_K] :
( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(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_442_2,plain,
! [U_1380,U_1379] :
( ( ( c_SEQ_OBseq(U_1379,U_1380)
| ! [U_1378] :
( ? [U_1377] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,U_1377))),U_1378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1378)) ) )
& ( ? [U_1376] :
( ! [U_1375] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,U_1375))),U_1376))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1376)) )
| ~ c_SEQ_OBseq(U_1379,U_1380) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1379) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
! [U_1380,U_1379] :
( ( ( c_SEQ_OBseq(U_1379,U_1380)
| ! [U_1378] :
( ? [U_1377] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,U_1377))),U_1378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1378)) ) )
& ( ( ! [U_1375] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,U_1375))),sK27(U_1380,U_1379)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK27(U_1380,U_1379))) )
| ~ c_SEQ_OBseq(U_1379,U_1380) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1379) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1376,sK27(U_1380,U_1379))],[f_442_2]) ).
fof(f_442_4,plain,
! [U_1380,U_1379] :
( ( ( c_SEQ_OBseq(U_1379,U_1380)
| ! [U_1378] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,sK28(U_1380,U_1379,U_1378)))),U_1378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1378)) ) )
& ( ( ! [U_1375] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,U_1375))),sK27(U_1380,U_1379)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK27(U_1380,U_1379))) )
| ~ c_SEQ_OBseq(U_1379,U_1380) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1379) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1377,sK28(U_1380,U_1379,U_1378))],[f_442_3]) ).
cnf(f_442_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK27(U_1380,U_1379)))
| ~ c_SEQ_OBseq(U_1379,U_1380)
| ~ class_RealVector_Oreal__normed__vector(U_1379) ),
inference(clausify,[status(thm)],[f_442_4]) ).
cnf(f_442_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,U_1375))),sK27(U_1380,U_1379)))
| ~ c_SEQ_OBseq(U_1379,U_1380)
| ~ class_RealVector_Oreal__normed__vector(U_1379) ),
inference(clausify,[status(thm)],[f_442_4]) ).
cnf(f_442_7,plain,
( c_SEQ_OBseq(U_1379,U_1380)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1379,hAPP(U_1380,sK28(U_1380,U_1379,U_1378)))),U_1378))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1378))
| ~ class_RealVector_Oreal__normed__vector(U_1379) ),
inference(clausify,[status(thm)],[f_442_4]) ).
fof(f_443_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Oincseq(T_a,V_X_2)
| ? [B_m,B_n] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) ) )
& ( ! [B_m,B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))
| ~ hBOOL(hAPP(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_443_2,plain,
! [U_1386,U_1385] :
( ( ( c_SEQ_Oincseq(U_1385,U_1386)
| ? [U_1384,U_1383] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,U_1384)),hAPP(U_1386,U_1383)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384),U_1383)) ) )
& ( ! [U_1382,U_1381] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,U_1382)),hAPP(U_1386,U_1381)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1382),U_1381)) )
| ~ c_SEQ_Oincseq(U_1385,U_1386) ) )
| ~ class_Orderings_Oorder(U_1385) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
! [U_1386,U_1385] :
( ( ( c_SEQ_Oincseq(U_1385,U_1386)
| ? [U_1383] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,sK29(U_1386,U_1385))),hAPP(U_1386,U_1383)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK29(U_1386,U_1385)),U_1383)) ) )
& ( ! [U_1382,U_1381] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,U_1382)),hAPP(U_1386,U_1381)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1382),U_1381)) )
| ~ c_SEQ_Oincseq(U_1385,U_1386) ) )
| ~ class_Orderings_Oorder(U_1385) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1384,sK29(U_1386,U_1385))],[f_443_2]) ).
fof(f_443_4,plain,
! [U_1386,U_1385] :
( ( ( c_SEQ_Oincseq(U_1385,U_1386)
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,sK29(U_1386,U_1385))),hAPP(U_1386,sK30(U_1386,U_1385))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK29(U_1386,U_1385)),sK30(U_1386,U_1385))) ) )
& ( ! [U_1382,U_1381] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,U_1382)),hAPP(U_1386,U_1381)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1382),U_1381)) )
| ~ c_SEQ_Oincseq(U_1385,U_1386) ) )
| ~ class_Orderings_Oorder(U_1385) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1383,sK30(U_1386,U_1385))],[f_443_3]) ).
cnf(f_443_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,U_1382)),hAPP(U_1386,U_1381)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1382),U_1381))
| ~ c_SEQ_Oincseq(U_1385,U_1386)
| ~ class_Orderings_Oorder(U_1385) ),
inference(clausify,[status(thm)],[f_443_4]) ).
cnf(f_443_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK29(U_1386,U_1385)),sK30(U_1386,U_1385)))
| c_SEQ_Oincseq(U_1385,U_1386)
| ~ class_Orderings_Oorder(U_1385) ),
inference(clausify,[status(thm)],[f_443_4]) ).
cnf(f_443_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385,hAPP(U_1386,sK29(U_1386,U_1385))),hAPP(U_1386,sK30(U_1386,U_1385))))
| c_SEQ_Oincseq(U_1385,U_1386)
| ~ class_Orderings_Oorder(U_1385) ),
inference(clausify,[status(thm)],[f_443_4]) ).
fof(f_444_1,plain,
! [V_k_2,V_X_2,T_a] :
( c_SEQ_OBseq(T_a,V_X_2)
| ~ c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__offset]) ).
fof(f_444_2,plain,
! [U_1389,U_1388,U_1387] :
( c_SEQ_OBseq(U_1387,U_1388)
| ~ c_SEQ_OBseq(U_1387,c_COMBB(tc_Nat_Onat,U_1387,tc_Nat_Onat,U_1388,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1389)))
| ~ class_RealVector_Oreal__normed__vector(U_1387) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( c_SEQ_OBseq(U_1387,U_1388)
| ~ c_SEQ_OBseq(U_1387,c_COMBB(tc_Nat_Onat,U_1387,tc_Nat_Onat,U_1388,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1389)))
| ~ class_RealVector_Oreal__normed__vector(U_1387) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_1,plain,
! [V_k_2,V_X_2,T_a] :
( c_SEQ_OBseq(T_a,c_COMBB(tc_Nat_Onat,T_a,tc_Nat_Onat,V_X_2,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2)))
| ~ c_SEQ_OBseq(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__ignore__initial__segment]) ).
fof(f_445_2,plain,
! [U_1392,U_1391,U_1390] :
( c_SEQ_OBseq(U_1390,c_COMBB(tc_Nat_Onat,U_1390,tc_Nat_Onat,U_1391,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1392)))
| ~ c_SEQ_OBseq(U_1390,U_1391)
| ~ class_RealVector_Oreal__normed__vector(U_1390) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
( c_SEQ_OBseq(U_1390,c_COMBB(tc_Nat_Onat,U_1390,tc_Nat_Onat,U_1391,c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1392)))
| ~ c_SEQ_OBseq(U_1390,U_1391)
| ~ class_RealVector_Oreal__normed__vector(U_1390) ),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_1,plain,
! [V_X_2] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,V_X_2)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__monoseq__convergent]) ).
fof(f_446_2,plain,
! [U_1393] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,U_1393)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,U_1393)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,U_1393) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,U_1393)
| ~ c_SEQ_Omonoseq(tc_RealDef_Oreal,U_1393)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,U_1393) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_1,plain,
! [V_X_2,T_a] :
( c_SEQ_Omonoseq(T_a,V_X_2)
| ~ c_SEQ_Oincseq(T_a,V_X_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_incseq__imp__monoseq]) ).
fof(f_447_2,plain,
! [U_1395,U_1394] :
( c_SEQ_Omonoseq(U_1394,U_1395)
| ~ c_SEQ_Oincseq(U_1394,U_1395)
| ~ class_Orderings_Oorder(U_1394) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( c_SEQ_Omonoseq(U_1394,U_1395)
| ~ c_SEQ_Oincseq(U_1394,U_1395)
| ~ class_Orderings_Oorder(U_1394) ),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_1,plain,
! [V_X_2,V_K_2,T_a] :
( c_SEQ_OBseq(T_a,V_X_2)
| ? [B_n] : ~ hBOOL(hAPP(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))
| ~ hBOOL(hAPP(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_448_2,plain,
! [U_1399,U_1398,U_1397] :
( c_SEQ_OBseq(U_1397,U_1399)
| ? [U_1396] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1397,hAPP(U_1399,U_1396))),U_1398))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1398))
| ~ class_RealVector_Oreal__normed__vector(U_1397) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
! [U_1399,U_1398,U_1397] :
( c_SEQ_OBseq(U_1397,U_1399)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1397,hAPP(U_1399,sK31(U_1399,U_1398,U_1397)))),U_1398))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1398))
| ~ class_RealVector_Oreal__normed__vector(U_1397) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1396,sK31(U_1399,U_1398,U_1397))],[f_448_2]) ).
cnf(f_448_4,plain,
( c_SEQ_OBseq(U_1397,U_1399)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1397,hAPP(U_1399,sK31(U_1399,U_1398,U_1397)))),U_1398))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1398))
| ~ class_RealVector_Oreal__normed__vector(U_1397) ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_1,plain,
! [V_X_2,T_a] :
( ? [B_K] :
( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(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_449_2,plain,
! [U_1403,U_1402] :
( ? [U_1401] :
( ! [U_1400] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1402,hAPP(U_1403,U_1400))),U_1401))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1401)) )
| ~ c_SEQ_OBseq(U_1402,U_1403)
| ~ class_RealVector_Oreal__normed__vector(U_1402) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
! [U_1403,U_1402] :
( ( ! [U_1400] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1402,hAPP(U_1403,U_1400))),sK32(U_1403,U_1402)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK32(U_1403,U_1402))) )
| ~ c_SEQ_OBseq(U_1402,U_1403)
| ~ class_RealVector_Oreal__normed__vector(U_1402) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1401,sK32(U_1403,U_1402))],[f_449_2]) ).
cnf(f_449_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK32(U_1403,U_1402)))
| ~ c_SEQ_OBseq(U_1402,U_1403)
| ~ class_RealVector_Oreal__normed__vector(U_1402) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1402,hAPP(U_1403,U_1400))),sK32(U_1403,U_1402)))
| ~ c_SEQ_OBseq(U_1402,U_1403)
| ~ class_RealVector_Oreal__normed__vector(U_1402) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_1,plain,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_expi__zero]) ).
cnf(f_450_2,plain,
c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_450_1]) ).
fof(f_451_1,plain,
! [V_x] :
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(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_451_2,plain,
! [U_1404] :
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1404),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(U_1404)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1404)) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1404),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(U_1404)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1404)) ),
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_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]) ).
cnf(f_452_2,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_452_1]) ).
fof(f_453_1,plain,
! [V_x] : hBOOL(hAPP(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_453_2,plain,
! [U_1405] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(U_1405))),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatceiling(U_1405))),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),c_RComplete_Onatceiling(V_y)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__mono]) ).
fof(f_454_2,plain,
! [U_1407,U_1406] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1406)),c_RComplete_Onatceiling(U_1407)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1406),U_1407)) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1406)),c_RComplete_Onatceiling(U_1407)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1406),U_1407)) ),
inference(clausify,[status(thm)],[f_454_2]) ).
fof(f_455_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]) ).
cnf(f_455_2,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_455_1]) ).
fof(f_456_1,plain,
! [V_x] :
( c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_456_2,plain,
! [U_1408] :
( c_RComplete_Onatceiling(U_1408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1408),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
cnf(f_456_3,plain,
( c_RComplete_Onatceiling(U_1408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1408),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_456_2]) ).
fof(f_457_1,plain,
! [V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(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_457_2,plain,
! [U_1409] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1409)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1409),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1409),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1409)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
( ! [U_1411] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1411)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1411),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ! [U_1410] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1410),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1410)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_457_2]) ).
cnf(f_457_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1410),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1410)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_457_3]) ).
cnf(f_457_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1411)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1411),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_457_3]) ).
fof(f_458_1,plain,
! [V_b,V_a] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)),
inference(fof_nnf,[status(thm)],[fact_expi__add]) ).
fof(f_458_2,plain,
! [U_1413,U_1412] : c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_1412),U_1413)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(U_1412)),c_Complex_Oexpi(U_1413)),
inference(variable_rename,[status(thm)],[f_458_1]) ).
cnf(f_458_3,plain,
c_Complex_Oexpi(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_1412),U_1413)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(U_1412)),c_Complex_Oexpi(U_1413)),
inference(clausify,[status(thm)],[f_458_2]) ).
fof(f_459_1,plain,
! [V_x] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(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_459_2,plain,
! [U_1414] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1414),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(U_1414)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1414)) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
cnf(f_459_3,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1414),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(U_1414)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1414)) ),
inference(clausify,[status(thm)],[f_459_2]) ).
fof(f_460_1,plain,
! [V_x,V_n] :
( c_RComplete_Onatceiling(V_x) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(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_460_2,plain,
! [U_1416,U_1415] :
( c_RComplete_Onatceiling(U_1416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1415),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1415)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1415)),U_1416)) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( c_RComplete_Onatceiling(U_1416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1415),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1415)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1415)),U_1416)) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_b))
| ~ hBOOL(hAPP(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_461_2,plain,
! [U_1418,U_1417] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1417)),c_RComplete_Onatfloor(U_1418))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1417),U_1418))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1418))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1417)) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1417)),c_RComplete_Onatfloor(U_1418))),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1417),U_1418))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1418))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1417)) ),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_1,plain,
! [V_X_2] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,V_X_2)
| ? [B_m,B_n] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(V_X_2,B_m)),hAPP(V_X_2,B_n)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m),B_n)) )
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,V_X_2) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__mono__convergent]) ).
fof(f_462_2,plain,
! [U_1421] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,U_1421)
| ? [U_1420,U_1419] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(U_1421,U_1420)),hAPP(U_1421,U_1419)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1420),U_1419)) )
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,U_1421) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_1421] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,U_1421)
| ? [U_1419] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(U_1421,sK33(U_1421))),hAPP(U_1421,U_1419)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK33(U_1421)),U_1419)) )
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,U_1421) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1420,sK33(U_1421))],[f_462_2]) ).
fof(f_462_4,plain,
! [U_1421] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,U_1421)
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(U_1421,sK33(U_1421))),hAPP(U_1421,sK34(U_1421))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK33(U_1421)),sK34(U_1421))) )
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,U_1421) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1419,sK34(U_1421))],[f_462_3]) ).
cnf(f_462_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK33(U_1421)),sK34(U_1421)))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,U_1421)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,U_1421) ),
inference(clausify,[status(thm)],[f_462_4]) ).
cnf(f_462_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(U_1421,sK33(U_1421))),hAPP(U_1421,sK34(U_1421))))
| c_SEQ_Oconvergent(tc_RealDef_Oreal,U_1421)
| ~ c_SEQ_OBseq(tc_RealDef_Oreal,U_1421) ),
inference(clausify,[status(thm)],[f_462_4]) ).
fof(f_463_1,plain,
! [V_n] : hBOOL(hAPP(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_463_2,plain,
! [U_1422] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1422))),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1422))),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_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_464_2,plain,
! [U_1423] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_1423)) = U_1423,
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_1423)) = U_1423,
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_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_465_2,plain,
! [U_1424] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_1424)) = U_1424,
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_1424)) = U_1424,
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_1,plain,
! [V_a,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x),c_RComplete_Onatfloor(V_a)))
| ~ hBOOL(hAPP(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_466_2,plain,
! [U_1426,U_1425] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1425),c_RComplete_Onatfloor(U_1426)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1425)),U_1426)) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
cnf(f_466_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1425),c_RComplete_Onatfloor(U_1426)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1425)),U_1426)) ),
inference(clausify,[status(thm)],[f_466_2]) ).
fof(f_467_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),V_x))
| ~ hBOOL(hAPP(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_467_2,plain,
! [U_1427] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_1427))),U_1427))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1427)) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_1427))),U_1427))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1427)) ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_1,plain,
! [V_m_2,V_n_2] :
( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_RealDef_Oreal(tc_Nat_Onat,V_m_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject]) ).
fof(f_468_2,plain,
! [U_1429,U_1428] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_1428) = c_RealDef_Oreal(tc_Nat_Onat,U_1429)
| U_1428 != U_1429 )
& ( U_1428 = U_1429
| c_RealDef_Oreal(tc_Nat_Onat,U_1428) != c_RealDef_Oreal(tc_Nat_Onat,U_1429) ) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
( ! [U_1433,U_1431] :
( c_RealDef_Oreal(tc_Nat_Onat,U_1431) = c_RealDef_Oreal(tc_Nat_Onat,U_1433)
| U_1431 != U_1433 )
& ! [U_1432,U_1430] :
( U_1430 = U_1432
| c_RealDef_Oreal(tc_Nat_Onat,U_1430) != c_RealDef_Oreal(tc_Nat_Onat,U_1432) ) ),
inference(miniscope,[status(thm)],[f_468_2]) ).
cnf(f_468_4,plain,
( U_1430 = U_1432
| c_RealDef_Oreal(tc_Nat_Onat,U_1430) != c_RealDef_Oreal(tc_Nat_Onat,U_1432) ),
inference(clausify,[status(thm)],[f_468_3]) ).
cnf(f_468_5,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_1431) = c_RealDef_Oreal(tc_Nat_Onat,U_1433)
| U_1431 != U_1433 ),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_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_469_2,plain,
! [U_1434] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1434)) = c_RealDef_Oreal(tc_Nat_Onat,U_1434),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1434)) = c_RealDef_Oreal(tc_Nat_Onat,U_1434),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_1,plain,
! [V_a_2,V_x_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2),c_RComplete_Onatfloor(V_x_2))) ) )
| ~ hBOOL(hAPP(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_470_2,plain,
! [U_1436,U_1435] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1436),c_RComplete_Onatfloor(U_1435)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1436)),U_1435)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1436)),U_1435))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1436),c_RComplete_Onatfloor(U_1435))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1435)) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1436)),U_1435))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1436),c_RComplete_Onatfloor(U_1435)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1435)) ),
inference(clausify,[status(thm)],[f_470_2]) ).
cnf(f_470_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1436),c_RComplete_Onatfloor(U_1435)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1436)),U_1435))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1435)) ),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(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_471_2,plain,
! [U_1437] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_1437))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_1437))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_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]) ).
cnf(f_472_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(clausify,[status(thm)],[f_472_1]) ).
fof(f_473_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_473_2,plain,
! [U_1438] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_1438) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1438 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_1438) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
( ! [U_1440] :
( c_RealDef_Oreal(tc_Nat_Onat,U_1440) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1440 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1439] :
( U_1439 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_1439) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_473_2]) ).
cnf(f_473_4,plain,
( U_1439 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_1439) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_473_3]) ).
cnf(f_473_5,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_1440) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1440 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [V_n] : ~ hBOOL(hAPP(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_474_2,plain,
! [U_1441] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1441)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1441)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff]) ).
fof(f_475_2,plain,
! [U_1443,U_1442] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1442)),c_RealDef_Oreal(tc_Nat_Onat,U_1443)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1442),U_1443)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1442),U_1443))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1442)),c_RealDef_Oreal(tc_Nat_Onat,U_1443))) ) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
( ! [U_1447,U_1445] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1445)),c_RealDef_Oreal(tc_Nat_Onat,U_1447)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1445),U_1447)) )
& ! [U_1446,U_1444] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1444),U_1446))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1444)),c_RealDef_Oreal(tc_Nat_Onat,U_1446))) ) ),
inference(miniscope,[status(thm)],[f_475_2]) ).
cnf(f_475_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1444),U_1446))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1444)),c_RealDef_Oreal(tc_Nat_Onat,U_1446))) ),
inference(clausify,[status(thm)],[f_475_3]) ).
cnf(f_475_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1445)),c_RealDef_Oreal(tc_Nat_Onat,U_1447)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1445),U_1447)) ),
inference(clausify,[status(thm)],[f_475_3]) ).
fof(f_476_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(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_m_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2))
| ~ hBOOL(hAPP(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_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff]) ).
fof(f_476_2,plain,
! [U_1449,U_1448] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1448)),c_RealDef_Oreal(tc_Nat_Onat,U_1449)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1448),U_1449)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1448),U_1449))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1448)),c_RealDef_Oreal(tc_Nat_Onat,U_1449))) ) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
( ! [U_1453,U_1451] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1451)),c_RealDef_Oreal(tc_Nat_Onat,U_1453)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1451),U_1453)) )
& ! [U_1452,U_1450] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1450),U_1452))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1450)),c_RealDef_Oreal(tc_Nat_Onat,U_1452))) ) ),
inference(miniscope,[status(thm)],[f_476_2]) ).
cnf(f_476_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1450),U_1452))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1450)),c_RealDef_Oreal(tc_Nat_Onat,U_1452))) ),
inference(clausify,[status(thm)],[f_476_3]) ).
cnf(f_476_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1451)),c_RealDef_Oreal(tc_Nat_Onat,U_1453)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1451),U_1453)) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [V_n,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_RealDef_Oreal(tc_Nat_Onat,V_n)))
| ~ hBOOL(hAPP(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_477_2,plain,
! [U_1455,U_1454] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_1454)),U_1455))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1454),c_RealDef_Oreal(tc_Nat_Onat,U_1455)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1454)) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
cnf(f_477_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_1454)),U_1455))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1454),c_RealDef_Oreal(tc_Nat_Onat,U_1455)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1454)) ),
inference(clausify,[status(thm)],[f_477_2]) ).
fof(f_478_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_478_2,plain,
! [U_1457,U_1456] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1456),U_1457)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1456)),c_RealDef_Oreal(tc_Nat_Onat,U_1457)),
inference(variable_rename,[status(thm)],[f_478_1]) ).
cnf(f_478_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1456),U_1457)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1456)),c_RealDef_Oreal(tc_Nat_Onat,U_1457)),
inference(clausify,[status(thm)],[f_478_2]) ).
fof(f_479_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(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_479_2,plain,
! [U_1459,U_1458] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1458),U_1459)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1458)),c_RealDef_Oreal(tc_Nat_Onat,U_1459)),
inference(variable_rename,[status(thm)],[f_479_1]) ).
cnf(f_479_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1458),U_1459)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1458)),c_RealDef_Oreal(tc_Nat_Onat,U_1459)),
inference(clausify,[status(thm)],[f_479_2]) ).
fof(f_480_1,plain,
! [V_a,V_x] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_a)
| ~ hBOOL(hAPP(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_480_2,plain,
! [U_1461,U_1460] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1460),c_RealDef_Oreal(tc_Nat_Onat,U_1461))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(U_1460)),U_1461)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1460)) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1460),c_RealDef_Oreal(tc_Nat_Onat,U_1461))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(U_1460)),U_1461)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1460)) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_1,plain,
! [V_n,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z),c_RealDef_Oreal(tc_Nat_Onat,V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(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_481_2,plain,
! [U_1463,U_1462] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1462),c_RealDef_Oreal(tc_Nat_Onat,U_1463)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(U_1462)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1463)) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1462),c_RealDef_Oreal(tc_Nat_Onat,U_1463)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatfloor(U_1462)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1463)) ),
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_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]) ).
cnf(f_482_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(clausify,[status(thm)],[f_482_1]) ).
fof(f_483_1,plain,
! [V_x,V_n] :
( c_RComplete_Onatfloor(V_x) = V_n
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(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_483_2,plain,
! [U_1465,U_1464] :
( c_RComplete_Onatfloor(U_1465) = U_1464
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1464)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1464)),U_1465)) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
( c_RComplete_Onatfloor(U_1465) = U_1464
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1464)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1464)),U_1465)) ),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_1,plain,
! [V_x] : hBOOL(hAPP(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_484_2,plain,
! [U_1466] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1466),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_1466)))),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1466),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_1466)))),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_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]) ).
cnf(f_485_2,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_485_1]) ).
fof(f_486_1,plain,
! [V_x] : hBOOL(hAPP(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_486_2,plain,
! [U_1467] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1467))),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1467))),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_RComplete_Onatfloor(V_y)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__mono]) ).
fof(f_487_2,plain,
! [U_1469,U_1468] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1468)),c_RComplete_Onatfloor(U_1469)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1468),U_1469)) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_1468)),c_RComplete_Onatfloor(U_1469)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1468),U_1469)) ),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_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]) ).
cnf(f_488_2,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_488_1]) ).
fof(f_489_1,plain,
! [V_n_2] :
( ( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_489_2,plain,
! [U_1470] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1470)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| U_1470 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1470 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1470)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
( ! [U_1472] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1472)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| U_1472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1471] :
( U_1471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1471)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) ),
inference(miniscope,[status(thm)],[f_489_2]) ).
cnf(f_489_4,plain,
( U_1471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1471)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_489_3]) ).
cnf(f_489_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1472)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| U_1472 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_1,plain,
! [V_a,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x)),V_a))
| ~ hBOOL(hAPP(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_490_2,plain,
! [U_1474,U_1473] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1473)),U_1474))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1473),c_RealDef_Oreal(tc_Nat_Onat,U_1474))) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1473)),U_1474))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1473),c_RealDef_Oreal(tc_Nat_Onat,U_1474))) ),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_1,plain,
! [V_x] :
( c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_491_2,plain,
! [U_1475] :
( c_RComplete_Onatfloor(U_1475) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1475),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
( c_RComplete_Onatfloor(U_1475) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1475),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_1,plain,
! [V_n_2] :
( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| ~ hBOOL(hAPP(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_492_2,plain,
! [U_1476] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1476)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1476)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1476))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1476))) ) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
( ! [U_1478] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1478)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1478)) )
& ! [U_1477] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1477))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1477))) ) ),
inference(miniscope,[status(thm)],[f_492_2]) ).
cnf(f_492_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1477))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1477))) ),
inference(clausify,[status(thm)],[f_492_3]) ).
cnf(f_492_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_1478)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1478)) ),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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_m_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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_m_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__real__le]) ).
fof(f_493_2,plain,
! [U_1480,U_1479] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1479),U_1480))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1479)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,U_1480))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1479)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,U_1480)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1479),U_1480)) ) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
( ! [U_1484,U_1482] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1482),U_1484))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1482)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,U_1484))) )
& ! [U_1483,U_1481] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1481)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,U_1483)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1481),U_1483)) ) ),
inference(miniscope,[status(thm)],[f_493_2]) ).
cnf(f_493_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1481)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,U_1483)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1481),U_1483)) ),
inference(clausify,[status(thm)],[f_493_3]) ).
cnf(f_493_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1482),U_1484))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1482)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,U_1484))) ),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__real__less]) ).
fof(f_494_2,plain,
! [U_1486,U_1485] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1485),U_1486))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1485)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1486)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1485)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1486)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1485),U_1486)) ) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
( ! [U_1490,U_1488] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1488),U_1490))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1488)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1490)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) )
& ! [U_1489,U_1487] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1487)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1489)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1487),U_1489)) ) ),
inference(miniscope,[status(thm)],[f_494_2]) ).
cnf(f_494_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1487)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1489)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1487),U_1489)) ),
inference(clausify,[status(thm)],[f_494_3]) ).
cnf(f_494_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1488),U_1490))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_1488)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1490)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(clausify,[status(thm)],[f_494_3]) ).
fof(f_495_1,plain,
! [V_a_2,V_x_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_RealDef_Oreal(tc_Nat_Onat,V_a_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(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_495_2,plain,
! [U_1492,U_1491] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1491)),U_1492))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1491),c_RealDef_Oreal(tc_Nat_Onat,U_1492))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1491),c_RealDef_Oreal(tc_Nat_Onat,U_1492)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1491)),U_1492)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1491)) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1491),c_RealDef_Oreal(tc_Nat_Onat,U_1492)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1491)),U_1492))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1491)) ),
inference(clausify,[status(thm)],[f_495_2]) ).
cnf(f_495_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1491)),U_1492))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1491),c_RealDef_Oreal(tc_Nat_Onat,U_1492)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1491)) ),
inference(clausify,[status(thm)],[f_495_2]) ).
fof(f_496_1,plain,
! [V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(V_x_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))
| ~ hBOOL(hAPP(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_496_2,plain,
! [U_1493] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1493)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1493)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1493))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1493))) ) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
( ! [U_1495] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1495)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1495)) )
& ! [U_1494] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1494))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1494))) ) ),
inference(miniscope,[status(thm)],[f_496_2]) ).
cnf(f_496_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1494))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1494))) ),
inference(clausify,[status(thm)],[f_496_3]) ).
cnf(f_496_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_RComplete_Onatfloor(U_1495)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1495)) ),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_1,plain,
! [V_a,V_x] :
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_a))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),V_a)
| ~ hBOOL(hAPP(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_497_2,plain,
! [U_1497,U_1496] :
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1496),c_RealDef_Oreal(tc_Nat_Onat,U_1497))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(U_1496)),U_1497)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1496)) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
( c_RComplete_Onatceiling(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1496),c_RealDef_Oreal(tc_Nat_Onat,U_1497))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_RComplete_Onatceiling(U_1496)),U_1497)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1496)) ),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_1,plain,
! [V_n,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)))
| ~ hBOOL(hAPP(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_498_2,plain,
! [U_1499,U_1498] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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_1499)),U_1498)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1498),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_1499)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1498)) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(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_1499)),U_1498)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_1498),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_1499)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1498)) ),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_1,plain,
! [V_K_2,V_X_2,V_N_2,T_a] :
( c_SEQ_OBseq(T_a,V_X_2)
| ? [B_n] :
( ~ hBOOL(hAPP(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))
& hBOOL(hAPP(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_499_2,plain,
! [U_1504,U_1503,U_1502,U_1501] :
( c_SEQ_OBseq(U_1501,U_1503)
| ? [U_1500] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1501,hAPP(U_1503,U_1500))),U_1504))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1502),U_1500)) )
| ~ class_RealVector_Oreal__normed__vector(U_1501) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
! [U_1504,U_1503,U_1502,U_1501] :
( c_SEQ_OBseq(U_1501,U_1503)
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1501,hAPP(U_1503,sK35(U_1504,U_1503,U_1502,U_1501)))),U_1504))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1502),sK35(U_1504,U_1503,U_1502,U_1501))) )
| ~ class_RealVector_Oreal__normed__vector(U_1501) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_1500,sK35(U_1504,U_1503,U_1502,U_1501))],[f_499_2]) ).
cnf(f_499_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1502),sK35(U_1504,U_1503,U_1502,U_1501)))
| c_SEQ_OBseq(U_1501,U_1503)
| ~ class_RealVector_Oreal__normed__vector(U_1501) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1501,hAPP(U_1503,sK35(U_1504,U_1503,U_1502,U_1501)))),U_1504))
| c_SEQ_OBseq(U_1501,U_1503)
| ~ class_RealVector_Oreal__normed__vector(U_1501) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) )
| ! [B_N] :
? [B_n] : ~ hBOOL(hAPP(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] : hBOOL(hAPP(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] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))
| ~ hBOOL(hAPP(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_500_2,plain,
! [U_1514,U_1513] :
( ( ( ? [U_1512] :
( ! [U_1511] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1511))),U_1512))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1512)) )
| ! [U_1510] :
? [U_1509] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1509))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1510)))) )
& ( ? [U_1508] :
! [U_1507] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1507))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1508))))
| ! [U_1506] :
( ? [U_1505] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1505))),U_1506))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1506)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
! [U_1514,U_1513] :
( ( ( ? [U_1512] :
( ! [U_1511] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1511))),U_1512))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1512)) )
| ! [U_1510] :
? [U_1509] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1509))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1510)))) )
& ( ? [U_1508] :
! [U_1507] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1507))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1508))))
| ! [U_1506] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK36(U_1514,U_1513,U_1506)))),U_1506))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1506)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_1505,sK36(U_1514,U_1513,U_1506))],[f_500_2]) ).
fof(f_500_4,plain,
! [U_1514,U_1513] :
( ( ( ? [U_1512] :
( ! [U_1511] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1511))),U_1512))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1512)) )
| ! [U_1510] :
? [U_1509] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1509))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1510)))) )
& ( ! [U_1507] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1507))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK37(U_1514,U_1513)))))
| ! [U_1506] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK36(U_1514,U_1513,U_1506)))),U_1506))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1506)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_1508,sK37(U_1514,U_1513))],[f_500_3]) ).
fof(f_500_5,plain,
! [U_1514,U_1513] :
( ( ( ? [U_1512] :
( ! [U_1511] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1511))),U_1512))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1512)) )
| ! [U_1510] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK38(U_1514,U_1513,U_1510)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1510)))) )
& ( ! [U_1507] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1507))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK37(U_1514,U_1513)))))
| ! [U_1506] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK36(U_1514,U_1513,U_1506)))),U_1506))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1506)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_1509,sK38(U_1514,U_1513,U_1510))],[f_500_4]) ).
fof(f_500_6,plain,
! [U_1514,U_1513] :
( ( ( ( ! [U_1511] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1511))),sK39(U_1514,U_1513)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK39(U_1514,U_1513))) )
| ! [U_1510] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK38(U_1514,U_1513,U_1510)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1510)))) )
& ( ! [U_1507] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1507))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK37(U_1514,U_1513)))))
| ! [U_1506] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK36(U_1514,U_1513,U_1506)))),U_1506))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1506)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_1512,sK39(U_1514,U_1513))],[f_500_5]) ).
cnf(f_500_7,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1507))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK37(U_1514,U_1513)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK36(U_1514,U_1513,U_1506)))),U_1506))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1506))
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(clausify,[status(thm)],[f_500_6]) ).
cnf(f_500_8,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK39(U_1514,U_1513)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK38(U_1514,U_1513,U_1510)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1510))))
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(clausify,[status(thm)],[f_500_6]) ).
cnf(f_500_9,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,U_1511))),sK39(U_1514,U_1513)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1513,hAPP(U_1514,sK38(U_1514,U_1513,U_1510)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1510))))
| ~ class_RealVector_Oreal__normed__vector(U_1513) ),
inference(clausify,[status(thm)],[f_500_6]) ).
fof(f_501_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_K)) )
| ! [B_N] :
? [B_n] : ~ hBOOL(hAPP(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] : hBOOL(hAPP(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] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),B_K))
| ~ hBOOL(hAPP(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_501_2,plain,
! [U_1524,U_1523] :
( ( ( ? [U_1522] :
( ! [U_1521] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1521))),U_1522))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1522)) )
| ! [U_1520] :
? [U_1519] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1519))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1520)))) )
& ( ? [U_1518] :
! [U_1517] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1517))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1518))))
| ! [U_1516] :
( ? [U_1515] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1515))),U_1516))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1516)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
! [U_1524,U_1523] :
( ( ( ? [U_1522] :
( ! [U_1521] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1521))),U_1522))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1522)) )
| ! [U_1520] :
? [U_1519] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1519))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1520)))) )
& ( ? [U_1518] :
! [U_1517] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1517))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1518))))
| ! [U_1516] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK40(U_1524,U_1523,U_1516)))),U_1516))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1516)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_1515,sK40(U_1524,U_1523,U_1516))],[f_501_2]) ).
fof(f_501_4,plain,
! [U_1524,U_1523] :
( ( ( ? [U_1522] :
( ! [U_1521] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1521))),U_1522))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1522)) )
| ! [U_1520] :
? [U_1519] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1519))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1520)))) )
& ( ! [U_1517] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1517))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK41(U_1524,U_1523)))))
| ! [U_1516] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK40(U_1524,U_1523,U_1516)))),U_1516))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1516)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_1518,sK41(U_1524,U_1523))],[f_501_3]) ).
fof(f_501_5,plain,
! [U_1524,U_1523] :
( ( ( ? [U_1522] :
( ! [U_1521] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1521))),U_1522))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1522)) )
| ! [U_1520] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK42(U_1524,U_1523,U_1520)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1520)))) )
& ( ! [U_1517] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1517))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK41(U_1524,U_1523)))))
| ! [U_1516] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK40(U_1524,U_1523,U_1516)))),U_1516))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1516)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_1519,sK42(U_1524,U_1523,U_1520))],[f_501_4]) ).
fof(f_501_6,plain,
! [U_1524,U_1523] :
( ( ( ( ! [U_1521] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1521))),sK43(U_1524,U_1523)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK43(U_1524,U_1523))) )
| ! [U_1520] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK42(U_1524,U_1523,U_1520)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1520)))) )
& ( ! [U_1517] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1517))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK41(U_1524,U_1523)))))
| ! [U_1516] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK40(U_1524,U_1523,U_1516)))),U_1516))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1516)) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_1522,sK43(U_1524,U_1523))],[f_501_5]) ).
cnf(f_501_7,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1517))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK41(U_1524,U_1523)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK40(U_1524,U_1523,U_1516)))),U_1516))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1516))
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(clausify,[status(thm)],[f_501_6]) ).
cnf(f_501_8,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK43(U_1524,U_1523)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK42(U_1524,U_1523,U_1520)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1520))))
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(clausify,[status(thm)],[f_501_6]) ).
cnf(f_501_9,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,U_1521))),sK43(U_1524,U_1523)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1523,hAPP(U_1524,sK42(U_1524,U_1523,U_1520)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1520))))
| ~ class_RealVector_Oreal__normed__vector(U_1523) ),
inference(clausify,[status(thm)],[f_501_6]) ).
fof(f_502_1,plain,
! [V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_n))),
inference(fof_nnf,[status(thm)],[fact_lessI]) ).
fof(f_502_2,plain,
! [U_1525] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1525),c_Nat_OSuc(U_1525))),
inference(variable_rename,[status(thm)],[f_502_1]) ).
cnf(f_502_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1525),c_Nat_OSuc(U_1525))),
inference(clausify,[status(thm)],[f_502_2]) ).
fof(f_503_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),c_Nat_OSuc(V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).
fof(f_503_2,plain,
! [U_1527,U_1526] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1526)),c_Nat_OSuc(U_1527)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1526),U_1527)) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
cnf(f_503_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1526)),c_Nat_OSuc(U_1527)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1526),U_1527)) ),
inference(clausify,[status(thm)],[f_503_2]) ).
fof(f_504_1,plain,
! [V_n] : hBOOL(hAPP(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_504_2,plain,
! [U_1528] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(U_1528))),
inference(variable_rename,[status(thm)],[f_504_1]) ).
cnf(f_504_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Nat_OSuc(U_1528))),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_1,plain,
! [V_n,V_r,T_a] :
( hBOOL(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_r),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(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_505_2,plain,
! [U_1531,U_1530,U_1529] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529,hAPP(hAPP(c_Power_Opower__class_Opower(U_1529),U_1530),c_Nat_OSuc(U_1531))),U_1530))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529,U_1530),c_Groups_Oone__class_Oone(U_1529)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529,c_Groups_Ozero__class_Ozero(U_1529)),U_1530))
| ~ class_Rings_Olinordered__semidom(U_1529) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
cnf(f_505_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529,hAPP(hAPP(c_Power_Opower__class_Opower(U_1529),U_1530),c_Nat_OSuc(U_1531))),U_1530))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529,U_1530),c_Groups_Oone__class_Oone(U_1529)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1529,c_Groups_Ozero__class_Ozero(U_1529)),U_1530))
| ~ class_Rings_Olinordered__semidom(U_1529) ),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_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_506_2,plain,
! [U_1534,U_1533,U_1532] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1532),U_1533),c_Nat_OSuc(U_1534)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1532),U_1533),hAPP(hAPP(c_Power_Opower__class_Opower(U_1532),U_1533),U_1534))
| ~ class_Rings_Ocomm__semiring__1(U_1532) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
cnf(f_506_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1532),U_1533),c_Nat_OSuc(U_1534)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1532),U_1533),hAPP(hAPP(c_Power_Opower__class_Opower(U_1532),U_1533),U_1534))
| ~ class_Rings_Ocomm__semiring__1(U_1532) ),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_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_507_2,plain,
! [U_1537,U_1536,U_1535] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),hAPP(hAPP(c_Power_Opower__class_Opower(U_1535),U_1536),U_1537)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1535),U_1536),c_Nat_OSuc(U_1537))
| ~ class_Rings_Ocomm__semiring__1(U_1535) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
cnf(f_507_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1535),U_1536),hAPP(hAPP(c_Power_Opower__class_Opower(U_1535),U_1536),U_1537)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1535),U_1536),c_Nat_OSuc(U_1537))
| ~ class_Rings_Ocomm__semiring__1(U_1535) ),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_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_508_2,plain,
! [U_1540,U_1539,U_1538] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1538),hAPP(hAPP(c_Power_Opower__class_Opower(U_1538),U_1539),U_1540)),U_1539) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1538),U_1539),c_Nat_OSuc(U_1540))
| ~ class_Rings_Ocomm__semiring__1(U_1538) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1538),hAPP(hAPP(c_Power_Opower__class_Opower(U_1538),U_1539),U_1540)),U_1539) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1538),U_1539),c_Nat_OSuc(U_1540))
| ~ class_Rings_Ocomm__semiring__1(U_1538) ),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_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_509_2,plain,
! [U_1544,U_1543,U_1542,U_1541] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1541),hAPP(hAPP(c_Power_Opower__class_Opower(U_1541),U_1542),U_1543)),U_1544) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1543),U_1544))
| ~ class_Rings_Ocomm__semiring__1(U_1541) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
cnf(f_509_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1541),hAPP(hAPP(c_Power_Opower__class_Opower(U_1541),U_1542),U_1543)),U_1544) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1543),U_1544))
| ~ class_Rings_Ocomm__semiring__1(U_1541) ),
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_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_510_2,plain,
! [U_1548,U_1547,U_1546,U_1545] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547)),U_1548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),hAPP(hAPP(c_Power_Opower__class_Opower(U_1545),U_1546),U_1548)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1545),U_1547),U_1548))
| ~ class_Rings_Ocomm__semiring__1(U_1545) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
cnf(f_510_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1545),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),U_1546),U_1547)),U_1548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1545),hAPP(hAPP(c_Power_Opower__class_Opower(U_1545),U_1546),U_1548)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1545),U_1547),U_1548))
| ~ class_Rings_Ocomm__semiring__1(U_1545) ),
inference(clausify,[status(thm)],[f_510_2]) ).
fof(f_511_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_511_2,plain,
! [U_1550,U_1549] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1549),U_1550),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1550
| ~ class_Rings_Ocomm__semiring__1(U_1549) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
cnf(f_511_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1549),U_1550),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1550
| ~ class_Rings_Ocomm__semiring__1(U_1549) ),
inference(clausify,[status(thm)],[f_511_2]) ).
fof(f_512_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(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_512_2,plain,
! [U_1552,U_1551] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1551),U_1552))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1551)),c_Nat_OSuc(U_1552))) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
cnf(f_512_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1551),U_1552))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1551)),c_Nat_OSuc(U_1552))) ),
inference(clausify,[status(thm)],[f_512_2]) ).
fof(f_513_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(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_513_2,plain,
! [U_1554,U_1553] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1553),U_1554))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1553)),U_1554)) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1553),U_1554))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1553)),U_1554)) ),
inference(clausify,[status(thm)],[f_513_2]) ).
fof(f_514_1,plain,
! [V_n,V_m] :
( V_m = V_n
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(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_514_2,plain,
! [U_1556,U_1555] :
( U_1555 = U_1556
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1555),U_1556))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1555),c_Nat_OSuc(U_1556))) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
( U_1555 = U_1556
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1555),U_1556))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1555),c_Nat_OSuc(U_1556))) ),
inference(clausify,[status(thm)],[f_514_2]) ).
fof(f_515_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i)),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).
fof(f_515_2,plain,
! [U_1559,U_1558,U_1557] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1557)),U_1559))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1558),U_1559))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1557),U_1558)) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
cnf(f_515_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1557)),U_1559))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1558),U_1559))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1557),U_1558)) ),
inference(clausify,[status(thm)],[f_515_2]) ).
fof(f_516_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
| c_Nat_OSuc(V_m) = V_n
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).
fof(f_516_2,plain,
! [U_1561,U_1560] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1560)),U_1561))
| c_Nat_OSuc(U_1560) = U_1561
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1560),U_1561)) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
cnf(f_516_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1560)),U_1561))
| c_Nat_OSuc(U_1560) = U_1561
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1560),U_1561)) ),
inference(clausify,[status(thm)],[f_516_2]) ).
fof(f_517_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).
fof(f_517_2,plain,
! [U_1563,U_1562] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1562),c_Nat_OSuc(U_1563)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1562),U_1563)) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1562),c_Nat_OSuc(U_1563)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1562),U_1563)) ),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_1,plain,
! [V_m,V_n] :
( V_m = V_n
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),c_Nat_OSuc(V_m)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).
fof(f_518_2,plain,
! [U_1565,U_1564] :
( U_1565 = U_1564
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1564),c_Nat_OSuc(U_1565)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1564),U_1565)) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
cnf(f_518_3,plain,
( U_1565 = U_1564
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1564),c_Nat_OSuc(U_1565)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1564),U_1565)) ),
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_1,plain,
! [V_m_2,V_n_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) ) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(f_519_2,plain,
! [U_1567,U_1566] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1566),c_Nat_OSuc(U_1567)))
| U_1566 != U_1567 )
& ( U_1566 = U_1567
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1566),c_Nat_OSuc(U_1567))) ) )
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1566),U_1567)) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
cnf(f_519_3,plain,
( U_1566 = U_1567
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1566),c_Nat_OSuc(U_1567)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1566),U_1567)) ),
inference(clausify,[status(thm)],[f_519_2]) ).
cnf(f_519_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1566),c_Nat_OSuc(U_1567)))
| U_1566 != U_1567
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1566),U_1567)) ),
inference(clausify,[status(thm)],[f_519_2]) ).
fof(f_520_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),c_Nat_OSuc(V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).
fof(f_520_2,plain,
! [U_1569,U_1568] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1568)),c_Nat_OSuc(U_1569)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1568),U_1569)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1568),U_1569))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1568)),c_Nat_OSuc(U_1569))) ) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
( ! [U_1573,U_1571] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1571)),c_Nat_OSuc(U_1573)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1571),U_1573)) )
& ! [U_1572,U_1570] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1570),U_1572))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1570)),c_Nat_OSuc(U_1572))) ) ),
inference(miniscope,[status(thm)],[f_520_2]) ).
cnf(f_520_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1570),U_1572))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1570)),c_Nat_OSuc(U_1572))) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1571)),c_Nat_OSuc(U_1573)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1571),U_1573)) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
| ( V_m_2 != V_n_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) )
& ( V_m_2 = V_n_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).
fof(f_521_2,plain,
! [U_1575,U_1574] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1574),c_Nat_OSuc(U_1575)))
| ( U_1574 != U_1575
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1574),U_1575)) ) )
& ( U_1574 = U_1575
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1574),U_1575))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1574),c_Nat_OSuc(U_1575))) ) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
( ! [U_1579,U_1577] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1577),c_Nat_OSuc(U_1579)))
| ( U_1577 != U_1579
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1577),U_1579)) ) )
& ! [U_1578,U_1576] :
( U_1576 = U_1578
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1576),U_1578))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1576),c_Nat_OSuc(U_1578))) ) ),
inference(miniscope,[status(thm)],[f_521_2]) ).
cnf(f_521_4,plain,
( U_1576 = U_1578
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1576),U_1578))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1576),c_Nat_OSuc(U_1578))) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1577),U_1579))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1577),c_Nat_OSuc(U_1579))) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_6,plain,
( U_1577 != U_1579
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1577),c_Nat_OSuc(U_1579))) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_1,plain,
! [V_n_2,V_m_2] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).
fof(f_522_2,plain,
! [U_1581,U_1580] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1580),U_1581))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1581),c_Nat_OSuc(U_1580))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1581),c_Nat_OSuc(U_1580)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1580),U_1581)) ) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
( ! [U_1585,U_1583] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1583),U_1585))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585),c_Nat_OSuc(U_1583))) )
& ! [U_1584,U_1582] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1584),c_Nat_OSuc(U_1582)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582),U_1584)) ) ),
inference(miniscope,[status(thm)],[f_522_2]) ).
cnf(f_522_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1584),c_Nat_OSuc(U_1582)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582),U_1584)) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1583),U_1585))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585),c_Nat_OSuc(U_1583))) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(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_523_2,plain,
! [U_1587,U_1586] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(U_1586)),U_1587) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),c_Nat_OSuc(U_1587)),
inference(variable_rename,[status(thm)],[f_523_1]) ).
cnf(f_523_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(U_1586)),U_1587) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),c_Nat_OSuc(U_1587)),
inference(clausify,[status(thm)],[f_523_2]) ).
fof(f_524_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).
fof(f_524_2,plain,
! [U_1589,U_1588] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(U_1588)),U_1589) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1588),U_1589)),
inference(variable_rename,[status(thm)],[f_524_1]) ).
cnf(f_524_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_OSuc(U_1588)),U_1589) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1588),U_1589)),
inference(clausify,[status(thm)],[f_524_2]) ).
fof(f_525_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).
fof(f_525_2,plain,
! [U_1591,U_1590] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1590),c_Nat_OSuc(U_1591)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1590),U_1591)),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1590),c_Nat_OSuc(U_1591)) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1590),U_1591)),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(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_526_2,plain,
! [U_1593,U_1592] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1592),U_1593))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1592)),U_1593)) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
cnf(f_526_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1592),U_1593))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1592)),U_1593)) ),
inference(clausify,[status(thm)],[f_526_2]) ).
fof(f_527_1,plain,
! [V_n,V_m] :
( V_m = c_Nat_OSuc(V_n)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(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_527_2,plain,
! [U_1595,U_1594] :
( U_1594 = c_Nat_OSuc(U_1595)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1594),U_1595))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1594),c_Nat_OSuc(U_1595))) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
( U_1594 = c_Nat_OSuc(U_1595)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1594),U_1595))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1594),c_Nat_OSuc(U_1595))) ),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).
fof(f_528_2,plain,
! [U_1597,U_1596] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1596),c_Nat_OSuc(U_1597)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1596),U_1597)) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
cnf(f_528_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1596),c_Nat_OSuc(U_1597)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1596),U_1597)) ),
inference(clausify,[status(thm)],[f_528_2]) ).
fof(f_529_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2),V_m_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),c_Nat_OSuc(V_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).
fof(f_529_2,plain,
! [U_1599,U_1598] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1598)),c_Nat_OSuc(U_1599)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1598),U_1599)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1598),U_1599))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1598)),c_Nat_OSuc(U_1599))) ) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
( ! [U_1603,U_1601] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1601)),c_Nat_OSuc(U_1603)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1601),U_1603)) )
& ! [U_1602,U_1600] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1600),U_1602))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1600)),c_Nat_OSuc(U_1602))) ) ),
inference(miniscope,[status(thm)],[f_529_2]) ).
cnf(f_529_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1600),U_1602))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1600)),c_Nat_OSuc(U_1602))) ),
inference(clausify,[status(thm)],[f_529_3]) ).
cnf(f_529_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1601)),c_Nat_OSuc(U_1603)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1601),U_1603)) ),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
| ( V_m_2 != c_Nat_OSuc(V_n_2)
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) )
& ( V_m_2 = c_Nat_OSuc(V_n_2)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).
fof(f_530_2,plain,
! [U_1605,U_1604] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1604),c_Nat_OSuc(U_1605)))
| ( U_1604 != c_Nat_OSuc(U_1605)
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1604),U_1605)) ) )
& ( U_1604 = c_Nat_OSuc(U_1605)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1604),U_1605))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1604),c_Nat_OSuc(U_1605))) ) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
( ! [U_1609,U_1607] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1607),c_Nat_OSuc(U_1609)))
| ( U_1607 != c_Nat_OSuc(U_1609)
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1607),U_1609)) ) )
& ! [U_1608,U_1606] :
( U_1606 = c_Nat_OSuc(U_1608)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1606),U_1608))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1606),c_Nat_OSuc(U_1608))) ) ),
inference(miniscope,[status(thm)],[f_530_2]) ).
cnf(f_530_4,plain,
( U_1606 = c_Nat_OSuc(U_1608)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1606),U_1608))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1606),c_Nat_OSuc(U_1608))) ),
inference(clausify,[status(thm)],[f_530_3]) ).
cnf(f_530_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1607),U_1609))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1607),c_Nat_OSuc(U_1609))) ),
inference(clausify,[status(thm)],[f_530_3]) ).
cnf(f_530_6,plain,
( U_1607 != c_Nat_OSuc(U_1609)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1607),c_Nat_OSuc(U_1609))) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_1,plain,
! [V_n_2,V_m_2] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).
fof(f_531_2,plain,
! [U_1611,U_1610] :
( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1610),U_1611))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1611)),U_1610)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1611)),U_1610))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1610),U_1611)) ) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
( ! [U_1615,U_1613] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1613),U_1615))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1615)),U_1613)) )
& ! [U_1614,U_1612] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1614)),U_1612))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1612),U_1614)) ) ),
inference(miniscope,[status(thm)],[f_531_2]) ).
cnf(f_531_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1614)),U_1612))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1612),U_1614)) ),
inference(clausify,[status(thm)],[f_531_3]) ).
cnf(f_531_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1613),U_1615))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1615)),U_1613)) ),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [V_n] : ~ hBOOL(hAPP(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_532_2,plain,
! [U_1616] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1616)),U_1616)),
inference(variable_rename,[status(thm)],[f_532_1]) ).
cnf(f_532_3,plain,
~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1616)),U_1616)),
inference(clausify,[status(thm)],[f_532_2]) ).
fof(f_533_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_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_533_2,plain,
! [U_1619,U_1618,U_1617] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1617)),U_1618) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1617)),U_1619)
| U_1618 != U_1619 )
& ( U_1618 = U_1619
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1617)),U_1618) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1617)),U_1619) ) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
( ! [U_1625,U_1623] :
( ! [U_1621] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1621)),U_1623) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1621)),U_1625)
| U_1623 != U_1625 )
& ! [U_1624,U_1622] :
( ! [U_1620] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1620)),U_1622) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1620)),U_1624)
| U_1622 = U_1624 ) ),
inference(miniscope,[status(thm)],[f_533_2]) ).
cnf(f_533_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1620)),U_1622) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1620)),U_1624)
| U_1622 = U_1624 ),
inference(clausify,[status(thm)],[f_533_3]) ).
cnf(f_533_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1621)),U_1623) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1621)),U_1625)
| U_1623 != U_1625 ),
inference(clausify,[status(thm)],[f_533_3]) ).
fof(f_534_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_534_2,plain,
! [U_1628,U_1627,U_1626] :
( c_RealVector_Onorm__class_Onorm(U_1626,hAPP(hAPP(c_Power_Opower__class_Opower(U_1626),U_1627),U_1628)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1626,U_1627)),U_1628)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1626) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
cnf(f_534_3,plain,
( c_RealVector_Onorm__class_Onorm(U_1626,hAPP(hAPP(c_Power_Opower__class_Opower(U_1626),U_1627),U_1628)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1626,U_1627)),U_1628)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1626) ),
inference(clausify,[status(thm)],[f_534_2]) ).
fof(f_535_1,plain,
! [V_n] : V_n != c_Nat_OSuc(V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_535_2,plain,
! [U_1629] : U_1629 != c_Nat_OSuc(U_1629),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
U_1629 != c_Nat_OSuc(U_1629),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_1,plain,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_536_2,plain,
! [U_1630] : c_Nat_OSuc(U_1630) != U_1630,
inference(variable_rename,[status(thm)],[f_536_1]) ).
cnf(f_536_3,plain,
c_Nat_OSuc(U_1630) != U_1630,
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_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_537_2,plain,
! [U_1632,U_1631] :
( ( c_Nat_OSuc(U_1631) = c_Nat_OSuc(U_1632)
| U_1631 != U_1632 )
& ( U_1631 = U_1632
| c_Nat_OSuc(U_1631) != c_Nat_OSuc(U_1632) ) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
( ! [U_1636,U_1634] :
( c_Nat_OSuc(U_1634) = c_Nat_OSuc(U_1636)
| U_1634 != U_1636 )
& ! [U_1635,U_1633] :
( U_1633 = U_1635
| c_Nat_OSuc(U_1633) != c_Nat_OSuc(U_1635) ) ),
inference(miniscope,[status(thm)],[f_537_2]) ).
cnf(f_537_4,plain,
( U_1633 = U_1635
| c_Nat_OSuc(U_1633) != c_Nat_OSuc(U_1635) ),
inference(clausify,[status(thm)],[f_537_3]) ).
cnf(f_537_5,plain,
( c_Nat_OSuc(U_1634) = c_Nat_OSuc(U_1636)
| U_1634 != U_1636 ),
inference(clausify,[status(thm)],[f_537_3]) ).
fof(f_538_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_538_2,plain,
! [U_1638,U_1637] :
( U_1637 = U_1638
| c_Nat_OSuc(U_1637) != c_Nat_OSuc(U_1638) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
cnf(f_538_3,plain,
( U_1637 = U_1638
| c_Nat_OSuc(U_1637) != c_Nat_OSuc(U_1638) ),
inference(clausify,[status(thm)],[f_538_2]) ).
fof(f_539_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_539_2,plain,
! [U_1639] : c_Nat_OSuc(U_1639) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_539_1]) ).
cnf(f_539_3,plain,
c_Nat_OSuc(U_1639) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_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_540_2,plain,
! [U_1640] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1640),
inference(variable_rename,[status(thm)],[f_540_1]) ).
cnf(f_540_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1640),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_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_541_2,plain,
! [U_1641] : c_Nat_OSuc(U_1641) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_541_1]) ).
cnf(f_541_3,plain,
c_Nat_OSuc(U_1641) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_541_2]) ).
fof(f_542_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_542_2,plain,
! [U_1642] : c_Nat_OSuc(U_1642) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_542_1]) ).
cnf(f_542_3,plain,
c_Nat_OSuc(U_1642) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_542_2]) ).
fof(f_543_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_543_2,plain,
! [U_1643] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1643),
inference(variable_rename,[status(thm)],[f_543_1]) ).
cnf(f_543_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1643),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_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_544_2,plain,
! [U_1644] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1644),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1644),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
! [V_n,V_x,T_a] :
( hBOOL(hAPP(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_545_2,plain,
! [U_1647,U_1646,U_1645] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1645,hAPP(hAPP(c_Power_Opower__class_Opower(U_1645),U_1646),U_1647))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1645,U_1646)),U_1647)))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1645) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
cnf(f_545_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1645,hAPP(hAPP(c_Power_Opower__class_Opower(U_1645),U_1646),U_1647))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1645,U_1646)),U_1647)))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1645) ),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_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_546_2,plain,
! [U_1649,U_1648] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1648),U_1649),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1648)
| ~ class_Rings_Ocomm__semiring__1(U_1648) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
cnf(f_546_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1648),U_1649),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1648)
| ~ class_Rings_Ocomm__semiring__1(U_1648) ),
inference(clausify,[status(thm)],[f_546_2]) ).
fof(f_547_1,plain,
! [V_q,V_p,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_547_2,plain,
! [U_1653,U_1652,U_1651,U_1650] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1650),hAPP(hAPP(c_Power_Opower__class_Opower(U_1650),U_1651),U_1652)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1650),U_1651),U_1653)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1650),U_1651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1652),U_1653))
| ~ class_Rings_Ocomm__semiring__1(U_1650) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
cnf(f_547_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1650),hAPP(hAPP(c_Power_Opower__class_Opower(U_1650),U_1651),U_1652)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1650),U_1651),U_1653)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1650),U_1651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1652),U_1653))
| ~ class_Rings_Ocomm__semiring__1(U_1650) ),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_1,plain,
! [V_n_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
| ! [B_m] : V_n_2 != c_Nat_OSuc(B_m) )
& ( ? [B_m] : V_n_2 = c_Nat_OSuc(B_m)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).
fof(f_548_2,plain,
! [U_1656] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1656))
| ! [U_1655] : U_1656 != c_Nat_OSuc(U_1655) )
& ( ? [U_1654] : U_1656 = c_Nat_OSuc(U_1654)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1656)) ) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
( ! [U_1658] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1658))
| ! [U_1655] : U_1658 != c_Nat_OSuc(U_1655) )
& ! [U_1657] :
( ? [U_1654] : U_1657 = c_Nat_OSuc(U_1654)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1657)) ) ),
inference(miniscope,[status(thm)],[f_548_2]) ).
fof(f_548_4,plain,
( ! [U_1658] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1658))
| ! [U_1655] : U_1658 != c_Nat_OSuc(U_1655) )
& ! [U_1657] :
( U_1657 = c_Nat_OSuc(sK44(U_1657))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1657)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_1654,sK44(U_1657))],[f_548_3]) ).
cnf(f_548_5,plain,
( U_1657 = c_Nat_OSuc(sK44(U_1657))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1657)) ),
inference(clausify,[status(thm)],[f_548_4]) ).
cnf(f_548_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1658))
| U_1658 != c_Nat_OSuc(U_1655) ),
inference(clausify,[status(thm)],[f_548_4]) ).
fof(f_549_1,plain,
! [V_n_2] :
( ( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_549_2,plain,
! [U_1659] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1659),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_1659 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1659),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
( ! [U_1661] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1661),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_1661 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1660] :
( U_1660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1660),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(miniscope,[status(thm)],[f_549_2]) ).
cnf(f_549_4,plain,
( U_1660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1660),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_549_3]) ).
cnf(f_549_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1661),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_1661 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_549_3]) ).
fof(f_550_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
| ( ! [B_j] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2))
| V_m_2 != c_Nat_OSuc(B_j) )
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [B_j] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j),V_n_2))
& V_m_2 = c_Nat_OSuc(B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).
fof(f_550_2,plain,
! [U_1665,U_1664] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1664),c_Nat_OSuc(U_1665)))
| ( ! [U_1663] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1663),U_1665))
| U_1664 != c_Nat_OSuc(U_1663) )
& U_1664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_1662] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1662),U_1665))
& U_1664 = c_Nat_OSuc(U_1662) )
| U_1664 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1664),c_Nat_OSuc(U_1665))) ) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
( ! [U_1669,U_1667] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1667),c_Nat_OSuc(U_1669)))
| ( ! [U_1663] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1663),U_1669))
| U_1667 != c_Nat_OSuc(U_1663) )
& U_1667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1668,U_1666] :
( ? [U_1662] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1662),U_1668))
& U_1666 = c_Nat_OSuc(U_1662) )
| U_1666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1666),c_Nat_OSuc(U_1668))) ) ),
inference(miniscope,[status(thm)],[f_550_2]) ).
fof(f_550_4,plain,
( ! [U_1669,U_1667] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1667),c_Nat_OSuc(U_1669)))
| ( ! [U_1663] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1663),U_1669))
| U_1667 != c_Nat_OSuc(U_1663) )
& U_1667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1668,U_1666] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK45(U_1668,U_1666)),U_1668))
& U_1666 = c_Nat_OSuc(sK45(U_1668,U_1666)) )
| U_1666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1666),c_Nat_OSuc(U_1668))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_1662,sK45(U_1668,U_1666))],[f_550_3]) ).
cnf(f_550_5,plain,
( U_1666 = c_Nat_OSuc(sK45(U_1668,U_1666))
| U_1666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1666),c_Nat_OSuc(U_1668))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK45(U_1668,U_1666)),U_1668))
| U_1666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1666),c_Nat_OSuc(U_1668))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_7,plain,
( U_1667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1667),c_Nat_OSuc(U_1669))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_8,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1663),U_1669))
| U_1667 != c_Nat_OSuc(U_1663)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1667),c_Nat_OSuc(U_1669))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
fof(f_551_1,plain,
! [V_n_2,V_m_2] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
| ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != 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_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).
fof(f_551_2,plain,
! [U_1671,U_1670] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1670),U_1671)
| ( ( U_1671 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1670 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1671 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1670 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_1671 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1671 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1670 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1670),U_1671) ) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
( ! [U_1675,U_1673] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1673),U_1675)
| ( ( U_1675 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1673 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1675 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1673 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_1674,U_1672] :
( ( U_1674 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1672 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1672 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1672),U_1674) ) ),
inference(miniscope,[status(thm)],[f_551_2]) ).
cnf(f_551_4,plain,
( U_1672 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1672 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1672),U_1674) ),
inference(clausify,[status(thm)],[f_551_3]) ).
cnf(f_551_5,plain,
( U_1674 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1672 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1672),U_1674) ),
inference(clausify,[status(thm)],[f_551_3]) ).
cnf(f_551_6,plain,
( U_1672 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1672),U_1674) ),
inference(clausify,[status(thm)],[f_551_3]) ).
cnf(f_551_7,plain,
( U_1674 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1672),U_1674) ),
inference(clausify,[status(thm)],[f_551_3]) ).
cnf(f_551_8,plain,
( U_1675 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1673 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1673),U_1675) ),
inference(clausify,[status(thm)],[f_551_3]) ).
cnf(f_551_9,plain,
( U_1675 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1673 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1673),U_1675) ),
inference(clausify,[status(thm)],[f_551_3]) ).
fof(f_552_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_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_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_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_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).
fof(f_552_2,plain,
! [U_1677,U_1676] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1676),U_1677) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_1677 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1676 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1677 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1676 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_1677 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1676 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1676),U_1677) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
( ! [U_1681,U_1679] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1681) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_1681 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1679 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1681 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1679 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_1680,U_1678] :
( ( U_1680 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1680 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1678 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1680) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_552_2]) ).
cnf(f_552_4,plain,
( U_1678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1678 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1680) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_552_3]) ).
cnf(f_552_5,plain,
( U_1680 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1678 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1680) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_552_3]) ).
cnf(f_552_6,plain,
( U_1678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1680 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1680) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_552_3]) ).
cnf(f_552_7,plain,
( U_1680 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1680 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1678),U_1680) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_552_3]) ).
cnf(f_552_8,plain,
( U_1681 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1679 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1681) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_552_3]) ).
cnf(f_552_9,plain,
( U_1681 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1679 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1681) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_552_3]) ).
fof(f_553_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_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_m_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_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff]) ).
fof(f_553_2,plain,
! [U_1683,U_1682] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1682),U_1683) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1683 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1682 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_1683 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1682 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1682),U_1683) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
( ! [U_1687,U_1685] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1685),U_1687) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1687 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1685 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_1686,U_1684] :
( ( U_1686 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1684 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1686) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_553_2]) ).
cnf(f_553_4,plain,
( U_1684 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1686) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_553_3]) ).
cnf(f_553_5,plain,
( U_1686 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1686) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_553_3]) ).
cnf(f_553_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1685),U_1687) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1687 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1685 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_553_3]) ).
fof(f_554_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ! [B_k] : V_n_2 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) )
& ( ? [B_k] : V_n_2 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).
fof(f_554_2,plain,
! [U_1691,U_1690] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1690),U_1691))
| ! [U_1689] : U_1691 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1690),U_1689)) )
& ( ? [U_1688] : U_1691 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1690),U_1688))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1690),U_1691)) ) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
( ! [U_1695,U_1693] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1693),U_1695))
| ! [U_1689] : U_1695 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1693),U_1689)) )
& ! [U_1694,U_1692] :
( ? [U_1688] : U_1694 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1692),U_1688))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1692),U_1694)) ) ),
inference(miniscope,[status(thm)],[f_554_2]) ).
fof(f_554_4,plain,
( ! [U_1695,U_1693] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1693),U_1695))
| ! [U_1689] : U_1695 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1693),U_1689)) )
& ! [U_1694,U_1692] :
( U_1694 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1692),sK46(U_1694,U_1692)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1692),U_1694)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_1688,sK46(U_1694,U_1692))],[f_554_3]) ).
cnf(f_554_5,plain,
( U_1694 = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1692),sK46(U_1694,U_1692)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1692),U_1694)) ),
inference(clausify,[status(thm)],[f_554_4]) ).
cnf(f_554_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1693),U_1695))
| U_1695 != c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1693),U_1689)) ),
inference(clausify,[status(thm)],[f_554_4]) ).
fof(f_555_1,plain,
! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).
fof(f_555_2,plain,
! [U_1697,U_1696] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1696),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1697),U_1696)))),
inference(variable_rename,[status(thm)],[f_555_1]) ).
cnf(f_555_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1696),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1697),U_1696)))),
inference(clausify,[status(thm)],[f_555_2]) ).
fof(f_556_1,plain,
! [V_m,V_i] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).
fof(f_556_2,plain,
! [U_1699,U_1698] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1698),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1698),U_1699)))),
inference(variable_rename,[status(thm)],[f_556_1]) ).
cnf(f_556_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1698),c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1698),U_1699)))),
inference(clausify,[status(thm)],[f_556_2]) ).
fof(f_557_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),V_m_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).
fof(f_557_2,plain,
! [U_1701,U_1700] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1700),U_1701))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1700)),U_1701)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1700)),U_1701))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1700),U_1701)) ) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
( ! [U_1705,U_1703] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1703),U_1705))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1703)),U_1705)) )
& ! [U_1704,U_1702] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1702)),U_1704))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1702),U_1704)) ) ),
inference(miniscope,[status(thm)],[f_557_2]) ).
cnf(f_557_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1702)),U_1704))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1702),U_1704)) ),
inference(clausify,[status(thm)],[f_557_3]) ).
cnf(f_557_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1703),U_1705))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1703)),U_1705)) ),
inference(clausify,[status(thm)],[f_557_3]) ).
fof(f_558_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),c_Nat_OSuc(V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).
fof(f_558_2,plain,
! [U_1707,U_1706] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1706),c_Nat_OSuc(U_1707)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706),U_1707)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706),U_1707))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1706),c_Nat_OSuc(U_1707))) ) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
( ! [U_1711,U_1709] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1709),c_Nat_OSuc(U_1711)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709),U_1711)) )
& ! [U_1710,U_1708] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1708),U_1710))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1708),c_Nat_OSuc(U_1710))) ) ),
inference(miniscope,[status(thm)],[f_558_2]) ).
cnf(f_558_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1708),U_1710))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1708),c_Nat_OSuc(U_1710))) ),
inference(clausify,[status(thm)],[f_558_3]) ).
cnf(f_558_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1709),c_Nat_OSuc(U_1711)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709),U_1711)) ),
inference(clausify,[status(thm)],[f_558_3]) ).
fof(f_559_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).
fof(f_559_2,plain,
! [U_1713,U_1712] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1712)),U_1713))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1712),U_1713)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1712),U_1713))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1712)),U_1713)) ) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
( ! [U_1717,U_1715] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1715)),U_1717))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1715),U_1717)) )
& ! [U_1716,U_1714] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1714),U_1716))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1714)),U_1716)) ) ),
inference(miniscope,[status(thm)],[f_559_2]) ).
cnf(f_559_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1714),U_1716))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1714)),U_1716)) ),
inference(clausify,[status(thm)],[f_559_3]) ).
cnf(f_559_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1715)),U_1717))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1715),U_1717)) ),
inference(clausify,[status(thm)],[f_559_3]) ).
fof(f_560_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),c_Nat_OSuc(V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc]) ).
fof(f_560_2,plain,
! [U_1719,U_1718] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1718),c_Nat_OSuc(U_1719)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1718),U_1719)) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
cnf(f_560_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1718),c_Nat_OSuc(U_1719)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1718),U_1719)) ),
inference(clausify,[status(thm)],[f_560_2]) ).
fof(f_561_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m)),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).
fof(f_561_2,plain,
! [U_1721,U_1720] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1720)),U_1721))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1720),U_1721)) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
cnf(f_561_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1720)),U_1721))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1720),U_1721)) ),
inference(clausify,[status(thm)],[f_561_2]) ).
fof(f_562_1,plain,
! [V_n_2,V_m_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2)))
| V_n_2 != V_m_2 )
& ( V_n_2 = V_m_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2),c_Nat_OSuc(V_m_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).
fof(f_562_2,plain,
! [U_1723,U_1722] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1723),c_Nat_OSuc(U_1722)))
| U_1723 != U_1722 )
& ( U_1723 = U_1722
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1723),c_Nat_OSuc(U_1722))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1722),U_1723)) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
cnf(f_562_3,plain,
( U_1723 = U_1722
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1723),c_Nat_OSuc(U_1722)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1722),U_1723)) ),
inference(clausify,[status(thm)],[f_562_2]) ).
cnf(f_562_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1723),c_Nat_OSuc(U_1722)))
| U_1723 != U_1722
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1722),U_1723)) ),
inference(clausify,[status(thm)],[f_562_2]) ).
fof(f_563_1,plain,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(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_563_2,plain,
! [U_1725,U_1724] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1724),U_1725))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1724)),U_1725)) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
cnf(f_563_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1724),U_1725))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1724)),U_1725)) ),
inference(clausify,[status(thm)],[f_563_2]) ).
fof(f_564_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]) ).
cnf(f_564_2,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_564_1]) ).
fof(f_565_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hBOOL(hAPP(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_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(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_m_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_565_2,plain,
! [U_1728,U_1727,U_1726] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1726)),U_1727)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1726)),U_1728)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1727),U_1728)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1727),U_1728))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1726)),U_1727)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1726)),U_1728))) ) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
( ! [U_1734,U_1732] :
( ! [U_1730] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1730)),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1730)),U_1734)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1732),U_1734)) )
& ! [U_1733,U_1731] :
( ! [U_1729] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1729)),U_1731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1729)),U_1733)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1731),U_1733)) ) ),
inference(miniscope,[status(thm)],[f_565_2]) ).
cnf(f_565_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1729)),U_1731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1729)),U_1733)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1731),U_1733)) ),
inference(clausify,[status(thm)],[f_565_3]) ).
cnf(f_565_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1730)),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1730)),U_1734)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1732),U_1734)) ),
inference(clausify,[status(thm)],[f_565_3]) ).
fof(f_566_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc__right]) ).
fof(f_566_2,plain,
! [U_1736,U_1735] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1735),c_Nat_OSuc(U_1736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1735),U_1736)),
inference(variable_rename,[status(thm)],[f_566_1]) ).
cnf(f_566_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1735),c_Nat_OSuc(U_1736)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1735),U_1736)),
inference(clausify,[status(thm)],[f_566_2]) ).
fof(f_567_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc]) ).
fof(f_567_2,plain,
! [U_1738,U_1737] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1737)),U_1738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1737),U_1738)),
inference(variable_rename,[status(thm)],[f_567_1]) ).
cnf(f_567_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1737)),U_1738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1737),U_1738)),
inference(clausify,[status(thm)],[f_567_2]) ).
fof(f_568_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hBOOL(hAPP(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_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(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_m_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_568_2,plain,
! [U_1741,U_1740,U_1739] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1739)),U_1740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1739)),U_1741)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1740),U_1741)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1740),U_1741))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1739)),U_1740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1739)),U_1741))) ) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
( ! [U_1747,U_1745] :
( ! [U_1743] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1743)),U_1745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1743)),U_1747)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1745),U_1747)) )
& ! [U_1746,U_1744] :
( ! [U_1742] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1742)),U_1744)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1742)),U_1746)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1744),U_1746)) ) ),
inference(miniscope,[status(thm)],[f_568_2]) ).
cnf(f_568_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1742)),U_1744)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1742)),U_1746)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1744),U_1746)) ),
inference(clausify,[status(thm)],[f_568_3]) ).
cnf(f_568_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1743)),U_1745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1743)),U_1747)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1745),U_1747)) ),
inference(clausify,[status(thm)],[f_568_3]) ).
fof(f_569_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(f_569_2,plain,
! [U_1748] : c_Nat_OSuc(U_1748) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1748),
inference(variable_rename,[status(thm)],[f_569_1]) ).
cnf(f_569_3,plain,
c_Nat_OSuc(U_1748) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1748),
inference(clausify,[status(thm)],[f_569_2]) ).
fof(f_570_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(f_570_2,plain,
! [U_1749] : c_Nat_OSuc(U_1749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1749),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_570_1]) ).
cnf(f_570_3,plain,
c_Nat_OSuc(U_1749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1749),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_570_2]) ).
fof(f_571_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Omonoseq(T_a,V_X_2)
| ( ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n)))
& ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n)))) ) )
& ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,c_Nat_OSuc(B_n))),hAPP(V_X_2,B_n)))
| ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n)),hAPP(V_X_2,c_Nat_OSuc(B_n))))
| ~ c_SEQ_Omonoseq(T_a,V_X_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_monoseq__Suc]) ).
fof(f_571_2,plain,
! [U_1755,U_1754] :
( ( ( c_SEQ_Omonoseq(U_1754,U_1755)
| ( ? [U_1753] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(U_1753))),hAPP(U_1755,U_1753)))
& ? [U_1752] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,U_1752)),hAPP(U_1755,c_Nat_OSuc(U_1752)))) ) )
& ( ! [U_1751] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(U_1751))),hAPP(U_1755,U_1751)))
| ! [U_1750] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,U_1750)),hAPP(U_1755,c_Nat_OSuc(U_1750))))
| ~ c_SEQ_Omonoseq(U_1754,U_1755) ) )
| ~ class_Orderings_Oorder(U_1754) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
! [U_1755,U_1754] :
( ( ( c_SEQ_Omonoseq(U_1754,U_1755)
| ( ? [U_1753] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(U_1753))),hAPP(U_1755,U_1753)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,sK47(U_1755,U_1754))),hAPP(U_1755,c_Nat_OSuc(sK47(U_1755,U_1754))))) ) )
& ( ! [U_1751] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(U_1751))),hAPP(U_1755,U_1751)))
| ! [U_1750] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,U_1750)),hAPP(U_1755,c_Nat_OSuc(U_1750))))
| ~ c_SEQ_Omonoseq(U_1754,U_1755) ) )
| ~ class_Orderings_Oorder(U_1754) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_1752,sK47(U_1755,U_1754))],[f_571_2]) ).
fof(f_571_4,plain,
! [U_1755,U_1754] :
( ( ( c_SEQ_Omonoseq(U_1754,U_1755)
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(sK48(U_1755,U_1754)))),hAPP(U_1755,sK48(U_1755,U_1754))))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,sK47(U_1755,U_1754))),hAPP(U_1755,c_Nat_OSuc(sK47(U_1755,U_1754))))) ) )
& ( ! [U_1751] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(U_1751))),hAPP(U_1755,U_1751)))
| ! [U_1750] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,U_1750)),hAPP(U_1755,c_Nat_OSuc(U_1750))))
| ~ c_SEQ_Omonoseq(U_1754,U_1755) ) )
| ~ class_Orderings_Oorder(U_1754) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_1753,sK48(U_1755,U_1754))],[f_571_3]) ).
cnf(f_571_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(U_1751))),hAPP(U_1755,U_1751)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,U_1750)),hAPP(U_1755,c_Nat_OSuc(U_1750))))
| ~ c_SEQ_Omonoseq(U_1754,U_1755)
| ~ class_Orderings_Oorder(U_1754) ),
inference(clausify,[status(thm)],[f_571_4]) ).
cnf(f_571_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,sK47(U_1755,U_1754))),hAPP(U_1755,c_Nat_OSuc(sK47(U_1755,U_1754)))))
| c_SEQ_Omonoseq(U_1754,U_1755)
| ~ class_Orderings_Oorder(U_1754) ),
inference(clausify,[status(thm)],[f_571_4]) ).
cnf(f_571_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1754,hAPP(U_1755,c_Nat_OSuc(sK48(U_1755,U_1754)))),hAPP(U_1755,sK48(U_1755,U_1754))))
| c_SEQ_Omonoseq(U_1754,U_1755)
| ~ class_Orderings_Oorder(U_1754) ),
inference(clausify,[status(thm)],[f_571_4]) ).
fof(f_572_1,plain,
! [V_fa_2] :
( ( c_SEQ_Osubseq(V_fa_2)
| ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n)))) )
& ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(V_fa_2,B_n)),hAPP(V_fa_2,c_Nat_OSuc(B_n))))
| ~ c_SEQ_Osubseq(V_fa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_subseq__Suc__iff]) ).
fof(f_572_2,plain,
! [U_1758] :
( ( c_SEQ_Osubseq(U_1758)
| ? [U_1757] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1758,U_1757)),hAPP(U_1758,c_Nat_OSuc(U_1757)))) )
& ( ! [U_1756] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1758,U_1756)),hAPP(U_1758,c_Nat_OSuc(U_1756))))
| ~ c_SEQ_Osubseq(U_1758) ) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
( ! [U_1760] :
( c_SEQ_Osubseq(U_1760)
| ? [U_1757] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1760,U_1757)),hAPP(U_1760,c_Nat_OSuc(U_1757)))) )
& ! [U_1759] :
( ! [U_1756] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1759,U_1756)),hAPP(U_1759,c_Nat_OSuc(U_1756))))
| ~ c_SEQ_Osubseq(U_1759) ) ),
inference(miniscope,[status(thm)],[f_572_2]) ).
fof(f_572_4,plain,
( ! [U_1760] :
( c_SEQ_Osubseq(U_1760)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1760,sK49(U_1760))),hAPP(U_1760,c_Nat_OSuc(sK49(U_1760))))) )
& ! [U_1759] :
( ! [U_1756] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1759,U_1756)),hAPP(U_1759,c_Nat_OSuc(U_1756))))
| ~ c_SEQ_Osubseq(U_1759) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_1757,sK49(U_1760))],[f_572_3]) ).
cnf(f_572_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1759,U_1756)),hAPP(U_1759,c_Nat_OSuc(U_1756))))
| ~ c_SEQ_Osubseq(U_1759) ),
inference(clausify,[status(thm)],[f_572_4]) ).
cnf(f_572_6,plain,
( c_SEQ_Osubseq(U_1760)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(U_1760,sK49(U_1760))),hAPP(U_1760,c_Nat_OSuc(sK49(U_1760))))) ),
inference(clausify,[status(thm)],[f_572_4]) ).
fof(f_573_1,plain,
! [V_n_2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2)),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(f_573_2,plain,
! [U_1761] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1761) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1761)),
inference(variable_rename,[status(thm)],[f_573_1]) ).
cnf(f_573_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1761) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1761)),
inference(clausify,[status(thm)],[f_573_2]) ).
fof(f_574_1,plain,
! [V_m,V_n] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
| ~ hBOOL(hAPP(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_574_2,plain,
! [U_1763,U_1762] :
( hBOOL(hAPP(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_1763),U_1762)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1763))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1762)) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
cnf(f_574_3,plain,
( hBOOL(hAPP(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_1763),U_1762)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1763))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1762)) ),
inference(clausify,[status(thm)],[f_574_2]) ).
fof(f_575_1,plain,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
| ~ hBOOL(hAPP(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_575_2,plain,
! [U_1765,U_1764] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1764),U_1765)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1765))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1764)) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
cnf(f_575_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1764),U_1765)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1765))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1764)) ),
inference(clausify,[status(thm)],[f_575_2]) ).
fof(f_576_1,plain,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
| ~ hBOOL(hAPP(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_576_2,plain,
! [U_1767,U_1766] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1767),U_1766)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1767))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1766)) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
cnf(f_576_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1767),U_1766)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1767))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1766)) ),
inference(clausify,[status(thm)],[f_576_2]) ).
fof(f_577_1,plain,
! [V_n_2,V_m_2] :
( ( hBOOL(hAPP(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_m_2),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) )
| ~ hBOOL(hAPP(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_m_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).
fof(f_577_2,plain,
! [U_1769,U_1768] :
( ( hBOOL(hAPP(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_1768),U_1769)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1769))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1768)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1769))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1768)) )
| ~ hBOOL(hAPP(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_1768),U_1769))) ) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
( ! [U_1773,U_1771] :
( hBOOL(hAPP(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_1771),U_1773)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1773))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1771)) )
& ! [U_1772,U_1770] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1772))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1770)) )
| ~ hBOOL(hAPP(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_1770),U_1772))) ) ),
inference(miniscope,[status(thm)],[f_577_2]) ).
cnf(f_577_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1770))
| ~ hBOOL(hAPP(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_1770),U_1772))) ),
inference(clausify,[status(thm)],[f_577_3]) ).
cnf(f_577_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1772))
| ~ hBOOL(hAPP(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_1770),U_1772))) ),
inference(clausify,[status(thm)],[f_577_3]) ).
cnf(f_577_6,plain,
( hBOOL(hAPP(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_1771),U_1773)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1773))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1771)) ),
inference(clausify,[status(thm)],[f_577_3]) ).
fof(f_578_1,plain,
! [V_n] : hBOOL(hAPP(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_578_2,plain,
! [U_1774] : hBOOL(hAPP(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_1774)))),
inference(variable_rename,[status(thm)],[f_578_1]) ).
cnf(f_578_3,plain,
hBOOL(hAPP(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_1774)))),
inference(clausify,[status(thm)],[f_578_2]) ).
fof(f_579_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]) ).
cnf(f_579_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(clausify,[status(thm)],[f_579_1]) ).
fof(f_580_1,plain,
! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = hAPP(hAPP(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_580_2,plain,
! [U_1775] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1775)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1775)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_580_1]) ).
cnf(f_580_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1775)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1775)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_580_2]) ).
fof(f_581_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_N] :
? [B_n] : ~ hBOOL(hAPP(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] : hBOOL(hAPP(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_581_2,plain,
! [U_1781,U_1780] :
( ( ( c_SEQ_OBseq(U_1780,U_1781)
| ! [U_1779] :
? [U_1778] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,U_1778))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1779)))) )
& ( ? [U_1777] :
! [U_1776] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,U_1776))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1777))))
| ~ c_SEQ_OBseq(U_1780,U_1781) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1780) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
! [U_1781,U_1780] :
( ( ( c_SEQ_OBseq(U_1780,U_1781)
| ! [U_1779] :
? [U_1778] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,U_1778))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1779)))) )
& ( ! [U_1776] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,U_1776))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK50(U_1781,U_1780)))))
| ~ c_SEQ_OBseq(U_1780,U_1781) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1780) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_1777,sK50(U_1781,U_1780))],[f_581_2]) ).
fof(f_581_4,plain,
! [U_1781,U_1780] :
( ( ( c_SEQ_OBseq(U_1780,U_1781)
| ! [U_1779] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,sK51(U_1781,U_1780,U_1779)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1779)))) )
& ( ! [U_1776] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,U_1776))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK50(U_1781,U_1780)))))
| ~ c_SEQ_OBseq(U_1780,U_1781) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1780) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_1778,sK51(U_1781,U_1780,U_1779))],[f_581_3]) ).
cnf(f_581_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,U_1776))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK50(U_1781,U_1780)))))
| ~ c_SEQ_OBseq(U_1780,U_1781)
| ~ class_RealVector_Oreal__normed__vector(U_1780) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_6,plain,
( c_SEQ_OBseq(U_1780,U_1781)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1780,hAPP(U_1781,sK51(U_1781,U_1780,U_1779)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1779))))
| ~ class_RealVector_Oreal__normed__vector(U_1780) ),
inference(clausify,[status(thm)],[f_581_4]) ).
fof(f_582_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_N] :
? [B_n] : ~ hBOOL(hAPP(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] : hBOOL(hAPP(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_582_2,plain,
! [U_1787,U_1786] :
( ( ( c_SEQ_OBseq(U_1786,U_1787)
| ! [U_1785] :
? [U_1784] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,U_1784))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1785)))) )
& ( ? [U_1783] :
! [U_1782] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,U_1782))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1783))))
| ~ c_SEQ_OBseq(U_1786,U_1787) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1786) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
! [U_1787,U_1786] :
( ( ( c_SEQ_OBseq(U_1786,U_1787)
| ! [U_1785] :
? [U_1784] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,U_1784))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1785)))) )
& ( ! [U_1782] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,U_1782))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK52(U_1787,U_1786)))))
| ~ c_SEQ_OBseq(U_1786,U_1787) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1786) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_1783,sK52(U_1787,U_1786))],[f_582_2]) ).
fof(f_582_4,plain,
! [U_1787,U_1786] :
( ( ( c_SEQ_OBseq(U_1786,U_1787)
| ! [U_1785] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,sK53(U_1787,U_1786,U_1785)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1785)))) )
& ( ! [U_1782] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,U_1782))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK52(U_1787,U_1786)))))
| ~ c_SEQ_OBseq(U_1786,U_1787) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1786) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_1784,sK53(U_1787,U_1786,U_1785))],[f_582_3]) ).
cnf(f_582_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,U_1782))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK52(U_1787,U_1786)))))
| ~ c_SEQ_OBseq(U_1786,U_1787)
| ~ class_RealVector_Oreal__normed__vector(U_1786) ),
inference(clausify,[status(thm)],[f_582_4]) ).
cnf(f_582_6,plain,
( c_SEQ_OBseq(U_1786,U_1787)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1786,hAPP(U_1787,sK53(U_1787,U_1786,U_1785)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_1785))))
| ~ class_RealVector_Oreal__normed__vector(U_1786) ),
inference(clausify,[status(thm)],[f_582_4]) ).
fof(f_583_1,plain,
! [V_x_2] :
( c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(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_monoseq__realpow]) ).
fof(f_583_2,plain,
! [U_1788] :
( c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1788))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1788),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1788)) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
cnf(f_583_3,plain,
( c_SEQ_Omonoseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1788))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1788),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1788)) ),
inference(clausify,[status(thm)],[f_583_2]) ).
fof(f_584_1,plain,
! [V_x_2] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(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_convergent__realpow]) ).
fof(f_584_2,plain,
! [U_1789] :
( c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1789))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1789),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1789)) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
cnf(f_584_3,plain,
( c_SEQ_Oconvergent(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1789))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1789),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1789)) ),
inference(clausify,[status(thm)],[f_584_2]) ).
fof(f_585_1,plain,
! [V_x_2] :
( c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(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_Bseq__realpow]) ).
fof(f_585_2,plain,
! [U_1790] :
( c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1790))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1790),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1790)) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
cnf(f_585_3,plain,
( c_SEQ_OBseq(tc_RealDef_Oreal,hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1790))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1790),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_1790)) ),
inference(clausify,[status(thm)],[f_585_2]) ).
fof(f_586_1,plain,
! [V_n,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).
fof(f_586_2,plain,
! [U_1794,U_1793,U_1792,U_1791] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1791,hAPP(hAPP(c_Power_Opower__class_Opower(U_1791),U_1792),U_1794)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1791),U_1793),U_1794)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1794))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1791,c_Groups_Ozero__class_Ozero(U_1791)),U_1792))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1791,U_1792),U_1793))
| ~ class_Rings_Olinordered__semidom(U_1791) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
cnf(f_586_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1791,hAPP(hAPP(c_Power_Opower__class_Opower(U_1791),U_1792),U_1794)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1791),U_1793),U_1794)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1794))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1791,c_Groups_Ozero__class_Ozero(U_1791)),U_1792))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1791,U_1792),U_1793))
| ~ class_Rings_Olinordered__semidom(U_1791) ),
inference(clausify,[status(thm)],[f_586_2]) ).
fof(f_587_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).
fof(f_587_2,plain,
! [U_1797,U_1796,U_1795] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1795,c_Groups_Oone__class_Oone(U_1795)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1795),U_1796),U_1797)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1797))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1795,c_Groups_Oone__class_Oone(U_1795)),U_1796))
| ~ class_Rings_Olinordered__semidom(U_1795) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
cnf(f_587_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1795,c_Groups_Oone__class_Oone(U_1795)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1795),U_1796),U_1797)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1797))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1795,c_Groups_Oone__class_Oone(U_1795)),U_1796))
| ~ class_Rings_Olinordered__semidom(U_1795) ),
inference(clausify,[status(thm)],[f_587_2]) ).
fof(f_588_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(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_588_2,plain,
! [U_1801,U_1800,U_1799,U_1798] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1798,hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1800)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1801)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1800),U_1801)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1800),U_1801))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1798,hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1800)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1801))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1798,c_Groups_Oone__class_Oone(U_1798)),U_1799))
| ~ class_Rings_Olinordered__semidom(U_1798) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
cnf(f_588_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1800),U_1801))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1798,hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1800)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1801)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1798,c_Groups_Oone__class_Oone(U_1798)),U_1799))
| ~ class_Rings_Olinordered__semidom(U_1798) ),
inference(clausify,[status(thm)],[f_588_2]) ).
cnf(f_588_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1798,hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1800)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1801)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1800),U_1801))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1798,c_Groups_Oone__class_Oone(U_1798)),U_1799))
| ~ class_Rings_Olinordered__semidom(U_1798) ),
inference(clausify,[status(thm)],[f_588_2]) ).
fof(f_589_1,plain,
! [V_n,V_m,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(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_589_2,plain,
! [U_1805,U_1804,U_1803,U_1802] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1804),U_1805))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1802,hAPP(hAPP(c_Power_Opower__class_Opower(U_1802),U_1803),U_1804)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1802),U_1803),U_1805)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1802,c_Groups_Oone__class_Oone(U_1802)),U_1803))
| ~ class_Rings_Olinordered__semidom(U_1802) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
cnf(f_589_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1804),U_1805))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1802,hAPP(hAPP(c_Power_Opower__class_Opower(U_1802),U_1803),U_1804)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1802),U_1803),U_1805)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1802,c_Groups_Oone__class_Oone(U_1802)),U_1803))
| ~ class_Rings_Olinordered__semidom(U_1802) ),
inference(clausify,[status(thm)],[f_589_2]) ).
fof(f_590_1,plain,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(f_590_2,plain,
! [U_1808,U_1807,U_1806] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1807),U_1808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1806),U_1807)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1806),U_1808)),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1807),U_1808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1806),U_1807)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1806),U_1808)),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_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_591_2,plain,
! [U_1811,U_1810,U_1809] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1809),U_1810)),U_1811) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1810),U_1811)),
inference(variable_rename,[status(thm)],[f_591_1]) ).
cnf(f_591_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1809),U_1810)),U_1811) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1810),U_1811)),
inference(clausify,[status(thm)],[f_591_2]) ).
fof(f_592_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_592_2,plain,
! [U_1812] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1812) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_592_1]) ).
cnf(f_592_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1812) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_592_2]) ).
fof(f_593_1,plain,
! [V_m_2,V_x_2] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_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_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) != 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_593_2,plain,
! [U_1814,U_1813] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1813),U_1814) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_1813 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1814 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1813 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1813),U_1814) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
( ! [U_1818,U_1816] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1816),U_1818) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_1816 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1818 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1817,U_1815] :
( U_1815 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1815),U_1817) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_593_2]) ).
cnf(f_593_4,plain,
( U_1815 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1815),U_1817) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_593_3]) ).
cnf(f_593_5,plain,
( U_1818 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1816),U_1818) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_593_3]) ).
cnf(f_593_6,plain,
( U_1816 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1816),U_1818) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_593_3]) ).
fof(f_594_1,plain,
! [V_n_2,V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(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_594_2,plain,
! [U_1820,U_1819] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1819)),U_1820)))
| ( U_1820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1819 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_1820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1819 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1819)),U_1820))) ) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
( ! [U_1824,U_1822] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1822)),U_1824)))
| ( U_1824 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1822 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_1823,U_1821] :
( U_1823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1821 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1821)),U_1823))) ) ),
inference(miniscope,[status(thm)],[f_594_2]) ).
cnf(f_594_4,plain,
( U_1823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1821 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1821)),U_1823))) ),
inference(clausify,[status(thm)],[f_594_3]) ).
cnf(f_594_5,plain,
( U_1822 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1822)),U_1824))) ),
inference(clausify,[status(thm)],[f_594_3]) ).
cnf(f_594_6,plain,
( U_1824 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1822)),U_1824))) ),
inference(clausify,[status(thm)],[f_594_3]) ).
fof(f_595_1,plain,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
| ~ hBOOL(hAPP(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_595_2,plain,
! [U_1827,U_1826,U_1825] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1826),U_1827))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1825),U_1826)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1825),U_1827)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1825)) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1826),U_1827))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1825),U_1826)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1825),U_1827)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1825)) ),
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_1,plain,
! [V_n_2,V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_596_2,plain,
! [U_1829,U_1828] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1828),U_1829)))
| ( U_1829 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1828)) ) )
& ( U_1829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1828))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1828),U_1829))) ) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
( ! [U_1833,U_1831] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1831),U_1833)))
| ( U_1833 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1831)) ) )
& ! [U_1832,U_1830] :
( U_1832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1830))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1830),U_1832))) ) ),
inference(miniscope,[status(thm)],[f_596_2]) ).
cnf(f_596_4,plain,
( U_1832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1830))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1830),U_1832))) ),
inference(clausify,[status(thm)],[f_596_3]) ).
cnf(f_596_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1831))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1831),U_1833))) ),
inference(clausify,[status(thm)],[f_596_3]) ).
cnf(f_596_6,plain,
( U_1833 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1831),U_1833))) ),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_1,plain,
! [V_n,V_i] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_597_2,plain,
! [U_1835,U_1834] :
( hBOOL(hAPP(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_1834),U_1835)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1834)) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
cnf(f_597_3,plain,
( hBOOL(hAPP(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_1834),U_1835)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_1834)) ),
inference(clausify,[status(thm)],[f_597_2]) ).
fof(f_598_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_598_2,plain,
! [U_1837,U_1836] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1836),U_1837)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1836)),U_1837),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1836),U_1837)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1836)),U_1837),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_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_599_2,plain,
! [U_1839,U_1838] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1838)),U_1839) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1838),U_1839)),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_1838)),U_1839) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1838),U_1839)),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_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_600_2,plain,
! [U_1841,U_1840] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1840),U_1841)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_1840)),U_1841)
| U_1840 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_1840)) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
cnf(f_600_3,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1840),U_1841)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_1840)),U_1841)
| U_1840 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_1840)) ),
inference(clausify,[status(thm)],[f_600_2]) ).
fof(f_601_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_601_2,plain,
! [U_1844,U_1843,U_1842] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1842),U_1843),U_1844) != c_Groups_Ozero__class_Ozero(U_1842)
| U_1843 = c_Groups_Ozero__class_Ozero(U_1842)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1842) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
cnf(f_601_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1842),U_1843),U_1844) != c_Groups_Ozero__class_Ozero(U_1842)
| U_1843 = c_Groups_Ozero__class_Ozero(U_1842)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1842) ),
inference(clausify,[status(thm)],[f_601_2]) ).
fof(f_602_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_602_2,plain,
! [U_1848,U_1847,U_1846,U_1845] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1847)),U_1848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),hAPP(hAPP(c_Power_Opower__class_Opower(U_1845),U_1846),U_1848)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1845),U_1847),U_1848))
| ~ class_Groups_Ocomm__monoid__mult(U_1845) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
cnf(f_602_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1847)),U_1848) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),hAPP(hAPP(c_Power_Opower__class_Opower(U_1845),U_1846),U_1848)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1845),U_1847),U_1848))
| ~ class_Groups_Ocomm__monoid__mult(U_1845) ),
inference(clausify,[status(thm)],[f_602_2]) ).
fof(f_603_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_603_2,plain,
! [U_1851,U_1850,U_1849] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1849),hAPP(hAPP(c_Power_Opower__class_Opower(U_1849),U_1850),U_1851)),U_1850) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1849),U_1850),hAPP(hAPP(c_Power_Opower__class_Opower(U_1849),U_1850),U_1851))
| ~ class_Groups_Omonoid__mult(U_1849) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
cnf(f_603_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1849),hAPP(hAPP(c_Power_Opower__class_Opower(U_1849),U_1850),U_1851)),U_1850) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1849),U_1850),hAPP(hAPP(c_Power_Opower__class_Opower(U_1849),U_1850),U_1851))
| ~ class_Groups_Omonoid__mult(U_1849) ),
inference(clausify,[status(thm)],[f_603_2]) ).
fof(f_604_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_604_2,plain,
! [U_1853,U_1852] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1852),c_Groups_Oone__class_Oone(U_1852)),U_1853) = c_Groups_Oone__class_Oone(U_1852)
| ~ class_Groups_Omonoid__mult(U_1852) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
cnf(f_604_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1852),c_Groups_Oone__class_Oone(U_1852)),U_1853) = c_Groups_Oone__class_Oone(U_1852)
| ~ class_Groups_Omonoid__mult(U_1852) ),
inference(clausify,[status(thm)],[f_604_2]) ).
fof(f_605_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_605_2,plain,
! [U_1856,U_1855,U_1854] :
( c_Groups_Oabs__class_Oabs(U_1854,hAPP(hAPP(c_Power_Opower__class_Opower(U_1854),U_1855),U_1856)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1854),c_Groups_Oabs__class_Oabs(U_1854,U_1855)),U_1856)
| ~ class_Rings_Olinordered__idom(U_1854) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( c_Groups_Oabs__class_Oabs(U_1854,hAPP(hAPP(c_Power_Opower__class_Opower(U_1854),U_1855),U_1856)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1854),c_Groups_Oabs__class_Oabs(U_1854,U_1855)),U_1856)
| ~ class_Rings_Olinordered__idom(U_1854) ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_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_606_2,plain,
! [U_1860,U_1859,U_1858,U_1857] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1857),U_1858),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1859),U_1860)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1857),hAPP(hAPP(c_Power_Opower__class_Opower(U_1857),U_1858),U_1859)),U_1860)
| ~ class_Groups_Omonoid__mult(U_1857) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
cnf(f_606_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1857),U_1858),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1859),U_1860)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1857),hAPP(hAPP(c_Power_Opower__class_Opower(U_1857),U_1858),U_1859)),U_1860)
| ~ class_Groups_Omonoid__mult(U_1857) ),
inference(clausify,[status(thm)],[f_606_2]) ).
fof(f_607_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_607_2,plain,
! [U_1862,U_1861] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1861),U_1862),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1862
| ~ class_Groups_Omonoid__mult(U_1861) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
cnf(f_607_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1861),U_1862),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1862
| ~ class_Groups_Omonoid__mult(U_1861) ),
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(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_608_2,plain,
! [U_1865,U_1864,U_1863] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1863,c_Groups_Ozero__class_Ozero(U_1863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1863),U_1864),U_1865)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1863,c_Groups_Ozero__class_Ozero(U_1863)),U_1864))
| ~ class_Rings_Olinordered__semidom(U_1863) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
cnf(f_608_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1863,c_Groups_Ozero__class_Ozero(U_1863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1863),U_1864),U_1865)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1863,c_Groups_Ozero__class_Ozero(U_1863)),U_1864))
| ~ class_Rings_Olinordered__semidom(U_1863) ),
inference(clausify,[status(thm)],[f_608_2]) ).
fof(f_609_1,plain,
! [V_n,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mono]) ).
fof(f_609_2,plain,
! [U_1869,U_1868,U_1867,U_1866] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1866,hAPP(hAPP(c_Power_Opower__class_Opower(U_1866),U_1867),U_1869)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1866),U_1868),U_1869)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1866,c_Groups_Ozero__class_Ozero(U_1866)),U_1867))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1866,U_1867),U_1868))
| ~ class_Rings_Olinordered__semidom(U_1866) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
cnf(f_609_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1866,hAPP(hAPP(c_Power_Opower__class_Opower(U_1866),U_1867),U_1869)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1866),U_1868),U_1869)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1866,c_Groups_Ozero__class_Ozero(U_1866)),U_1867))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1866,U_1867),U_1868))
| ~ class_Rings_Olinordered__semidom(U_1866) ),
inference(clausify,[status(thm)],[f_609_2]) ).
fof(f_610_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(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_610_2,plain,
! [U_1872,U_1871,U_1870] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1870,c_Groups_Ozero__class_Ozero(U_1870)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1870),U_1871),U_1872)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1870,c_Groups_Ozero__class_Ozero(U_1870)),U_1871))
| ~ class_Rings_Olinordered__semidom(U_1870) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
cnf(f_610_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1870,c_Groups_Ozero__class_Ozero(U_1870)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1870),U_1871),U_1872)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1870,c_Groups_Ozero__class_Ozero(U_1870)),U_1871))
| ~ class_Rings_Olinordered__semidom(U_1870) ),
inference(clausify,[status(thm)],[f_610_2]) ).
fof(f_611_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(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_611_2,plain,
! [U_1875,U_1874,U_1873] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1873,c_Groups_Oone__class_Oone(U_1873)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1873),U_1874),U_1875)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1873,c_Groups_Oone__class_Oone(U_1873)),U_1874))
| ~ class_Rings_Olinordered__semidom(U_1873) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
cnf(f_611_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1873,c_Groups_Oone__class_Oone(U_1873)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1873),U_1874),U_1875)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1873,c_Groups_Oone__class_Oone(U_1873)),U_1874))
| ~ class_Rings_Olinordered__semidom(U_1873) ),
inference(clausify,[status(thm)],[f_611_2]) ).
fof(f_612_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_612_2,plain,
! [U_1878,U_1877,U_1876] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1876),U_1877),U_1878) = c_Groups_Ozero__class_Ozero(U_1876)
| U_1878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1877 != c_Groups_Ozero__class_Ozero(U_1876) )
& ( ( U_1878 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1877 = c_Groups_Ozero__class_Ozero(U_1876) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1876),U_1877),U_1878) != c_Groups_Ozero__class_Ozero(U_1876) ) )
| ~ class_Rings_Ozero__neq__one(U_1876)
| ~ class_Rings_Ono__zero__divisors(U_1876)
| ~ class_Rings_Omult__zero(U_1876)
| ~ class_Power_Opower(U_1876) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
cnf(f_612_3,plain,
( U_1877 = c_Groups_Ozero__class_Ozero(U_1876)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1876),U_1877),U_1878) != c_Groups_Ozero__class_Ozero(U_1876)
| ~ class_Rings_Ozero__neq__one(U_1876)
| ~ class_Rings_Ono__zero__divisors(U_1876)
| ~ class_Rings_Omult__zero(U_1876)
| ~ class_Power_Opower(U_1876) ),
inference(clausify,[status(thm)],[f_612_2]) ).
cnf(f_612_4,plain,
( U_1878 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1876),U_1877),U_1878) != c_Groups_Ozero__class_Ozero(U_1876)
| ~ class_Rings_Ozero__neq__one(U_1876)
| ~ class_Rings_Ono__zero__divisors(U_1876)
| ~ class_Rings_Omult__zero(U_1876)
| ~ class_Power_Opower(U_1876) ),
inference(clausify,[status(thm)],[f_612_2]) ).
cnf(f_612_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1876),U_1877),U_1878) = c_Groups_Ozero__class_Ozero(U_1876)
| U_1878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1877 != c_Groups_Ozero__class_Ozero(U_1876)
| ~ class_Rings_Ozero__neq__one(U_1876)
| ~ class_Rings_Ono__zero__divisors(U_1876)
| ~ class_Rings_Omult__zero(U_1876)
| ~ class_Power_Opower(U_1876) ),
inference(clausify,[status(thm)],[f_612_2]) ).
fof(f_613_1,plain,
! [V_n_2,V_m_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) ) )
| ~ hBOOL(hAPP(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_613_2,plain,
! [U_1882,U_1881,U_1880,U_1879] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1881) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1882)
| U_1881 != U_1882 )
& ( U_1881 = U_1882
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1881) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1882) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1879,c_Groups_Oone__class_Oone(U_1879)),U_1880))
| ~ class_Rings_Olinordered__semidom(U_1879) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( U_1881 = U_1882
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1881) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1882)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1879,c_Groups_Oone__class_Oone(U_1879)),U_1880))
| ~ class_Rings_Olinordered__semidom(U_1879) ),
inference(clausify,[status(thm)],[f_613_2]) ).
cnf(f_613_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1881) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1879),U_1880),U_1882)
| U_1881 != U_1882
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1879,c_Groups_Oone__class_Oone(U_1879)),U_1880))
| ~ class_Rings_Olinordered__semidom(U_1879) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_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_614_2,plain,
! [U_1884,U_1883] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1883),c_Groups_Ozero__class_Ozero(U_1883)),c_Nat_OSuc(U_1884)) = c_Groups_Ozero__class_Ozero(U_1883)
| ~ class_Rings_Osemiring__0(U_1883)
| ~ class_Power_Opower(U_1883) ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
cnf(f_614_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1883),c_Groups_Ozero__class_Ozero(U_1883)),c_Nat_OSuc(U_1884)) = c_Groups_Ozero__class_Ozero(U_1883)
| ~ class_Rings_Osemiring__0(U_1883)
| ~ class_Power_Opower(U_1883) ),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_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_615_2,plain,
! [U_1887,U_1886,U_1885] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1885),U_1886),c_Nat_OSuc(U_1887)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1885),hAPP(hAPP(c_Power_Opower__class_Opower(U_1885),U_1886),U_1887)),U_1886)
| ~ class_Groups_Omonoid__mult(U_1885) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
cnf(f_615_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1885),U_1886),c_Nat_OSuc(U_1887)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1885),hAPP(hAPP(c_Power_Opower__class_Opower(U_1885),U_1886),U_1887)),U_1886)
| ~ class_Groups_Omonoid__mult(U_1885) ),
inference(clausify,[status(thm)],[f_615_2]) ).
fof(f_616_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_616_2,plain,
! [U_1890,U_1889,U_1888] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1888),U_1889),c_Nat_OSuc(U_1890)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1888),U_1889),hAPP(hAPP(c_Power_Opower__class_Opower(U_1888),U_1889),U_1890))
| ~ class_Power_Opower(U_1888) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
cnf(f_616_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1888),U_1889),c_Nat_OSuc(U_1890)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1888),U_1889),hAPP(hAPP(c_Power_Opower__class_Opower(U_1888),U_1889),U_1890))
| ~ class_Power_Opower(U_1888) ),
inference(clausify,[status(thm)],[f_616_2]) ).
fof(f_617_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_617_2,plain,
! [U_1892,U_1891] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1891),U_1892),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1891)
| ~ class_Power_Opower(U_1891) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
cnf(f_617_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1891),U_1892),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1891)
| ~ class_Power_Opower(U_1891) ),
inference(clausify,[status(thm)],[f_617_2]) ).
fof(f_618_1,plain,
! [V_n,V_m,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__add]) ).
fof(f_618_2,plain,
! [U_1896,U_1895,U_1894,U_1893] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1893),U_1894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1895),U_1896)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Power_Opower__class_Opower(U_1893),U_1894),U_1895)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1893),U_1894),U_1896))
| ~ class_Groups_Omonoid__mult(U_1893) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
cnf(f_618_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1893),U_1894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1895),U_1896)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),hAPP(hAPP(c_Power_Opower__class_Opower(U_1893),U_1894),U_1895)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1893),U_1894),U_1896))
| ~ class_Groups_Omonoid__mult(U_1893) ),
inference(clausify,[status(thm)],[f_618_2]) ).
fof(f_619_1,plain,
! [V_b,V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).
fof(f_619_2,plain,
! [U_1900,U_1899,U_1898,U_1897] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1897,U_1898),U_1900))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897,c_Groups_Ozero__class_Ozero(U_1897)),U_1900))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1897,hAPP(hAPP(c_Power_Opower__class_Opower(U_1897),U_1898),U_1899)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1897),U_1900),U_1899)))
| ~ class_Rings_Olinordered__semidom(U_1897) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
cnf(f_619_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1897,U_1898),U_1900))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897,c_Groups_Ozero__class_Ozero(U_1897)),U_1900))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1897,hAPP(hAPP(c_Power_Opower__class_Opower(U_1897),U_1898),U_1899)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1897),U_1900),U_1899)))
| ~ class_Rings_Olinordered__semidom(U_1897) ),
inference(clausify,[status(thm)],[f_619_2]) ).
fof(f_620_1,plain,
! [V_b,V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(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_620_2,plain,
! [U_1904,U_1903,U_1902,U_1901] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901,U_1902),U_1904))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901)),U_1904))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901,hAPP(hAPP(c_Power_Opower__class_Opower(U_1901),U_1902),c_Nat_OSuc(U_1903))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1901),U_1904),c_Nat_OSuc(U_1903))))
| ~ class_Rings_Olinordered__semidom(U_1901) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
cnf(f_620_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901,U_1902),U_1904))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901,c_Groups_Ozero__class_Ozero(U_1901)),U_1904))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901,hAPP(hAPP(c_Power_Opower__class_Opower(U_1901),U_1902),c_Nat_OSuc(U_1903))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1901),U_1904),c_Nat_OSuc(U_1903))))
| ~ class_Rings_Olinordered__semidom(U_1901) ),
inference(clausify,[status(thm)],[f_620_2]) ).
fof(f_621_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),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_621_2,plain,
! [U_1908,U_1907,U_1906,U_1905] :
( U_1906 = U_1908
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905,c_Groups_Ozero__class_Ozero(U_1905)),U_1908))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905,c_Groups_Ozero__class_Ozero(U_1905)),U_1906))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1905),U_1906),c_Nat_OSuc(U_1907)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1905),U_1908),c_Nat_OSuc(U_1907))
| ~ class_Rings_Olinordered__semidom(U_1905) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
cnf(f_621_3,plain,
( U_1906 = U_1908
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905,c_Groups_Ozero__class_Ozero(U_1905)),U_1908))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905,c_Groups_Ozero__class_Ozero(U_1905)),U_1906))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1905),U_1906),c_Nat_OSuc(U_1907)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1905),U_1908),c_Nat_OSuc(U_1907))
| ~ class_Rings_Olinordered__semidom(U_1905) ),
inference(clausify,[status(thm)],[f_621_2]) ).
fof(f_622_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))
| ~ hBOOL(hAPP(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_622_2,plain,
! [U_1911,U_1910,U_1909] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Power_Opower__class_Opower(U_1909),U_1910),U_1911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),hAPP(hAPP(c_Power_Opower__class_Opower(U_1909),U_1910),U_1911))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1909,c_Groups_Oone__class_Oone(U_1909)),U_1910))
| ~ class_Rings_Olinordered__semidom(U_1909) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
cnf(f_622_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1909,hAPP(hAPP(c_Power_Opower__class_Opower(U_1909),U_1910),U_1911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1909),U_1910),hAPP(hAPP(c_Power_Opower__class_Opower(U_1909),U_1910),U_1911))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1909,c_Groups_Oone__class_Oone(U_1909)),U_1910))
| ~ class_Rings_Olinordered__semidom(U_1909) ),
inference(clausify,[status(thm)],[f_622_2]) ).
fof(f_623_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))
| ~ hBOOL(hAPP(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_623_2,plain,
! [U_1914,U_1913,U_1912] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1912,c_Groups_Oone__class_Oone(U_1912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1912),U_1913),hAPP(hAPP(c_Power_Opower__class_Opower(U_1912),U_1913),U_1914))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1912,c_Groups_Oone__class_Oone(U_1912)),U_1913))
| ~ class_Rings_Olinordered__semidom(U_1912) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
cnf(f_623_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1912,c_Groups_Oone__class_Oone(U_1912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1912),U_1913),hAPP(hAPP(c_Power_Opower__class_Opower(U_1912),U_1913),U_1914))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1912,c_Groups_Oone__class_Oone(U_1912)),U_1913))
| ~ class_Rings_Olinordered__semidom(U_1912) ),
inference(clausify,[status(thm)],[f_623_2]) ).
fof(f_624_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_624_2,plain,
! [U_1916,U_1915] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1915),c_Groups_Ozero__class_Ozero(U_1915)),U_1916) = c_Groups_Ozero__class_Ozero(U_1915)
| U_1916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1915),c_Groups_Ozero__class_Ozero(U_1915)),U_1916) = c_Groups_Oone__class_Oone(U_1915)
| U_1916 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_1915)
| ~ class_Power_Opower(U_1915) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
cnf(f_624_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1915),c_Groups_Ozero__class_Ozero(U_1915)),U_1916) = c_Groups_Oone__class_Oone(U_1915)
| U_1916 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_1915)
| ~ class_Power_Opower(U_1915) ),
inference(clausify,[status(thm)],[f_624_2]) ).
cnf(f_624_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1915),c_Groups_Ozero__class_Ozero(U_1915)),U_1916) = c_Groups_Ozero__class_Ozero(U_1915)
| U_1916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_1915)
| ~ class_Power_Opower(U_1915) ),
inference(clausify,[status(thm)],[f_624_2]) ).
fof(f_625_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),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_625_2,plain,
! [U_1919,U_1918,U_1917] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1917,c_Groups_Ozero__class_Ozero(U_1917)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1917),c_Groups_Oabs__class_Oabs(U_1917,U_1918)),U_1919)))
| ~ class_Rings_Olinordered__idom(U_1917) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
cnf(f_625_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1917,c_Groups_Ozero__class_Ozero(U_1917)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1917),c_Groups_Oabs__class_Oabs(U_1917,U_1918)),U_1919)))
| ~ class_Rings_Olinordered__idom(U_1917) ),
inference(clausify,[status(thm)],[f_625_2]) ).
fof(f_626_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__gt1]) ).
fof(f_626_2,plain,
! [U_1922,U_1921,U_1920] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1920,c_Groups_Oone__class_Oone(U_1920)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1920),U_1921),c_Nat_OSuc(U_1922))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1920,c_Groups_Oone__class_Oone(U_1920)),U_1921))
| ~ class_Rings_Olinordered__semidom(U_1920) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
cnf(f_626_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1920,c_Groups_Oone__class_Oone(U_1920)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1920),U_1921),c_Nat_OSuc(U_1922))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1920,c_Groups_Oone__class_Oone(U_1920)),U_1921))
| ~ class_Rings_Olinordered__semidom(U_1920) ),
inference(clausify,[status(thm)],[f_626_2]) ).
fof(f_627_1,plain,
! [V_a,V_N,V_n,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).
fof(f_627_2,plain,
! [U_1926,U_1925,U_1924,U_1923] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1923,hAPP(hAPP(c_Power_Opower__class_Opower(U_1923),U_1926),U_1924)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1923),U_1926),U_1925)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1923,c_Groups_Oone__class_Oone(U_1923)),U_1926))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1924),U_1925))
| ~ class_Rings_Olinordered__semidom(U_1923) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
cnf(f_627_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1923,hAPP(hAPP(c_Power_Opower__class_Opower(U_1923),U_1926),U_1924)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1923),U_1926),U_1925)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1923,c_Groups_Oone__class_Oone(U_1923)),U_1926))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1924),U_1925))
| ~ class_Rings_Olinordered__semidom(U_1923) ),
inference(clausify,[status(thm)],[f_627_2]) ).
fof(f_628_1,plain,
! [V_n,V_m,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(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_628_2,plain,
! [U_1930,U_1929,U_1928,U_1927] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1929),U_1930))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1927,hAPP(hAPP(c_Power_Opower__class_Opower(U_1927),U_1928),U_1929)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1927),U_1928),U_1930)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1927,c_Groups_Oone__class_Oone(U_1927)),U_1928))
| ~ class_Rings_Olinordered__semidom(U_1927) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
cnf(f_628_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1929),U_1930))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1927,hAPP(hAPP(c_Power_Opower__class_Opower(U_1927),U_1928),U_1929)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1927),U_1928),U_1930)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1927,c_Groups_Oone__class_Oone(U_1927)),U_1928))
| ~ class_Rings_Olinordered__semidom(U_1927) ),
inference(clausify,[status(thm)],[f_628_2]) ).
fof(f_629_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(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_629_2,plain,
! [U_1934,U_1933,U_1932,U_1931] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1931,hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1933)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1934)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1933),U_1934)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1933),U_1934))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1931,hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1933)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1934))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1931,c_Groups_Oone__class_Oone(U_1931)),U_1932))
| ~ class_Rings_Olinordered__semidom(U_1931) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
cnf(f_629_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1933),U_1934))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1931,hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1933)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1934)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1931,c_Groups_Oone__class_Oone(U_1931)),U_1932))
| ~ class_Rings_Olinordered__semidom(U_1931) ),
inference(clausify,[status(thm)],[f_629_2]) ).
cnf(f_629_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1931,hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1933)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1931),U_1932),U_1934)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1933),U_1934))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1931,c_Groups_Oone__class_Oone(U_1931)),U_1932))
| ~ class_Rings_Olinordered__semidom(U_1931) ),
inference(clausify,[status(thm)],[f_629_2]) ).
fof(f_630_1,plain,
! [V_a,V_N,V_n,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).
fof(f_630_2,plain,
! [U_1938,U_1937,U_1936,U_1935] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1935,hAPP(hAPP(c_Power_Opower__class_Opower(U_1935),U_1938),U_1936)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1935),U_1938),U_1937)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1935,c_Groups_Oone__class_Oone(U_1935)),U_1938))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1936),U_1937))
| ~ class_Rings_Olinordered__semidom(U_1935) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
cnf(f_630_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1935,hAPP(hAPP(c_Power_Opower__class_Opower(U_1935),U_1938),U_1936)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1935),U_1938),U_1937)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1935,c_Groups_Oone__class_Oone(U_1935)),U_1938))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1936),U_1937))
| ~ class_Rings_Olinordered__semidom(U_1935) ),
inference(clausify,[status(thm)],[f_630_2]) ).
fof(f_631_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).
fof(f_631_2,plain,
! [U_1941,U_1940,U_1939] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1940),hAPP(hAPP(c_Power_Opower__class_Opower(U_1939),U_1940),U_1941))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1939),U_1940),U_1941)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1939,U_1940),c_Groups_Oone__class_Oone(U_1939)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1939,c_Groups_Ozero__class_Ozero(U_1939)),U_1940))
| ~ class_Rings_Olinordered__semidom(U_1939) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
cnf(f_631_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1940),hAPP(hAPP(c_Power_Opower__class_Opower(U_1939),U_1940),U_1941))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1939),U_1940),U_1941)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1939,U_1940),c_Groups_Oone__class_Oone(U_1939)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1939,c_Groups_Ozero__class_Ozero(U_1939)),U_1940))
| ~ class_Rings_Olinordered__semidom(U_1939) ),
inference(clausify,[status(thm)],[f_631_2]) ).
fof(f_632_1,plain,
! [V_n,V_a,T_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one]) ).
fof(f_632_2,plain,
! [U_1944,U_1943,U_1942] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1942,hAPP(hAPP(c_Power_Opower__class_Opower(U_1942),U_1943),c_Nat_OSuc(U_1944))),c_Groups_Oone__class_Oone(U_1942)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1942,U_1943),c_Groups_Oone__class_Oone(U_1942)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1942,c_Groups_Ozero__class_Ozero(U_1942)),U_1943))
| ~ class_Rings_Olinordered__semidom(U_1942) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
cnf(f_632_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1942,hAPP(hAPP(c_Power_Opower__class_Opower(U_1942),U_1943),c_Nat_OSuc(U_1944))),c_Groups_Oone__class_Oone(U_1942)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1942,U_1943),c_Groups_Oone__class_Oone(U_1942)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1942,c_Groups_Ozero__class_Ozero(U_1942)),U_1943))
| ~ class_Rings_Olinordered__semidom(U_1942) ),
inference(clausify,[status(thm)],[f_632_2]) ).
fof(f_633_1,plain,
! [V_a,V_N,V_n,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).
fof(f_633_2,plain,
! [U_1948,U_1947,U_1946,U_1945] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1945,hAPP(hAPP(c_Power_Opower__class_Opower(U_1945),U_1948),U_1947)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1945),U_1948),U_1946)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1945,U_1948),c_Groups_Oone__class_Oone(U_1945)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1945,c_Groups_Ozero__class_Ozero(U_1945)),U_1948))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1946),U_1947))
| ~ class_Rings_Olinordered__semidom(U_1945) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
cnf(f_633_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1945,hAPP(hAPP(c_Power_Opower__class_Opower(U_1945),U_1948),U_1947)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1945),U_1948),U_1946)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1945,U_1948),c_Groups_Oone__class_Oone(U_1945)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_1945,c_Groups_Ozero__class_Ozero(U_1945)),U_1948))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1946),U_1947))
| ~ class_Rings_Olinordered__semidom(U_1945) ),
inference(clausify,[status(thm)],[f_633_2]) ).
fof(f_634_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).
fof(f_634_2,plain,
! [U_1952,U_1951,U_1950,U_1949] :
( U_1950 = U_1952
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1951))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1949,c_Groups_Ozero__class_Ozero(U_1949)),U_1952))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1949,c_Groups_Ozero__class_Ozero(U_1949)),U_1950))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1949),U_1950),U_1951) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1949),U_1952),U_1951)
| ~ class_Rings_Olinordered__semidom(U_1949) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
cnf(f_634_3,plain,
( U_1950 = U_1952
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1951))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1949,c_Groups_Ozero__class_Ozero(U_1949)),U_1952))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1949,c_Groups_Ozero__class_Ozero(U_1949)),U_1950))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1949),U_1950),U_1951) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1949),U_1952),U_1951)
| ~ class_Rings_Olinordered__semidom(U_1949) ),
inference(clausify,[status(thm)],[f_634_2]) ).
fof(f_635_1,plain,
! [V_a,V_N,V_n,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),c_Groups_Oone__class_Oone(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_N))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).
fof(f_635_2,plain,
! [U_1956,U_1955,U_1954,U_1953] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953,hAPP(hAPP(c_Power_Opower__class_Opower(U_1953),U_1956),U_1955)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1953),U_1956),U_1954)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953,U_1956),c_Groups_Oone__class_Oone(U_1953)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953,c_Groups_Ozero__class_Ozero(U_1953)),U_1956))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1954),U_1955))
| ~ class_Rings_Olinordered__semidom(U_1953) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
cnf(f_635_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953,hAPP(hAPP(c_Power_Opower__class_Opower(U_1953),U_1956),U_1955)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1953),U_1956),U_1954)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953,U_1956),c_Groups_Oone__class_Oone(U_1953)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953,c_Groups_Ozero__class_Ozero(U_1953)),U_1956))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1954),U_1955))
| ~ class_Rings_Olinordered__semidom(U_1953) ),
inference(clausify,[status(thm)],[f_635_2]) ).
fof(f_636_1,plain,
! [V_n,V_b] :
( ? [B_z] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_b = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_nnf,[status(thm)],[fact_reduce__poly__simple]) ).
fof(f_636_2,plain,
! [U_1959,U_1958] :
( ? [U_1957] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_1958),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),U_1957),U_1959))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| U_1959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1958 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
! [U_1959,U_1958] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_1958),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK54(U_1959,U_1958)),U_1959))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| U_1959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1958 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_1957,sK54(U_1959,U_1958))],[f_636_2]) ).
cnf(f_636_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_1958),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK54(U_1959,U_1958)),U_1959))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| U_1959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1958 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_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)
| ~ hBOOL(hAPP(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_637_2,plain,
! [U_1960] :
( U_1960 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1960 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1960),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
cnf(f_637_3,plain,
( U_1960 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1960 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1960),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
inference(clausify,[status(thm)],[f_637_2]) ).
fof(f_638_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_638_2,plain,
! [U_1961] :
( c_Power_Opower__class_Opower(U_1961) = c_Power_Opower_Opower(U_1961,c_Groups_Oone__class_Oone(U_1961),c_Groups_Otimes__class_Otimes(U_1961))
| ~ class_Power_Opower(U_1961) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
cnf(f_638_3,plain,
( c_Power_Opower__class_Opower(U_1961) = c_Power_Opower_Opower(U_1961,c_Groups_Oone__class_Oone(U_1961),c_Groups_Otimes__class_Otimes(U_1961))
| ~ class_Power_Opower(U_1961) ),
inference(clausify,[status(thm)],[f_638_2]) ).
fof(f_639_1,plain,
! [V_n,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n))),
inference(fof_nnf,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(f_639_2,plain,
! [U_1963,U_1962] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1962)),U_1963))),
inference(variable_rename,[status(thm)],[f_639_1]) ).
cnf(f_639_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1962)),U_1963))),
inference(clausify,[status(thm)],[f_639_2]) ).
fof(f_640_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_640_2,plain,
! [U_1964] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1964) = U_1964,
inference(variable_rename,[status(thm)],[f_640_1]) ).
cnf(f_640_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1964) = U_1964,
inference(clausify,[status(thm)],[f_640_2]) ).
fof(f_641_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_641_2,plain,
! [U_1965] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1965),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1965,
inference(variable_rename,[status(thm)],[f_641_1]) ).
cnf(f_641_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1965),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1965,
inference(clausify,[status(thm)],[f_641_2]) ).
fof(f_642_1,plain,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(f_642_2,plain,
! [U_1968,U_1967,U_1966] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1967),U_1968)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1966),U_1967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1966),U_1968)),
inference(variable_rename,[status(thm)],[f_642_1]) ).
cnf(f_642_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1967),U_1968)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1966),U_1967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1966),U_1968)),
inference(clausify,[status(thm)],[f_642_2]) ).
fof(f_643_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(f_643_2,plain,
! [U_1971,U_1970,U_1969] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1969),U_1970)),U_1971) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1969),U_1971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1970),U_1971)),
inference(variable_rename,[status(thm)],[f_643_1]) ).
cnf(f_643_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1969),U_1970)),U_1971) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1969),U_1971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1970),U_1971)),
inference(clausify,[status(thm)],[f_643_2]) ).
fof(f_644_1,plain,
! [V_n_2,V_m_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).
fof(f_644_2,plain,
! [U_1973,U_1972] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1972),U_1973) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1973 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1972 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_1973 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_1972 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1972),U_1973) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1972)) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
cnf(f_644_3,plain,
( U_1972 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1972),U_1973) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1972)) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_4,plain,
( U_1973 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1972),U_1973) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1972)) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1972),U_1973) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1973 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1972 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1972)) ),
inference(clausify,[status(thm)],[f_644_2]) ).
fof(f_645_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).
fof(f_645_2,plain,
! [U_1976,U_1975,U_1974] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1976),U_1974)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1976),U_1975)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1976))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1974),U_1975)) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
cnf(f_645_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1976),U_1974)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1976),U_1975)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1976))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1974),U_1975)) ),
inference(clausify,[status(thm)],[f_645_2]) ).
fof(f_646_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_646_2,plain,
! [U_1978,U_1977] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1977) = 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_1977),U_1978)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
cnf(f_646_3,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_1977) = 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_1977),U_1978)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_646_2]) ).
fof(f_647_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_647_2,plain,
! [U_1981,U_1980,U_1979] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1979),U_1980)),U_1981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1980),U_1981)),
inference(variable_rename,[status(thm)],[f_647_1]) ).
cnf(f_647_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1979),U_1980)),U_1981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1980),U_1981)),
inference(clausify,[status(thm)],[f_647_2]) ).
fof(f_648_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_648_2,plain,
! [U_1983,U_1982] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1982),U_1983) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1983),U_1982),
inference(variable_rename,[status(thm)],[f_648_1]) ).
cnf(f_648_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1982),U_1983) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1983),U_1982),
inference(clausify,[status(thm)],[f_648_2]) ).
fof(f_649_1,plain,
! [V_z,V_z_H,V_w,V_w_H] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).
fof(f_649_2,plain,
! [U_1987,U_1986,U_1985,U_1984] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1984),U_1986)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1985),U_1987)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1986),U_1987))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1984),U_1985)) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
cnf(f_649_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1984),U_1986)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1985),U_1987)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1986),U_1987))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1984),U_1985)) ),
inference(clausify,[status(thm)],[f_649_2]) ).
fof(f_650_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).
fof(f_650_2,plain,
! [U_1990,U_1989,U_1988] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1988),U_1990)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1989),U_1990)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1988),U_1989)) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
cnf(f_650_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1988),U_1990)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1989),U_1990)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1988),U_1989)) ),
inference(clausify,[status(thm)],[f_650_2]) ).
fof(f_651_1,plain,
! [V_z,V_w] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w),V_z)) ),
inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).
fof(f_651_2,plain,
! [U_1992,U_1991] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1991),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1992))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1991),U_1992)) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
cnf(f_651_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1991),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1992))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1991),U_1992)) ),
inference(clausify,[status(thm)],[f_651_2]) ).
fof(f_652_1,plain,
! [V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)))
| ~ hBOOL(hAPP(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_652_2,plain,
! [U_1993] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1993)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1993)) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
cnf(f_652_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1993)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1993)) ),
inference(clausify,[status(thm)],[f_652_2]) ).
fof(f_653_1,plain,
! [V_z_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).
fof(f_653_2,plain,
! [U_1994] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1994)),U_1994)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1994),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1994),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1994)),U_1994)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
( ! [U_1996] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1996)),U_1996)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_1995] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1995),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1995)),U_1995)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_653_2]) ).
cnf(f_653_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1995),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1995)),U_1995)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_653_3]) ).
cnf(f_653_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1996)),U_1996)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [V_z_2,V_w_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).
fof(f_654_2,plain,
! [U_1998,U_1997] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1997),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1998))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1997),U_1998)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1997),U_1998))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1997),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_1998)) ) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
( ! [U_2002,U_2000] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2000),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2002))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2000),U_2002)) )
& ! [U_2001,U_1999] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1999),U_2001))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2001)) ) ),
inference(miniscope,[status(thm)],[f_654_2]) ).
cnf(f_654_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1999),U_2001))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2001)) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2000),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2002))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2000),U_2002)) ),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_1,plain,
! [V_z_2] :
( ( hBOOL(hAPP(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)
| ~ hBOOL(hAPP(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_655_2,plain,
! [U_2003] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2003)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_2003 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_2003 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2003)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
( ! [U_2005] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2005)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_2005 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2004] :
( U_2004 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2004)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_655_2]) ).
cnf(f_655_4,plain,
( U_2004 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2004)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_655_3]) ).
cnf(f_655_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2005)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_2005 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_655_3]) ).
fof(f_656_1,plain,
! [V_z_2,V_w_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( V_w_2 != V_z_2
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) ) )
& ( V_w_2 = V_z_2
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).
fof(f_656_2,plain,
! [U_2007,U_2006] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2006),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2007),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_2006 != U_2007
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2006),U_2007)) ) )
& ( U_2006 = U_2007
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2006),U_2007))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2006),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2007),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
( ! [U_2011,U_2009] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2011),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_2009 != U_2011
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2009),U_2011)) ) )
& ! [U_2010,U_2008] :
( U_2008 = U_2010
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2008),U_2010))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2010),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_656_2]) ).
cnf(f_656_4,plain,
( U_2008 = U_2010
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2008),U_2010))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2010),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2009),U_2011))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2011),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_6,plain,
( U_2009 != U_2011
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2009),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2011),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_656_3]) ).
fof(f_657_1,plain,
! [V_z_2,V_w_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2),V_z_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).
fof(f_657_2,plain,
! [U_2013,U_2012] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2013),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2012),U_2013)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2012),U_2013))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2012),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2013),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
( ! [U_2017,U_2015] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2017),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2015),U_2017)) )
& ! [U_2016,U_2014] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2014),U_2016))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2014),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2016),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_657_2]) ).
cnf(f_657_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2014),U_2016))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2014),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2016),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_657_3]) ).
cnf(f_657_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2017),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2015),U_2017)) ),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y),V_x))
| V_x = V_y
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).
fof(f_658_2,plain,
! [U_2019,U_2018] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2019),U_2018))
| U_2018 = U_2019
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2018),U_2019)) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
cnf(f_658_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2019),U_2018))
| U_2018 = U_2019
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2018),U_2019)) ),
inference(clausify,[status(thm)],[f_658_2]) ).
fof(f_659_1,plain,
! [V_w_2,V_z_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2))
| V_z_2 = V_w_2
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2)) )
& ( ( V_z_2 != V_w_2
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2),V_w_2)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2),V_w_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_659_2,plain,
! [U_2021,U_2020] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2020),U_2021))
| U_2020 = U_2021
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2020),U_2021)) )
& ( ( U_2020 != U_2021
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2020),U_2021)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2020),U_2021)) ) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
( ! [U_2025,U_2023] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023),U_2025))
| U_2023 = U_2025
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2023),U_2025)) )
& ! [U_2024,U_2022] :
( ( U_2022 != U_2024
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2022),U_2024)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2022),U_2024)) ) ),
inference(miniscope,[status(thm)],[f_659_2]) ).
cnf(f_659_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2022),U_2024))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2022),U_2024)) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_5,plain,
( U_2022 != U_2024
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2022),U_2024)) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023),U_2025))
| U_2023 = U_2025
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2023),U_2025)) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0__right]) ).
fof(f_660_2,plain,
! [U_2026] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2026),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2026,
inference(variable_rename,[status(thm)],[f_660_1]) ).
cnf(f_660_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2026),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2026,
inference(clausify,[status(thm)],[f_660_2]) ).
fof(f_661_1,plain,
! [V_z_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).
fof(f_661_2,plain,
! [U_2027] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2027))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2027)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2027))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2027)) ) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
( ! [U_2029] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2029))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2029)) )
& ! [U_2028] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2028))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2028)) ) ),
inference(miniscope,[status(thm)],[f_661_2]) ).
cnf(f_661_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2028))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2028)) ),
inference(clausify,[status(thm)],[f_661_3]) ).
cnf(f_661_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2029))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2029)) ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0]) ).
fof(f_662_2,plain,
! [U_2030] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2030) = U_2030,
inference(variable_rename,[status(thm)],[f_662_1]) ).
cnf(f_662_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2030) = U_2030,
inference(clausify,[status(thm)],[f_662_2]) ).
fof(f_663_1,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).
cnf(f_663_2,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_663_1]) ).
fof(f_664_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_odd__nonzero]) ).
fof(f_664_2,plain,
! [U_2031] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2031)),U_2031) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_664_1]) ).
cnf(f_664_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2031)),U_2031) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_664_2]) ).
fof(f_665_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).
cnf(f_665_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_665_1]) ).
fof(f_666_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_666_2,plain,
! [U_2035,U_2034,U_2033,U_2032] : hAPP(hAPP(c_Power_Opower_Opower(U_2032,U_2033,U_2034),U_2035),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2033,
inference(variable_rename,[status(thm)],[f_666_1]) ).
cnf(f_666_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_2032,U_2033,U_2034),U_2035),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2033,
inference(clausify,[status(thm)],[f_666_2]) ).
fof(f_667_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_667_2,plain,
! [U_2040,U_2039,U_2038,U_2037,U_2036] : hAPP(hAPP(c_Power_Opower_Opower(U_2036,U_2037,U_2038),U_2039),c_Nat_OSuc(U_2040)) = hAPP(hAPP(U_2038,U_2039),hAPP(hAPP(c_Power_Opower_Opower(U_2036,U_2037,U_2038),U_2039),U_2040)),
inference(variable_rename,[status(thm)],[f_667_1]) ).
cnf(f_667_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_2036,U_2037,U_2038),U_2039),c_Nat_OSuc(U_2040)) = hAPP(hAPP(U_2038,U_2039),hAPP(hAPP(c_Power_Opower_Opower(U_2036,U_2037,U_2038),U_2039),U_2040)),
inference(clausify,[status(thm)],[f_667_2]) ).
fof(f_668_1,plain,
! [V_n_2,V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(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_668_2,plain,
! [U_2042,U_2041] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2041),U_2042)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2041))
& U_2042 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2041))
| U_2042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2041),U_2042))) ) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
( ! [U_2046,U_2044] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2044),U_2046)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2044))
& U_2046 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2045,U_2043] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2043))
| U_2045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2043),U_2045))) ) ),
inference(miniscope,[status(thm)],[f_668_2]) ).
cnf(f_668_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2043))
| U_2045 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2043),U_2045))) ),
inference(clausify,[status(thm)],[f_668_3]) ).
cnf(f_668_5,plain,
( U_2046 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2044),U_2046))) ),
inference(clausify,[status(thm)],[f_668_3]) ).
cnf(f_668_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2044))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2044),U_2046))) ),
inference(clausify,[status(thm)],[f_668_3]) ).
fof(f_669_1,plain,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
| V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ hBOOL(hAPP(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_669_2,plain,
! [U_2049,U_2048,U_2047] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2049),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2048))
| U_2047 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2047),U_2049))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2047)) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
cnf(f_669_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2049),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2048))
| U_2047 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2047),U_2049))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2047)) ),
inference(clausify,[status(thm)],[f_669_2]) ).
fof(f_670_1,plain,
! [V_q,V_r,V_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_a))
| V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ hBOOL(hAPP(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_670_2,plain,
! [U_2052,U_2051,U_2050] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2052))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2051),U_2050))
| U_2050 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2051),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2050),U_2052))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2050)) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
cnf(f_670_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2052))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2051),U_2050))
| U_2050 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2051),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2050),U_2052))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2050)) ),
inference(clausify,[status(thm)],[f_670_2]) ).
fof(f_671_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) ),
inference(fof_nnf,[status(thm)],[fact_q__pos__lemma]) ).
fof(f_671_2,plain,
! [U_2055,U_2054,U_2053] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2054))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2053))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2055),U_2053))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2053),U_2054)),U_2055))) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
cnf(f_671_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2054))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2053))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2055),U_2053))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2053),U_2054)),U_2055))) ),
inference(clausify,[status(thm)],[f_671_2]) ).
fof(f_672_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).
fof(f_672_2,plain,
! [U_2058,U_2057,U_2056] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2058),U_2056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2058),U_2057)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2056),U_2057)) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
cnf(f_672_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2058),U_2056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2058),U_2057)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2056),U_2057)) ),
inference(clausify,[status(thm)],[f_672_2]) ).
fof(f_673_1,plain,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)),
inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).
fof(f_673_2,plain,
! [U_2061,U_2060,U_2059] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2059),U_2060)),U_2061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2060),U_2061)),
inference(variable_rename,[status(thm)],[f_673_1]) ).
cnf(f_673_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2059),U_2060)),U_2061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2060),U_2061)),
inference(clausify,[status(thm)],[f_673_2]) ).
fof(f_674_1,plain,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)),
inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).
fof(f_674_2,plain,
! [U_2064,U_2063,U_2062] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2062),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2063),U_2064)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2062),U_2064)),
inference(variable_rename,[status(thm)],[f_674_1]) ).
cnf(f_674_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2062),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2063),U_2064)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2063),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2062),U_2064)),
inference(clausify,[status(thm)],[f_674_2]) ).
fof(f_675_1,plain,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).
fof(f_675_2,plain,
! [U_2066,U_2065] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2065),U_2066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2066),U_2065),
inference(variable_rename,[status(thm)],[f_675_1]) ).
cnf(f_675_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2065),U_2066) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2066),U_2065),
inference(clausify,[status(thm)],[f_675_2]) ).
fof(f_676_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).
fof(f_676_2,plain,
! [U_2068,U_2067] :
( U_2067 = U_2068
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2068),U_2067))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2067),U_2068)) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
cnf(f_676_3,plain,
( U_2067 = U_2068
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2068),U_2067))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2067),U_2068)) ),
inference(clausify,[status(thm)],[f_676_2]) ).
fof(f_677_1,plain,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).
fof(f_677_2,plain,
! [U_2071,U_2070,U_2069] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2069),U_2071))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2070),U_2071))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2069),U_2070)) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
cnf(f_677_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2069),U_2071))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2070),U_2071))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2069),U_2070)) ),
inference(clausify,[status(thm)],[f_677_2]) ).
fof(f_678_1,plain,
! [V_w,V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_z))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z),V_w)) ),
inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).
fof(f_678_2,plain,
! [U_2073,U_2072] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2073),U_2072))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2072),U_2073)) ),
inference(variable_rename,[status(thm)],[f_678_1]) ).
cnf(f_678_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2073),U_2072))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2072),U_2073)) ),
inference(clausify,[status(thm)],[f_678_2]) ).
fof(f_679_1,plain,
! [V_w] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w),V_w)),
inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).
fof(f_679_2,plain,
! [U_2074] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2074),U_2074)),
inference(variable_rename,[status(thm)],[f_679_1]) ).
cnf(f_679_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2074),U_2074)),
inference(clausify,[status(thm)],[f_679_2]) ).
fof(f_680_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma]) ).
fof(f_680_2,plain,
! [U_2080,U_2079,U_2078,U_2077,U_2076,U_2075] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2079),U_2076))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2078),U_2075))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2078))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2080))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2077),U_2075))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2078),U_2079)),U_2080)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2075),U_2076)),U_2077) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2078),U_2079)),U_2080) ),
inference(variable_rename,[status(thm)],[f_680_1]) ).
cnf(f_680_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2079),U_2076))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2078),U_2075))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2078))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2080))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2077),U_2075))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2078),U_2079)),U_2080)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2075),U_2076)),U_2077) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2078),U_2079)),U_2080) ),
inference(clausify,[status(thm)],[f_680_2]) ).
fof(f_681_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg]) ).
fof(f_681_2,plain,
! [U_2085,U_2084,U_2083,U_2082,U_2081] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2084),U_2082))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2081),U_2083))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2081),U_2085))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2081),U_2082)),U_2083)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2081),U_2084)),U_2085))) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
cnf(f_681_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2084),U_2082))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2081),U_2083))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2081),U_2085))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2085),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2081),U_2082)),U_2083)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2081),U_2084)),U_2085))) ),
inference(clausify,[status(thm)],[f_681_2]) ).
fof(f_682_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q),V_q_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma]) ).
fof(f_682_2,plain,
! [U_2091,U_2090,U_2089,U_2088,U_2087,U_2086] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2087),U_2090))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2089),U_2086))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2089))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2088))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2091),U_2089))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2090)),U_2091)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2086),U_2087)),U_2088) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2090)),U_2091) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
cnf(f_682_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2087),U_2090))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2089),U_2086))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2089))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2088))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2091),U_2089))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2090)),U_2091)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2086),U_2087)),U_2088) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2089),U_2090)),U_2091) ),
inference(clausify,[status(thm)],[f_682_2]) ).
fof(f_683_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),V_q))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma]) ).
fof(f_683_2,plain,
! [U_2096,U_2095,U_2094,U_2093,U_2092] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2093),U_2095))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2096),U_2092))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2094),U_2092))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2094))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2092),U_2093)),U_2094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2092),U_2095)),U_2096))) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
cnf(f_683_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2093),U_2095))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2096),U_2092))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2094),U_2092))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2094))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2092),U_2093)),U_2094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2092),U_2095)),U_2096))) ),
inference(clausify,[status(thm)],[f_683_2]) ).
fof(f_684_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_q__neg__lemma]) ).
fof(f_684_2,plain,
! [U_2099,U_2098,U_2097] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2098),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2097))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2099))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2097),U_2098)),U_2099)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
cnf(f_684_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2098),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2097))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2099))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2097),U_2098)),U_2099)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_684_2]) ).
fof(f_685_1,plain,
! [V_n,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))
| ~ hBOOL(hAPP(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_685_2,plain,
! [U_2101,U_2100] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2100),U_2101)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2100)) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
cnf(f_685_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2100),U_2101)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2100)) ),
inference(clausify,[status(thm)],[f_685_2]) ).
fof(f_686_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).
fof(f_686_2,plain,
! [U_2103,U_2102] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2102),U_2103)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2103))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2102)) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
cnf(f_686_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2102),U_2103)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2103))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2102)) ),
inference(clausify,[status(thm)],[f_686_2]) ).
fof(f_687_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_687_2,plain,
! [U_2105,U_2104] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2104),U_2105)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2105))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2104)) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
cnf(f_687_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2104),U_2105)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2105))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2104)) ),
inference(clausify,[status(thm)],[f_687_2]) ).
fof(f_688_1,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
cnf(f_688_2,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_688_1]) ).
fof(f_689_1,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
cnf(f_689_2,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_689_1]) ).
fof(f_690_1,plain,
! [V_n,V_a,V_r] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(V_r,V_a)),V_n) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_r),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)),
inference(fof_nnf,[status(thm)],[fact_DeMoivre2]) ).
fof(f_690_2,plain,
! [U_2108,U_2107,U_2106] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(U_2106,U_2107)),U_2108) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2106),U_2108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2108)),U_2107)),
inference(variable_rename,[status(thm)],[f_690_1]) ).
cnf(f_690_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Orcis(U_2106,U_2107)),U_2108) = c_Complex_Orcis(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2106),U_2108),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2108)),U_2107)),
inference(clausify,[status(thm)],[f_690_2]) ).
fof(f_691_1,plain,
! [V_r] :
( ? [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_r)) )
| ~ hBOOL(hAPP(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_691_2,plain,
! [U_2110] :
( ? [U_2109] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2109))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2109)),U_2110)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2110)) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
fof(f_691_3,plain,
! [U_2110] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK55(U_2110)))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK55(U_2110))),U_2110)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2110)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_2109,sK55(U_2110))],[f_691_2]) ).
cnf(f_691_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK55(U_2110))),U_2110))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2110)) ),
inference(clausify,[status(thm)],[f_691_3]) ).
cnf(f_691_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK55(U_2110)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2110)) ),
inference(clausify,[status(thm)],[f_691_3]) ).
fof(f_692_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
| ~ hBOOL(hAPP(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
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_x)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth__unique]) ).
fof(f_692_2,plain,
! [U_2114,U_2113] :
( ? [U_2112] :
( ! [U_2111] :
( U_2111 = U_2112
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2111),U_2113) != U_2114
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2111)) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2112),U_2113) = U_2114
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2112)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2114))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2113)) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
! [U_2114,U_2113] :
( ( ! [U_2111] :
( U_2111 = sK56(U_2114,U_2113)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2111),U_2113) != U_2114
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2111)) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK56(U_2114,U_2113)),U_2113) = U_2114
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK56(U_2114,U_2113))) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2114))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2113)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_2112,sK56(U_2114,U_2113))],[f_692_2]) ).
cnf(f_692_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK56(U_2114,U_2113)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2114))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2113)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
cnf(f_692_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK56(U_2114,U_2113)),U_2113) = U_2114
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2114))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2113)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
cnf(f_692_6,plain,
( U_2111 = sK56(U_2114,U_2113)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2111),U_2113) != U_2114
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2111))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2114))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2113)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_1,plain,
! [V_a,V_r] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(V_r,V_a)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r),
inference(fof_nnf,[status(thm)],[fact_complex__mod__rcis]) ).
fof(f_693_2,plain,
! [U_2116,U_2115] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(U_2115,U_2116)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2115),
inference(variable_rename,[status(thm)],[f_693_1]) ).
cnf(f_693_3,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(U_2115,U_2116)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2115),
inference(clausify,[status(thm)],[f_693_2]) ).
fof(f_694_1,plain,
! [V_a] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_rcis__zero__mod]) ).
fof(f_694_2,plain,
! [U_2117] : c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2117) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(variable_rename,[status(thm)],[f_694_1]) ).
cnf(f_694_3,plain,
c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2117) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_694_2]) ).
fof(f_695_1,plain,
! [V_b,V_r2,V_a,V_r1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(V_r1,V_a)),c_Complex_Orcis(V_r2,V_b)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r1),V_r2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)),
inference(fof_nnf,[status(thm)],[fact_rcis__mult]) ).
fof(f_695_2,plain,
! [U_2121,U_2120,U_2119,U_2118] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(U_2118,U_2119)),c_Complex_Orcis(U_2120,U_2121)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2118),U_2120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2119),U_2121)),
inference(variable_rename,[status(thm)],[f_695_1]) ).
cnf(f_695_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Orcis(U_2118,U_2119)),c_Complex_Orcis(U_2120,U_2121)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2118),U_2120),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2119),U_2121)),
inference(clausify,[status(thm)],[f_695_2]) ).
fof(f_696_1,plain,
! [V_a,V_n] :
( ? [B_r] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth]) ).
fof(f_696_2,plain,
! [U_2124,U_2123] :
( ? [U_2122] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2122),U_2123) = U_2124
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2122)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2124))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2123)) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
! [U_2124,U_2123] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK57(U_2124,U_2123)),U_2123) = U_2124
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK57(U_2124,U_2123))) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2124))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2123)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_2122,sK57(U_2124,U_2123))],[f_696_2]) ).
cnf(f_696_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK57(U_2124,U_2123)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2124))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2123)) ),
inference(clausify,[status(thm)],[f_696_3]) ).
cnf(f_696_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK57(U_2124,U_2123)),U_2123) = U_2124
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2124))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2123)) ),
inference(clausify,[status(thm)],[f_696_3]) ).
fof(f_697_1,plain,
! [V_a,V_n] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a))),
inference(fof_nnf,[status(thm)],[fact_cis__real__of__nat__Suc__mult]) ).
fof(f_697_2,plain,
! [U_2126,U_2125] : c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2125))),U_2126)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2126)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2125)),U_2126))),
inference(variable_rename,[status(thm)],[f_697_1]) ).
cnf(f_697_3,plain,
c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2125))),U_2126)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2126)),c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2125)),U_2126))),
inference(clausify,[status(thm)],[f_697_2]) ).
fof(f_698_1,plain,
! [V_x,V_y] :
( ? [B_n] :
( hBOOL(hAPP(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)))
& hBOOL(hAPP(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)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
| ~ hBOOL(hAPP(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_698_2,plain,
! [U_2129,U_2128] :
( ? [U_2127] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2127))),U_2128)))
& hBOOL(hAPP(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_2127)),U_2128)),U_2129)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2128)) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
fof(f_698_3,plain,
! [U_2129,U_2128] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK58(U_2129,U_2128)))),U_2128)))
& hBOOL(hAPP(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,sK58(U_2129,U_2128))),U_2128)),U_2129)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2128)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_2127,sK58(U_2129,U_2128))],[f_698_2]) ).
cnf(f_698_4,plain,
( hBOOL(hAPP(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,sK58(U_2129,U_2128))),U_2128)),U_2129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2128)) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2129),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK58(U_2129,U_2128)))),U_2128)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2129))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2128)) ),
inference(clausify,[status(thm)],[f_698_3]) ).
fof(f_699_1,plain,
! [V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_b)),
inference(fof_nnf,[status(thm)],[fact_cis__mult]) ).
fof(f_699_2,plain,
! [U_2131,U_2130] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2130)),c_Complex_Ocis(U_2131)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2130),U_2131)),
inference(variable_rename,[status(thm)],[f_699_1]) ).
cnf(f_699_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(U_2130)),c_Complex_Ocis(U_2131)) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2130),U_2131)),
inference(clausify,[status(thm)],[f_699_2]) ).
fof(f_700_1,plain,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_cis__zero]) ).
cnf(f_700_2,plain,
c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_700_1]) ).
fof(f_701_1,plain,
! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_a),
inference(fof_nnf,[status(thm)],[fact_cis__rcis__eq]) ).
fof(f_701_2,plain,
! [U_2132] : c_Complex_Ocis(U_2132) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2132),
inference(variable_rename,[status(thm)],[f_701_1]) ).
cnf(f_701_3,plain,
c_Complex_Ocis(U_2132) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2132),
inference(clausify,[status(thm)],[f_701_2]) ).
fof(f_702_1,plain,
! [V_n,V_a] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)),
inference(fof_nnf,[status(thm)],[fact_DeMoivre]) ).
fof(f_702_2,plain,
! [U_2134,U_2133] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2133)),U_2134) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2134)),U_2133)),
inference(variable_rename,[status(thm)],[f_702_1]) ).
cnf(f_702_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2133)),U_2134) = c_Complex_Ocis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2134)),U_2133)),
inference(clausify,[status(thm)],[f_702_2]) ).
fof(f_703_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))
| ~ hBOOL(hAPP(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_703_2,plain,
! [U_2136,U_2135] :
( c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2135),U_2136)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2136)),c_Transcendental_Oln(U_2135))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2135)) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
cnf(f_703_3,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2135),U_2136)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2136)),c_Transcendental_Oln(U_2135))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2135)) ),
inference(clausify,[status(thm)],[f_703_2]) ).
fof(f_704_1,plain,
! [V_a,V_n] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)),
inference(fof_nnf,[status(thm)],[fact_cos__n__Re__cis__pow__n]) ).
fof(f_704_2,plain,
! [U_2138,U_2137] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2137)),U_2138)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2138)),U_2137)),
inference(variable_rename,[status(thm)],[f_704_1]) ).
cnf(f_704_3,plain,
c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2137)),U_2138)) = hAPP(c_Complex_ORe,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2138)),U_2137)),
inference(clausify,[status(thm)],[f_704_2]) ).
fof(f_705_1,plain,
! [V_a,V_n] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_a)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),V_n)),
inference(fof_nnf,[status(thm)],[fact_sin__n__Im__cis__pow__n]) ).
fof(f_705_2,plain,
! [U_2140,U_2139] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2139)),U_2140)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2140)),U_2139)),
inference(variable_rename,[status(thm)],[f_705_1]) ).
cnf(f_705_3,plain,
c_Transcendental_Osin(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2139)),U_2140)) = hAPP(c_Complex_OIm,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Ocis(U_2140)),U_2139)),
inference(clausify,[status(thm)],[f_705_2]) ).
fof(f_706_1,plain,
! [V_y,V_x] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))),
inference(fof_nnf,[status(thm)],[fact_sin__add]) ).
fof(f_706_2,plain,
! [U_2142,U_2141] : c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2141),U_2142)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2141)),c_Transcendental_Ocos(U_2142))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2141)),c_Transcendental_Osin(U_2142))),
inference(variable_rename,[status(thm)],[f_706_1]) ).
cnf(f_706_3,plain,
c_Transcendental_Osin(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2141),U_2142)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2141)),c_Transcendental_Ocos(U_2142))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2141)),c_Transcendental_Osin(U_2142))),
inference(clausify,[status(thm)],[f_706_2]) ).
fof(f_707_1,plain,
! [V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_x))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_sin__cos__squared__add3]) ).
fof(f_707_2,plain,
! [U_2143] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2143)),c_Transcendental_Ocos(U_2143))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2143)),c_Transcendental_Osin(U_2143))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(variable_rename,[status(thm)],[f_707_1]) ).
cnf(f_707_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2143)),c_Transcendental_Ocos(U_2143))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2143)),c_Transcendental_Osin(U_2143))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_707_2]) ).
fof(f_708_1,plain,
! [V_x] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_sin__zero__abs__cos__one]) ).
fof(f_708_2,plain,
! [U_2144] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(U_2144)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(U_2144) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
cnf(f_708_3,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(U_2144)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Osin(U_2144) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_708_2]) ).
fof(f_709_1,plain,
! [V_x] :
( c_Transcendental_Osin(V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(V_x) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_cos__one__sin__zero]) ).
fof(f_709_2,plain,
! [U_2145] :
( c_Transcendental_Osin(U_2145) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(U_2145) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
cnf(f_709_3,plain,
( c_Transcendental_Osin(U_2145) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Transcendental_Ocos(U_2145) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_709_2]) ).
fof(f_710_1,plain,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_cos__zero]) ).
cnf(f_710_2,plain,
c_Transcendental_Ocos(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_710_1]) ).
fof(f_711_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_nnf,[status(thm)],[fact_cos__le__one]) ).
fof(f_711_2,plain,
! [U_2146] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(U_2146)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_711_1]) ).
cnf(f_711_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Ocos(U_2146)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_711_2]) ).
fof(f_712_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_nnf,[status(thm)],[fact_sin__le__one]) ).
fof(f_712_2,plain,
! [U_2147] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(U_2147)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_712_1]) ).
cnf(f_712_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Osin(U_2147)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_712_2]) ).
fof(f_713_1,plain,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_sin__zero]) ).
cnf(f_713_2,plain,
c_Transcendental_Osin(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_713_1]) ).
fof(f_714_1,plain,
! [V_a] : hAPP(c_Complex_OIm,c_Complex_Ocis(V_a)) = c_Transcendental_Osin(V_a),
inference(fof_nnf,[status(thm)],[fact_Im__cis]) ).
fof(f_714_2,plain,
! [U_2148] : hAPP(c_Complex_OIm,c_Complex_Ocis(U_2148)) = c_Transcendental_Osin(U_2148),
inference(variable_rename,[status(thm)],[f_714_1]) ).
cnf(f_714_3,plain,
hAPP(c_Complex_OIm,c_Complex_Ocis(U_2148)) = c_Transcendental_Osin(U_2148),
inference(clausify,[status(thm)],[f_714_2]) ).
fof(f_715_1,plain,
! [V_a] : hAPP(c_Complex_ORe,c_Complex_Ocis(V_a)) = c_Transcendental_Ocos(V_a),
inference(fof_nnf,[status(thm)],[fact_Re__cis]) ).
fof(f_715_2,plain,
! [U_2149] : hAPP(c_Complex_ORe,c_Complex_Ocis(U_2149)) = c_Transcendental_Ocos(U_2149),
inference(variable_rename,[status(thm)],[f_715_1]) ).
cnf(f_715_3,plain,
hAPP(c_Complex_ORe,c_Complex_Ocis(U_2149)) = c_Transcendental_Ocos(U_2149),
inference(clausify,[status(thm)],[f_715_2]) ).
fof(f_716_1,plain,
! [V_y_2,V_x_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
| ~ hBOOL(hAPP(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_716_2,plain,
! [U_2151,U_2150] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2150)),c_Transcendental_Oln(U_2151)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2150),U_2151)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2150),U_2151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2150)),c_Transcendental_Oln(U_2151))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2150)) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
cnf(f_716_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2150),U_2151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2150)),c_Transcendental_Oln(U_2151)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2150)) ),
inference(clausify,[status(thm)],[f_716_2]) ).
cnf(f_716_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2150)),c_Transcendental_Oln(U_2151)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2150),U_2151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2151))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2150)) ),
inference(clausify,[status(thm)],[f_716_2]) ).
fof(f_717_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) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
| ~ hBOOL(hAPP(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_717_2,plain,
! [U_2153,U_2152] :
( ( ( c_Transcendental_Oln(U_2152) = c_Transcendental_Oln(U_2153)
| U_2152 != U_2153 )
& ( U_2152 = U_2153
| c_Transcendental_Oln(U_2152) != c_Transcendental_Oln(U_2153) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2153))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2152)) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
cnf(f_717_3,plain,
( U_2152 = U_2153
| c_Transcendental_Oln(U_2152) != c_Transcendental_Oln(U_2153)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2153))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2152)) ),
inference(clausify,[status(thm)],[f_717_2]) ).
cnf(f_717_4,plain,
( c_Transcendental_Oln(U_2152) = c_Transcendental_Oln(U_2153)
| U_2152 != U_2153
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2153))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2152)) ),
inference(clausify,[status(thm)],[f_717_2]) ).
fof(f_718_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),V_x))
| ~ hBOOL(hAPP(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_718_2,plain,
! [U_2154] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2154)),U_2154))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2154)) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
cnf(f_718_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2154)),U_2154))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2154)) ),
inference(clausify,[status(thm)],[f_718_2]) ).
fof(f_719_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]) ).
cnf(f_719_2,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_719_1]) ).
fof(f_720_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_nnf,[status(thm)],[fact_abs__sin__le__one]) ).
fof(f_720_2,plain,
! [U_2155] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(U_2155))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_720_1]) ).
cnf(f_720_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Osin(U_2155))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_720_2]) ).
fof(f_721_1,plain,
! [V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(V_x))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_nnf,[status(thm)],[fact_abs__cos__le__one]) ).
fof(f_721_2,plain,
! [U_2156] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(U_2156))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_721_1]) ).
cnf(f_721_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Transcendental_Ocos(U_2156))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_721_2]) ).
fof(f_722_1,plain,
! [V_a,V_r] : hAPP(c_Complex_OIm,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Osin(V_a)),
inference(fof_nnf,[status(thm)],[fact_Im__rcis]) ).
fof(f_722_2,plain,
! [U_2158,U_2157] : hAPP(c_Complex_OIm,c_Complex_Orcis(U_2157,U_2158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2157),c_Transcendental_Osin(U_2158)),
inference(variable_rename,[status(thm)],[f_722_1]) ).
cnf(f_722_3,plain,
hAPP(c_Complex_OIm,c_Complex_Orcis(U_2157,U_2158)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2157),c_Transcendental_Osin(U_2158)),
inference(clausify,[status(thm)],[f_722_2]) ).
fof(f_723_1,plain,
! [V_a,V_r] : hAPP(c_Complex_ORe,c_Complex_Orcis(V_r,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),c_Transcendental_Ocos(V_a)),
inference(fof_nnf,[status(thm)],[fact_Re__rcis]) ).
fof(f_723_2,plain,
! [U_2160,U_2159] : hAPP(c_Complex_ORe,c_Complex_Orcis(U_2159,U_2160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2159),c_Transcendental_Ocos(U_2160)),
inference(variable_rename,[status(thm)],[f_723_1]) ).
cnf(f_723_3,plain,
hAPP(c_Complex_ORe,c_Complex_Orcis(U_2159,U_2160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2159),c_Transcendental_Ocos(U_2160)),
inference(clausify,[status(thm)],[f_723_2]) ).
fof(f_724_1,plain,
! [V_y_2,V_x_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Transcendental_Oln(V_y_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
| ~ hBOOL(hAPP(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_724_2,plain,
! [U_2162,U_2161] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2161)),c_Transcendental_Oln(U_2162)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2161),U_2162)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2161),U_2162))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2161)),c_Transcendental_Oln(U_2162))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2162))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2161)) ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
cnf(f_724_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2161),U_2162))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2161)),c_Transcendental_Oln(U_2162)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2162))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2161)) ),
inference(clausify,[status(thm)],[f_724_2]) ).
cnf(f_724_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(U_2161)),c_Transcendental_Oln(U_2162)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2161),U_2162))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2162))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2161)) ),
inference(clausify,[status(thm)],[f_724_2]) ).
fof(f_725_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
| ~ hBOOL(hAPP(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_725_2,plain,
! [U_2163] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2163)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2163)) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
cnf(f_725_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2163)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2163)) ),
inference(clausify,[status(thm)],[f_725_2]) ).
fof(f_726_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
| ~ hBOOL(hAPP(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_726_2,plain,
! [U_2164] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2164))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2164))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2164))) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
cnf(f_726_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2164))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2164))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2164))) ),
inference(clausify,[status(thm)],[f_726_2]) ).
fof(f_727_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(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_727_2,plain,
! [U_2165] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2165)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2165),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2165)) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
cnf(f_727_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2165)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2165),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2165)) ),
inference(clausify,[status(thm)],[f_727_2]) ).
fof(f_728_1,plain,
! [V_x_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(V_x_2)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
| ~ hBOOL(hAPP(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_728_2,plain,
! [U_2166] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2166)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2166),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2166),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2166)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2166)) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
cnf(f_728_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2166),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2166)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2166)) ),
inference(clausify,[status(thm)],[f_728_2]) ).
cnf(f_728_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oln(U_2166)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2166),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2166)) ),
inference(clausify,[status(thm)],[f_728_2]) ).
fof(f_729_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) ) )
| ~ hBOOL(hAPP(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_729_2,plain,
! [U_2167] :
( ( ( c_Transcendental_Oln(U_2167) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2167 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( U_2167 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(U_2167) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2167)) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
cnf(f_729_3,plain,
( U_2167 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Transcendental_Oln(U_2167) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2167)) ),
inference(clausify,[status(thm)],[f_729_2]) ).
cnf(f_729_4,plain,
( c_Transcendental_Oln(U_2167) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2167 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2167)) ),
inference(clausify,[status(thm)],[f_729_2]) ).
fof(f_730_1,plain,
! [V_x_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) ) )
| ~ hBOOL(hAPP(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_730_2,plain,
! [U_2168] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2168)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2168)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2168))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2168))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2168)) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
cnf(f_730_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2168))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2168)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2168)) ),
inference(clausify,[status(thm)],[f_730_2]) ).
cnf(f_730_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2168)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2168))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2168)) ),
inference(clausify,[status(thm)],[f_730_2]) ).
fof(f_731_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x)))
| ~ hBOOL(hAPP(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_731_2,plain,
! [U_2169] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2169)) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
cnf(f_731_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2169)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2169)) ),
inference(clausify,[status(thm)],[f_731_2]) ).
fof(f_732_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x))
| ~ hBOOL(hAPP(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_732_2,plain,
! [U_2170] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2170))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2170))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2170))) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
cnf(f_732_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2170))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2170))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2170))) ),
inference(clausify,[status(thm)],[f_732_2]) ).
fof(f_733_1,plain,
! [V_x_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(V_x_2))) ) )
| ~ hBOOL(hAPP(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_733_2,plain,
! [U_2171] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2171)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2171)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2171))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2171))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2171)) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
cnf(f_733_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2171))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2171)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2171)) ),
inference(clausify,[status(thm)],[f_733_2]) ).
cnf(f_733_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Transcendental_Oln(U_2171)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2171))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2171)) ),
inference(clausify,[status(thm)],[f_733_2]) ).
fof(f_734_1,plain,
! [V_y,V_x] :
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(V_x)),c_Transcendental_Oln(V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
| ~ hBOOL(hAPP(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_734_2,plain,
! [U_2173,U_2172] :
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2172),U_2173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(U_2172)),c_Transcendental_Oln(U_2173))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2173))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2172)) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
cnf(f_734_3,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2172),U_2173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Transcendental_Oln(U_2172)),c_Transcendental_Oln(U_2173))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2173))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2172)) ),
inference(clausify,[status(thm)],[f_734_2]) ).
fof(f_735_1,plain,
! [V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x))),V_x))
| ~ hBOOL(hAPP(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_735_2,plain,
! [U_2174] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2174))),U_2174))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2174)) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
cnf(f_735_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oln(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2174))),U_2174))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2174)) ),
inference(clausify,[status(thm)],[f_735_2]) ).
fof(f_736_1,plain,
! [V_y] :
( c_Transcendental_Ocos(c_Transcendental_Oarccos(V_y)) = V_y
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(fof_nnf,[status(thm)],[fact_cos__arccos__abs]) ).
fof(f_736_2,plain,
! [U_2175] :
( c_Transcendental_Ocos(c_Transcendental_Oarccos(U_2175)) = U_2175
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2175)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
cnf(f_736_3,plain,
( c_Transcendental_Ocos(c_Transcendental_Oarccos(U_2175)) = U_2175
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2175)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_736_2]) ).
fof(f_737_1,plain,
! [V_x] :
( ! [B_y] :
? [B_n] : hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_737_2,plain,
! [U_2178] :
( ! [U_2177] :
? [U_2176] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2176)),U_2178)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2178)) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
fof(f_737_3,plain,
! [U_2178] :
( ! [U_2177] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK59(U_2178,U_2177))),U_2178)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2178)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_2176,sK59(U_2178,U_2177))],[f_737_2]) ).
cnf(f_737_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK59(U_2178,U_2177))),U_2178)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2178)) ),
inference(clausify,[status(thm)],[f_737_3]) ).
fof(f_738_1,plain,
! [V_n,V_a] :
( ? [B_r] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),c_Nat_OSuc(V_n)) = V_a
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_r)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth2]) ).
fof(f_738_2,plain,
! [U_2181,U_2180] :
( ? [U_2179] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2179),c_Nat_OSuc(U_2181)) = U_2180
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2179)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2180)) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
! [U_2181,U_2180] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK60(U_2181,U_2180)),c_Nat_OSuc(U_2181)) = U_2180
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK60(U_2181,U_2180))) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2180)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_2179,sK60(U_2181,U_2180))],[f_738_2]) ).
cnf(f_738_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK60(U_2181,U_2180)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2180)) ),
inference(clausify,[status(thm)],[f_738_3]) ).
cnf(f_738_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK60(U_2181,U_2180)),c_Nat_OSuc(U_2181)) = U_2180
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2180)) ),
inference(clausify,[status(thm)],[f_738_3]) ).
fof(f_739_1,plain,
! [V_y,T_a] :
( ? [B_K] :
! [B_x] : hBOOL(hAPP(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_739_2,plain,
! [U_2185,U_2184] :
( ? [U_2183] :
! [U_2182] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2182),U_2185))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2184,U_2182)),U_2183)))
| ~ class_RealVector_Oreal__normed__algebra(U_2184) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
fof(f_739_3,plain,
! [U_2185,U_2184] :
( ! [U_2182] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2182),U_2185))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2184,U_2182)),sK61(U_2185,U_2184))))
| ~ class_RealVector_Oreal__normed__algebra(U_2184) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_2183,sK61(U_2185,U_2184))],[f_739_2]) ).
cnf(f_739_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2184),U_2182),U_2185))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2184,U_2182)),sK61(U_2185,U_2184))))
| ~ class_RealVector_Oreal__normed__algebra(U_2184) ),
inference(clausify,[status(thm)],[f_739_3]) ).
fof(f_740_1,plain,
! [V_x,T_a] :
( ? [B_K] :
! [B_x] : hBOOL(hAPP(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_740_2,plain,
! [U_2189,U_2188] :
( ? [U_2187] :
! [U_2186] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2188,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2186))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2188,U_2186)),U_2187)))
| ~ class_RealVector_Oreal__normed__algebra(U_2188) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
fof(f_740_3,plain,
! [U_2189,U_2188] :
( ! [U_2186] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2188,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2186))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2188,U_2186)),sK62(U_2189,U_2188))))
| ~ class_RealVector_Oreal__normed__algebra(U_2188) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_2187,sK62(U_2189,U_2188))],[f_740_2]) ).
cnf(f_740_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2188,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2186))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2188,U_2186)),sK62(U_2189,U_2188))))
| ~ class_RealVector_Oreal__normed__algebra(U_2188) ),
inference(clausify,[status(thm)],[f_740_3]) ).
fof(f_741_1,plain,
! [T_a] :
( ? [B_K] :
! [B_a,B_b] : hBOOL(hAPP(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_741_2,plain,
! [U_2193] :
( ? [U_2192] :
! [U_2191,U_2190] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2193,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2193),U_2191),U_2190))),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_2193,U_2191)),c_RealVector_Onorm__class_Onorm(U_2193,U_2190))),U_2192)))
| ~ class_RealVector_Oreal__normed__algebra(U_2193) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
fof(f_741_3,plain,
! [U_2193] :
( ! [U_2191,U_2190] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2193,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2193),U_2191),U_2190))),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_2193,U_2191)),c_RealVector_Onorm__class_Onorm(U_2193,U_2190))),sK63(U_2193))))
| ~ class_RealVector_Oreal__normed__algebra(U_2193) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_2192,sK63(U_2193))],[f_741_2]) ).
cnf(f_741_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2193,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2193),U_2191),U_2190))),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_2193,U_2191)),c_RealVector_Onorm__class_Onorm(U_2193,U_2190))),sK63(U_2193))))
| ~ class_RealVector_Oreal__normed__algebra(U_2193) ),
inference(clausify,[status(thm)],[f_741_3]) ).
fof(f_742_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)
| ~ hBOOL(hAPP(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_742_2,plain,
! [U_2196,U_2195,U_2194] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2194),hAPP(hAPP(c_Power_Opower__class_Opower(U_2194),U_2196),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2195,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2196) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2194),U_2196),U_2195)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2195))
| ~ class_Groups_Omonoid__mult(U_2194) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
cnf(f_742_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2194),hAPP(hAPP(c_Power_Opower__class_Opower(U_2194),U_2196),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2195,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2196) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2194),U_2196),U_2195)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2195))
| ~ class_Groups_Omonoid__mult(U_2194) ),
inference(clausify,[status(thm)],[f_742_2]) ).
fof(f_743_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_743_2,plain,
! [U_2197] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2197),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2197,
inference(variable_rename,[status(thm)],[f_743_1]) ).
cnf(f_743_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2197),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2197,
inference(clausify,[status(thm)],[f_743_2]) ).
fof(f_744_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_744_2,plain,
! [U_2199,U_2198] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2198,c_Nat_OSuc(U_2199)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2198,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2199),
inference(variable_rename,[status(thm)],[f_744_1]) ).
cnf(f_744_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2198,c_Nat_OSuc(U_2199)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2198,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2199),
inference(clausify,[status(thm)],[f_744_2]) ).
fof(f_745_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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_745_2,plain,
! [U_2202,U_2201,U_2200] :
( hBOOL(hAPP(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_2200,U_2201),c_RealVector_Onorm__class_Onorm(U_2200,U_2202)))),c_RealVector_Onorm__class_Onorm(U_2200,c_Groups_Ominus__class_Ominus(U_2200,U_2201,U_2202))))
| ~ class_RealVector_Oreal__normed__vector(U_2200) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
cnf(f_745_3,plain,
( hBOOL(hAPP(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_2200,U_2201),c_RealVector_Onorm__class_Onorm(U_2200,U_2202)))),c_RealVector_Onorm__class_Onorm(U_2200,c_Groups_Ominus__class_Ominus(U_2200,U_2201,U_2202))))
| ~ class_RealVector_Oreal__normed__vector(U_2200) ),
inference(clausify,[status(thm)],[f_745_2]) ).
fof(f_746_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(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))) )
& ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_746_2,plain,
! [U_2205,U_2204,U_2203] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,U_2204),U_2205))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,c_Groups_Ominus__class_Ominus(U_2203,U_2204,U_2205)),c_Groups_Ozero__class_Ozero(U_2203))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,c_Groups_Ominus__class_Ominus(U_2203,U_2204,U_2205)),c_Groups_Ozero__class_Ozero(U_2203)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,U_2204),U_2205)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2203) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
cnf(f_746_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,c_Groups_Ominus__class_Ominus(U_2203,U_2204,U_2205)),c_Groups_Ozero__class_Ozero(U_2203)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,U_2204),U_2205))
| ~ class_Groups_Oordered__ab__group__add(U_2203) ),
inference(clausify,[status(thm)],[f_746_2]) ).
cnf(f_746_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,U_2204),U_2205))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2203,c_Groups_Ominus__class_Ominus(U_2203,U_2204,U_2205)),c_Groups_Ozero__class_Ozero(U_2203)))
| ~ class_Groups_Oordered__ab__group__add(U_2203) ),
inference(clausify,[status(thm)],[f_746_2]) ).
fof(f_747_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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_747_2,plain,
! [U_2208,U_2207,U_2206] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2206,U_2207),c_RealVector_Onorm__class_Onorm(U_2206,U_2208))),c_RealVector_Onorm__class_Onorm(U_2206,c_Groups_Ominus__class_Ominus(U_2206,U_2207,U_2208))))
| ~ class_RealVector_Oreal__normed__vector(U_2206) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
cnf(f_747_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2206,U_2207),c_RealVector_Onorm__class_Onorm(U_2206,U_2208))),c_RealVector_Onorm__class_Onorm(U_2206,c_Groups_Ominus__class_Ominus(U_2206,U_2207,U_2208))))
| ~ class_RealVector_Oreal__normed__vector(U_2206) ),
inference(clausify,[status(thm)],[f_747_2]) ).
fof(f_748_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_d_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),V_d_2))
| ~ hBOOL(hAPP(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_c_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_748_2,plain,
! [U_2213,U_2212,U_2211,U_2210,U_2209] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2210),U_2211))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2212),U_2213)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2212),U_2213))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2210),U_2211)) ) )
| c_Groups_Ominus__class_Ominus(U_2209,U_2210,U_2211) != c_Groups_Ominus__class_Ominus(U_2209,U_2212,U_2213)
| ~ class_Groups_Oordered__ab__group__add(U_2209) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
cnf(f_748_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2212),U_2213))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2210),U_2211))
| c_Groups_Ominus__class_Ominus(U_2209,U_2210,U_2211) != c_Groups_Ominus__class_Ominus(U_2209,U_2212,U_2213)
| ~ class_Groups_Oordered__ab__group__add(U_2209) ),
inference(clausify,[status(thm)],[f_748_2]) ).
cnf(f_748_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2210),U_2211))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2209,U_2212),U_2213))
| c_Groups_Ominus__class_Ominus(U_2209,U_2210,U_2211) != c_Groups_Ominus__class_Ominus(U_2209,U_2212,U_2213)
| ~ class_Groups_Oordered__ab__group__add(U_2209) ),
inference(clausify,[status(thm)],[f_748_2]) ).
fof(f_749_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(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_749_2,plain,
! [U_2216,U_2215,U_2214] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),c_Groups_Ominus__class_Ominus(U_2214,U_2215,U_2216)),U_2216) = U_2215
| ~ class_Groups_Ogroup__add(U_2214) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
cnf(f_749_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2214),c_Groups_Ominus__class_Ominus(U_2214,U_2215,U_2216)),U_2216) = U_2215
| ~ class_Groups_Ogroup__add(U_2214) ),
inference(clausify,[status(thm)],[f_749_2]) ).
fof(f_750_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__cancel]) ).
fof(f_750_2,plain,
! [U_2219,U_2218,U_2217] :
( c_Groups_Ominus__class_Ominus(U_2217,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2218),U_2219),U_2219) = U_2218
| ~ class_Groups_Ogroup__add(U_2217) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
cnf(f_750_3,plain,
( c_Groups_Ominus__class_Ominus(U_2217,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2217),U_2218),U_2219),U_2219) = U_2218
| ~ class_Groups_Ogroup__add(U_2217) ),
inference(clausify,[status(thm)],[f_750_2]) ).
fof(f_751_1,plain,
! [V_n,V_m] : hBOOL(hAPP(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_751_2,plain,
! [U_2221,U_2220] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2220,U_2221)),U_2220)),
inference(variable_rename,[status(thm)],[f_751_1]) ).
cnf(f_751_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2220,U_2221)),U_2220)),
inference(clausify,[status(thm)],[f_751_2]) ).
fof(f_752_1,plain,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).
fof(f_752_2,plain,
! [U_2224,U_2223,U_2222] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2224,U_2223)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2224,U_2222)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2222),U_2223)) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
cnf(f_752_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2224,U_2223)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2224,U_2222)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2222),U_2223)) ),
inference(clausify,[status(thm)],[f_752_2]) ).
fof(f_753_1,plain,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).
fof(f_753_2,plain,
! [U_2227,U_2226,U_2225] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2225,U_2227)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2226,U_2227)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2225),U_2226)) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
cnf(f_753_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2225,U_2227)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2226,U_2227)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2225),U_2226)) ),
inference(clausify,[status(thm)],[f_753_2]) ).
fof(f_754_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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).
fof(f_754_2,plain,
! [U_2229,U_2228] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2229,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2229,U_2228)) = U_2228
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2228),U_2229)) ),
inference(variable_rename,[status(thm)],[f_754_1]) ).
cnf(f_754_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2229,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2229,U_2228)) = U_2228
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2228),U_2229)) ),
inference(clausify,[status(thm)],[f_754_2]) ).
fof(f_755_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).
fof(f_755_2,plain,
! [U_2232,U_2231,U_2230] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2231,U_2230) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2232,U_2230)
| U_2231 != U_2232 )
& ( U_2231 = U_2232
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2231,U_2230) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2232,U_2230) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2230),U_2232))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2230),U_2231)) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
cnf(f_755_3,plain,
( U_2231 = U_2232
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2231,U_2230) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2232,U_2230)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2230),U_2232))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2230),U_2231)) ),
inference(clausify,[status(thm)],[f_755_2]) ).
cnf(f_755_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2231,U_2230) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2232,U_2230)
| U_2231 != U_2232
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2230),U_2232))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2230),U_2231)) ),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq]) ).
fof(f_756_2,plain,
! [U_2235,U_2234,U_2233] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2234,U_2233),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2235,U_2233)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2234,U_2235)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2233),U_2235))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2233),U_2234)) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
cnf(f_756_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2234,U_2233),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2235,U_2233)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2234,U_2235)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2233),U_2235))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2233),U_2234)) ),
inference(clausify,[status(thm)],[f_756_2]) ).
fof(f_757_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).
fof(f_757_2,plain,
! [U_2238,U_2237,U_2236] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2237,U_2236)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2238,U_2236)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2237),U_2238)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2237),U_2238))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2237,U_2236)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2238,U_2236))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2236),U_2238))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2236),U_2237)) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
cnf(f_757_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2237),U_2238))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2237,U_2236)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2238,U_2236)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2236),U_2238))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2236),U_2237)) ),
inference(clausify,[status(thm)],[f_757_2]) ).
cnf(f_757_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2237,U_2236)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2238,U_2236)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2237),U_2238))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2236),U_2238))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2236),U_2237)) ),
inference(clausify,[status(thm)],[f_757_2]) ).
fof(f_758_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n),V_n) = V_m,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse2]) ).
fof(f_758_2,plain,
! [U_2240,U_2239] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2239),U_2240),U_2240) = U_2239,
inference(variable_rename,[status(thm)],[f_758_1]) ).
cnf(f_758_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2239),U_2240),U_2240) = U_2239,
inference(clausify,[status(thm)],[f_758_2]) ).
fof(f_759_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_n) = V_m,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse]) ).
fof(f_759_2,plain,
! [U_2242,U_2241] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2241),U_2242),U_2241) = U_2242,
inference(variable_rename,[status(thm)],[f_759_1]) ).
cnf(f_759_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2241),U_2242),U_2241) = U_2242,
inference(clausify,[status(thm)],[f_759_2]) ).
fof(f_760_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).
fof(f_760_2,plain,
! [U_2245,U_2244,U_2243] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2243,U_2244),U_2245) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2243,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2244),U_2245)),
inference(variable_rename,[status(thm)],[f_760_1]) ).
cnf(f_760_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2243,U_2244),U_2245) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2243,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2244),U_2245)),
inference(clausify,[status(thm)],[f_760_2]) ).
fof(f_761_1,plain,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).
fof(f_761_2,plain,
! [U_2248,U_2247,U_2246] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2246),U_2247),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2246),U_2248)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2247,U_2248),
inference(variable_rename,[status(thm)],[f_761_1]) ).
cnf(f_761_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2246),U_2247),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2246),U_2248)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2247,U_2248),
inference(clausify,[status(thm)],[f_761_2]) ).
fof(f_762_1,plain,
! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).
fof(f_762_2,plain,
! [U_2251,U_2250,U_2249] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2249),U_2250),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2251),U_2250)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2249,U_2251),
inference(variable_rename,[status(thm)],[f_762_1]) ).
cnf(f_762_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2249),U_2250),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2251),U_2250)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2249,U_2251),
inference(clausify,[status(thm)],[f_762_2]) ).
fof(f_763_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(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))) )
& ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_763_2,plain,
! [U_2254,U_2253,U_2252] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,U_2253),U_2254))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,c_Groups_Ominus__class_Ominus(U_2252,U_2253,U_2254)),c_Groups_Ozero__class_Ozero(U_2252))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,c_Groups_Ominus__class_Ominus(U_2252,U_2253,U_2254)),c_Groups_Ozero__class_Ozero(U_2252)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,U_2253),U_2254)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2252) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
cnf(f_763_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,c_Groups_Ominus__class_Ominus(U_2252,U_2253,U_2254)),c_Groups_Ozero__class_Ozero(U_2252)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,U_2253),U_2254))
| ~ class_Groups_Oordered__ab__group__add(U_2252) ),
inference(clausify,[status(thm)],[f_763_2]) ).
cnf(f_763_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,U_2253),U_2254))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2252,c_Groups_Ominus__class_Ominus(U_2252,U_2253,U_2254)),c_Groups_Ozero__class_Ozero(U_2252)))
| ~ class_Groups_Oordered__ab__group__add(U_2252) ),
inference(clausify,[status(thm)],[f_763_2]) ).
fof(f_764_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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_764_2,plain,
! [U_2259,U_2258,U_2257,U_2256,U_2255] :
( c_Groups_Ominus__class_Ominus(U_2255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),U_2256),U_2257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),U_2258),U_2259)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2258)),c_Groups_Ominus__class_Ominus(U_2255,U_2257,U_2259))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2258)),U_2259))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),U_2258),c_Groups_Ominus__class_Ominus(U_2255,U_2257,U_2259)))
| ~ class_RealVector_Oreal__normed__algebra(U_2255) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
cnf(f_764_3,plain,
( c_Groups_Ominus__class_Ominus(U_2255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),U_2256),U_2257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),U_2258),U_2259)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2255),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2258)),c_Groups_Ominus__class_Ominus(U_2255,U_2257,U_2259))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2258)),U_2259))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2255),U_2258),c_Groups_Ominus__class_Ominus(U_2255,U_2257,U_2259)))
| ~ class_RealVector_Oreal__normed__algebra(U_2255) ),
inference(clausify,[status(thm)],[f_764_2]) ).
fof(f_765_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(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)
| hAPP(hAPP(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_c_2) != V_d_2 )
& ( hAPP(hAPP(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_c_2) = V_d_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(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_765_2,plain,
! [U_2265,U_2264,U_2263,U_2262,U_2261,U_2260] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2261),U_2262)),U_2263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2264),U_2262)),U_2265)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),c_Groups_Ominus__class_Ominus(U_2260,U_2261,U_2264)),U_2262)),U_2263) != U_2265 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),c_Groups_Ominus__class_Ominus(U_2260,U_2261,U_2264)),U_2262)),U_2263) = U_2265
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2261),U_2262)),U_2263) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2264),U_2262)),U_2265) ) )
| ~ class_Rings_Oring(U_2260) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
cnf(f_765_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),c_Groups_Ominus__class_Ominus(U_2260,U_2261,U_2264)),U_2262)),U_2263) = U_2265
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2261),U_2262)),U_2263) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2264),U_2262)),U_2265)
| ~ class_Rings_Oring(U_2260) ),
inference(clausify,[status(thm)],[f_765_2]) ).
cnf(f_765_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2261),U_2262)),U_2263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),U_2264),U_2262)),U_2265)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2260),c_Groups_Ominus__class_Ominus(U_2260,U_2261,U_2264)),U_2262)),U_2263) != U_2265
| ~ class_Rings_Oring(U_2260) ),
inference(clausify,[status(thm)],[f_765_2]) ).
fof(f_766_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(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_c_2 != hAPP(hAPP(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_c_2 = hAPP(hAPP(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)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(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_766_2,plain,
! [U_2271,U_2270,U_2269,U_2268,U_2267,U_2266] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2267),U_2268)),U_2269) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2270),U_2268)),U_2271)
| U_2269 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),c_Groups_Ominus__class_Ominus(U_2266,U_2270,U_2267)),U_2268)),U_2271) )
& ( U_2269 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),c_Groups_Ominus__class_Ominus(U_2266,U_2270,U_2267)),U_2268)),U_2271)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2267),U_2268)),U_2269) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2270),U_2268)),U_2271) ) )
| ~ class_Rings_Oring(U_2266) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
cnf(f_766_3,plain,
( U_2269 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),c_Groups_Ominus__class_Ominus(U_2266,U_2270,U_2267)),U_2268)),U_2271)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2267),U_2268)),U_2269) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2270),U_2268)),U_2271)
| ~ class_Rings_Oring(U_2266) ),
inference(clausify,[status(thm)],[f_766_2]) ).
cnf(f_766_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2267),U_2268)),U_2269) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2270),U_2268)),U_2271)
| U_2269 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),c_Groups_Ominus__class_Ominus(U_2266,U_2270,U_2267)),U_2268)),U_2271)
| ~ class_Rings_Oring(U_2266) ),
inference(clausify,[status(thm)],[f_766_2]) ).
fof(f_767_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)) = hAPP(hAPP(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_767_2,plain,
! [U_2276,U_2275,U_2274,U_2273,U_2272] :
( c_Groups_Ominus__class_Ominus(U_2272,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),U_2273),U_2274),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),U_2275),U_2276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),U_2273),c_Groups_Ominus__class_Ominus(U_2272,U_2274,U_2276))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),c_Groups_Ominus__class_Ominus(U_2272,U_2273,U_2275)),U_2276))
| ~ class_Rings_Oring(U_2272) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
cnf(f_767_3,plain,
( c_Groups_Ominus__class_Ominus(U_2272,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),U_2273),U_2274),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),U_2275),U_2276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),U_2273),c_Groups_Ominus__class_Ominus(U_2272,U_2274,U_2276))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2272),c_Groups_Ominus__class_Ominus(U_2272,U_2273,U_2275)),U_2276))
| ~ class_Rings_Oring(U_2272) ),
inference(clausify,[status(thm)],[f_767_2]) ).
fof(f_768_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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_768_2,plain,
! [U_2279,U_2278,U_2277] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277,c_Groups_Ominus__class_Ominus(U_2277,c_Groups_Oabs__class_Oabs(U_2277,U_2278),c_Groups_Oabs__class_Oabs(U_2277,U_2279))),c_Groups_Oabs__class_Oabs(U_2277,c_Groups_Ominus__class_Ominus(U_2277,U_2279,U_2278))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2277) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
cnf(f_768_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2277,c_Groups_Ominus__class_Ominus(U_2277,c_Groups_Oabs__class_Oabs(U_2277,U_2278),c_Groups_Oabs__class_Oabs(U_2277,U_2279))),c_Groups_Oabs__class_Oabs(U_2277,c_Groups_Ominus__class_Ominus(U_2277,U_2279,U_2278))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2277) ),
inference(clausify,[status(thm)],[f_768_2]) ).
fof(f_769_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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_769_2,plain,
! [U_2282,U_2281,U_2280] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280,c_Groups_Ominus__class_Ominus(U_2280,c_Groups_Oabs__class_Oabs(U_2280,U_2281),c_Groups_Oabs__class_Oabs(U_2280,U_2282))),c_Groups_Oabs__class_Oabs(U_2280,c_Groups_Ominus__class_Ominus(U_2280,U_2281,U_2282))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2280) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
cnf(f_769_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2280,c_Groups_Ominus__class_Ominus(U_2280,c_Groups_Oabs__class_Oabs(U_2280,U_2281),c_Groups_Oabs__class_Oabs(U_2280,U_2282))),c_Groups_Oabs__class_Oabs(U_2280,c_Groups_Ominus__class_Ominus(U_2280,U_2281,U_2282))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2280) ),
inference(clausify,[status(thm)],[f_769_2]) ).
fof(f_770_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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_770_2,plain,
! [U_2285,U_2284,U_2283] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283,c_Groups_Oabs__class_Oabs(U_2283,c_Groups_Ominus__class_Ominus(U_2283,c_Groups_Oabs__class_Oabs(U_2283,U_2284),c_Groups_Oabs__class_Oabs(U_2283,U_2285)))),c_Groups_Oabs__class_Oabs(U_2283,c_Groups_Ominus__class_Ominus(U_2283,U_2284,U_2285))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2283) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
cnf(f_770_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2283,c_Groups_Oabs__class_Oabs(U_2283,c_Groups_Ominus__class_Ominus(U_2283,c_Groups_Oabs__class_Oabs(U_2283,U_2284),c_Groups_Oabs__class_Oabs(U_2283,U_2285)))),c_Groups_Oabs__class_Oabs(U_2283,c_Groups_Ominus__class_Ominus(U_2283,U_2284,U_2285))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2283) ),
inference(clausify,[status(thm)],[f_770_2]) ).
fof(f_771_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_771_2,plain,
! [U_2288,U_2287,U_2286] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2286,U_2287),U_2288) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2286,U_2288),U_2287),
inference(variable_rename,[status(thm)],[f_771_1]) ).
cnf(f_771_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2286,U_2287),U_2288) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2286,U_2288),U_2287),
inference(clausify,[status(thm)],[f_771_2]) ).
fof(f_772_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = V_b_2
| V_c_2 != V_d_2 )
& ( V_c_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_c_2,V_d_2)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_772_2,plain,
! [U_2293,U_2292,U_2291,U_2290,U_2289] :
( ( ( U_2290 = U_2291
| U_2292 != U_2293 )
& ( U_2292 = U_2293
| U_2290 != U_2291 ) )
| c_Groups_Ominus__class_Ominus(U_2289,U_2290,U_2291) != c_Groups_Ominus__class_Ominus(U_2289,U_2292,U_2293)
| ~ class_Groups_Oab__group__add(U_2289) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
cnf(f_772_3,plain,
( U_2292 = U_2293
| U_2290 != U_2291
| c_Groups_Ominus__class_Ominus(U_2289,U_2290,U_2291) != c_Groups_Ominus__class_Ominus(U_2289,U_2292,U_2293)
| ~ class_Groups_Oab__group__add(U_2289) ),
inference(clausify,[status(thm)],[f_772_2]) ).
cnf(f_772_4,plain,
( U_2290 = U_2291
| U_2292 != U_2293
| c_Groups_Ominus__class_Ominus(U_2289,U_2290,U_2291) != c_Groups_Ominus__class_Ominus(U_2289,U_2292,U_2293)
| ~ class_Groups_Oab__group__add(U_2289) ),
inference(clausify,[status(thm)],[f_772_2]) ).
fof(f_773_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_773_2,plain,
! [U_2296,U_2295,U_2294] :
( c_RealVector_Onorm__class_Onorm(U_2294,c_Groups_Ominus__class_Ominus(U_2294,U_2295,U_2296)) = c_RealVector_Onorm__class_Onorm(U_2294,c_Groups_Ominus__class_Ominus(U_2294,U_2296,U_2295))
| ~ class_RealVector_Oreal__normed__vector(U_2294) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
cnf(f_773_3,plain,
( c_RealVector_Onorm__class_Onorm(U_2294,c_Groups_Ominus__class_Ominus(U_2294,U_2295,U_2296)) = c_RealVector_Onorm__class_Onorm(U_2294,c_Groups_Ominus__class_Ominus(U_2294,U_2296,U_2295))
| ~ class_RealVector_Oreal__normed__vector(U_2294) ),
inference(clausify,[status(thm)],[f_773_2]) ).
fof(f_774_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_774_2,plain,
! [U_2299,U_2298,U_2297] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2297),U_2298),c_Nat_OSuc(U_2299)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2297,U_2298),U_2299),
inference(variable_rename,[status(thm)],[f_774_1]) ).
cnf(f_774_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2297),U_2298),c_Nat_OSuc(U_2299)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2297,U_2298),U_2299),
inference(clausify,[status(thm)],[f_774_2]) ).
fof(f_775_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_775_2,plain,
! [U_2301,U_2300] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2300),c_Nat_OSuc(U_2301)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2300,U_2301),
inference(variable_rename,[status(thm)],[f_775_1]) ).
cnf(f_775_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2300),c_Nat_OSuc(U_2301)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2300,U_2301),
inference(clausify,[status(thm)],[f_775_2]) ).
fof(f_776_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_776_2,plain,
! [U_2303,U_2302] :
( c_Groups_Ominus__class_Ominus(U_2302,U_2303,c_Groups_Ozero__class_Ozero(U_2302)) = U_2303
| ~ class_Groups_Ogroup__add(U_2302) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
cnf(f_776_3,plain,
( c_Groups_Ominus__class_Ominus(U_2302,U_2303,c_Groups_Ozero__class_Ozero(U_2302)) = U_2303
| ~ class_Groups_Ogroup__add(U_2302) ),
inference(clausify,[status(thm)],[f_776_2]) ).
fof(f_777_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_777_2,plain,
! [U_2305,U_2304] :
( c_Groups_Ominus__class_Ominus(U_2304,U_2305,U_2305) = c_Groups_Ozero__class_Ozero(U_2304)
| ~ class_Groups_Ogroup__add(U_2304) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
cnf(f_777_3,plain,
( c_Groups_Ominus__class_Ominus(U_2304,U_2305,U_2305) = c_Groups_Ozero__class_Ozero(U_2304)
| ~ class_Groups_Ogroup__add(U_2304) ),
inference(clausify,[status(thm)],[f_777_2]) ).
fof(f_778_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_778_2,plain,
! [U_2308,U_2307,U_2306] :
( ( ( U_2307 = U_2308
| c_Groups_Ominus__class_Ominus(U_2306,U_2307,U_2308) != c_Groups_Ozero__class_Ozero(U_2306) )
& ( c_Groups_Ominus__class_Ominus(U_2306,U_2307,U_2308) = c_Groups_Ozero__class_Ozero(U_2306)
| U_2307 != U_2308 ) )
| ~ class_Groups_Oab__group__add(U_2306) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
cnf(f_778_3,plain,
( c_Groups_Ominus__class_Ominus(U_2306,U_2307,U_2308) = c_Groups_Ozero__class_Ozero(U_2306)
| U_2307 != U_2308
| ~ class_Groups_Oab__group__add(U_2306) ),
inference(clausify,[status(thm)],[f_778_2]) ).
cnf(f_778_4,plain,
( U_2307 = U_2308
| c_Groups_Ominus__class_Ominus(U_2306,U_2307,U_2308) != c_Groups_Ozero__class_Ozero(U_2306)
| ~ class_Groups_Oab__group__add(U_2306) ),
inference(clausify,[status(thm)],[f_778_2]) ).
fof(f_779_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_779_2,plain,
! [U_2311,U_2310,U_2309] :
( ( ( c_Groups_Ominus__class_Ominus(U_2309,U_2310,U_2311) = c_Groups_Ozero__class_Ozero(U_2309)
| U_2310 != U_2311 )
& ( U_2310 = U_2311
| c_Groups_Ominus__class_Ominus(U_2309,U_2310,U_2311) != c_Groups_Ozero__class_Ozero(U_2309) ) )
| ~ class_Groups_Ogroup__add(U_2309) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
cnf(f_779_3,plain,
( U_2310 = U_2311
| c_Groups_Ominus__class_Ominus(U_2309,U_2310,U_2311) != c_Groups_Ozero__class_Ozero(U_2309)
| ~ class_Groups_Ogroup__add(U_2309) ),
inference(clausify,[status(thm)],[f_779_2]) ).
cnf(f_779_4,plain,
( c_Groups_Ominus__class_Ominus(U_2309,U_2310,U_2311) = c_Groups_Ozero__class_Ozero(U_2309)
| U_2310 != U_2311
| ~ class_Groups_Ogroup__add(U_2309) ),
inference(clausify,[status(thm)],[f_779_2]) ).
fof(f_780_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),V_d_2))
| ~ hBOOL(hAPP(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_c_2,V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_780_2,plain,
! [U_2316,U_2315,U_2314,U_2313,U_2312] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2313),U_2314))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2315),U_2316)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2315),U_2316))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2313),U_2314)) ) )
| c_Groups_Ominus__class_Ominus(U_2312,U_2313,U_2314) != c_Groups_Ominus__class_Ominus(U_2312,U_2315,U_2316)
| ~ class_Groups_Oordered__ab__group__add(U_2312) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
cnf(f_780_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2315),U_2316))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2313),U_2314))
| c_Groups_Ominus__class_Ominus(U_2312,U_2313,U_2314) != c_Groups_Ominus__class_Ominus(U_2312,U_2315,U_2316)
| ~ class_Groups_Oordered__ab__group__add(U_2312) ),
inference(clausify,[status(thm)],[f_780_2]) ).
cnf(f_780_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2313),U_2314))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2312,U_2315),U_2316))
| c_Groups_Ominus__class_Ominus(U_2312,U_2313,U_2314) != c_Groups_Ominus__class_Ominus(U_2312,U_2315,U_2316)
| ~ class_Groups_Oordered__ab__group__add(U_2312) ),
inference(clausify,[status(thm)],[f_780_2]) ).
fof(f_781_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_781_2,plain,
! [U_2317] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2317) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_781_1]) ).
cnf(f_781_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2317) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_781_2]) ).
fof(f_782_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_782_2,plain,
! [U_2318] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2318,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2318,
inference(variable_rename,[status(thm)],[f_782_1]) ).
cnf(f_782_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2318,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2318,
inference(clausify,[status(thm)],[f_782_2]) ).
fof(f_783_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_783_2,plain,
! [U_2319] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2319,U_2319) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_783_1]) ).
cnf(f_783_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2319,U_2319) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_783_2]) ).
fof(f_784_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_784_2,plain,
! [U_2321,U_2320] :
( U_2320 = U_2321
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2321,U_2320) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2320,U_2321) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_784_1]) ).
cnf(f_784_3,plain,
( U_2320 = U_2321
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2321,U_2320) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2320,U_2321) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_784_2]) ).
fof(f_785_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_785_2,plain,
! [U_2324,U_2323,U_2322] :
( c_Groups_Oabs__class_Oabs(U_2322,c_Groups_Ominus__class_Ominus(U_2322,U_2323,U_2324)) = c_Groups_Oabs__class_Oabs(U_2322,c_Groups_Ominus__class_Ominus(U_2322,U_2324,U_2323))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2322) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
cnf(f_785_3,plain,
( c_Groups_Oabs__class_Oabs(U_2322,c_Groups_Ominus__class_Ominus(U_2322,U_2323,U_2324)) = c_Groups_Oabs__class_Oabs(U_2322,c_Groups_Ominus__class_Ominus(U_2322,U_2324,U_2323))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2322) ),
inference(clausify,[status(thm)],[f_785_2]) ).
fof(f_786_1,plain,
! [V_n,V_k,V_j] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n)),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).
fof(f_786_2,plain,
! [U_2327,U_2326,U_2325] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2325,U_2327)),U_2326))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2325),U_2326)) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
cnf(f_786_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2325,U_2327)),U_2326))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2325),U_2326)) ),
inference(clausify,[status(thm)],[f_786_2]) ).
fof(f_787_1,plain,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_l))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).
fof(f_787_2,plain,
! [U_2330,U_2329,U_2328] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2330,U_2329)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2330,U_2328)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2328),U_2330))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2328),U_2329)) ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
cnf(f_787_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2330,U_2329)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2330,U_2328)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2328),U_2330))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2328),U_2329)) ),
inference(clausify,[status(thm)],[f_787_2]) ).
fof(f_788_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_788_2,plain,
! [U_2333,U_2332,U_2331] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2332,U_2333)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2333)),
inference(variable_rename,[status(thm)],[f_788_1]) ).
cnf(f_788_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2332,U_2333)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2332),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2331),U_2333)),
inference(clausify,[status(thm)],[f_788_2]) ).
fof(f_789_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_789_2,plain,
! [U_2336,U_2335,U_2334] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2334,U_2335)),U_2336) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2335),U_2336)),
inference(variable_rename,[status(thm)],[f_789_1]) ).
cnf(f_789_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2334,U_2335)),U_2336) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2334),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2335),U_2336)),
inference(clausify,[status(thm)],[f_789_2]) ).
fof(f_790_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_790_2,plain,
! [U_2340,U_2339,U_2338,U_2337] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),c_Groups_Ominus__class_Ominus(U_2337,U_2338,U_2339)),U_2340) = c_Groups_Ominus__class_Ominus(U_2337,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),U_2338),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),U_2339),U_2340))
| ~ class_RealVector_Oreal__normed__algebra(U_2337) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
cnf(f_790_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),c_Groups_Ominus__class_Ominus(U_2337,U_2338,U_2339)),U_2340) = c_Groups_Ominus__class_Ominus(U_2337,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),U_2338),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),U_2339),U_2340))
| ~ class_RealVector_Oreal__normed__algebra(U_2337) ),
inference(clausify,[status(thm)],[f_790_2]) ).
fof(f_791_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_791_2,plain,
! [U_2344,U_2343,U_2342,U_2341] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),c_Groups_Ominus__class_Ominus(U_2341,U_2342,U_2343)),U_2344) = c_Groups_Ominus__class_Ominus(U_2341,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2344))
| ~ class_RealVector_Oreal__normed__algebra(U_2341) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
cnf(f_791_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),c_Groups_Ominus__class_Ominus(U_2341,U_2342,U_2343)),U_2344) = c_Groups_Ominus__class_Ominus(U_2341,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2342),U_2344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2341),U_2343),U_2344))
| ~ class_RealVector_Oreal__normed__algebra(U_2341) ),
inference(clausify,[status(thm)],[f_791_2]) ).
fof(f_792_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_792_2,plain,
! [U_2348,U_2347,U_2346,U_2345] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),c_Groups_Ominus__class_Ominus(U_2345,U_2347,U_2348)) = c_Groups_Ominus__class_Ominus(U_2345,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),U_2347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),U_2348))
| ~ class_RealVector_Oreal__normed__algebra(U_2345) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
cnf(f_792_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),c_Groups_Ominus__class_Ominus(U_2345,U_2347,U_2348)) = c_Groups_Ominus__class_Ominus(U_2345,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),U_2347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),U_2348))
| ~ class_RealVector_Oreal__normed__algebra(U_2345) ),
inference(clausify,[status(thm)],[f_792_2]) ).
fof(f_793_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_793_2,plain,
! [U_2352,U_2351,U_2350,U_2349] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2349),U_2350),c_Groups_Ominus__class_Ominus(U_2349,U_2351,U_2352)) = c_Groups_Ominus__class_Ominus(U_2349,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2349),U_2350),U_2351),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2349),U_2350),U_2352))
| ~ class_RealVector_Oreal__normed__algebra(U_2349) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
cnf(f_793_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2349),U_2350),c_Groups_Ominus__class_Ominus(U_2349,U_2351,U_2352)) = c_Groups_Ominus__class_Ominus(U_2349,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2349),U_2350),U_2351),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2349),U_2350),U_2352))
| ~ class_RealVector_Oreal__normed__algebra(U_2349) ),
inference(clausify,[status(thm)],[f_793_2]) ).
fof(f_794_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k),V_j)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).
fof(f_794_2,plain,
! [U_2355,U_2354,U_2353] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2355,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2354,U_2353)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2355),U_2353),U_2354)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2353),U_2354)) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
cnf(f_794_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2355,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2354,U_2353)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2355),U_2353),U_2354)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2353),U_2354)) ),
inference(clausify,[status(thm)],[f_794_2]) ).
fof(f_795_1,plain,
! [V_i_2,V_k_2,V_j_2] :
( ( hBOOL(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)))
| ~ hBOOL(hAPP(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_795_2,plain,
! [U_2358,U_2357,U_2356] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2356,U_2357)),U_2358))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2358),U_2357))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2356),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2358),U_2357)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2356,U_2357)),U_2358)) ) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
fof(f_795_3,plain,
( ! [U_2364,U_2362,U_2360] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2360,U_2362)),U_2364))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2364),U_2362))) )
& ! [U_2363,U_2361,U_2359] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2363),U_2361)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2359,U_2361)),U_2363)) ) ),
inference(miniscope,[status(thm)],[f_795_2]) ).
cnf(f_795_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2359),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2363),U_2361)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2359,U_2361)),U_2363)) ),
inference(clausify,[status(thm)],[f_795_3]) ).
cnf(f_795_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2360,U_2362)),U_2364))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2364),U_2362))) ),
inference(clausify,[status(thm)],[f_795_3]) ).
fof(f_796_1,plain,
! [V_m,V_n,V_k] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_k)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).
fof(f_796_2,plain,
! [U_2367,U_2366,U_2365] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2367),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2366),U_2367),U_2365)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2365),U_2366)) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
cnf(f_796_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2367),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2366),U_2367),U_2365)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2365),U_2366)) ),
inference(clausify,[status(thm)],[f_796_2]) ).
fof(f_797_1,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse]) ).
fof(f_797_2,plain,
! [U_2369,U_2368] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2368),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2369,U_2368)) = U_2369
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2368),U_2369)) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
cnf(f_797_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2368),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2369,U_2368)) = U_2369
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2368),U_2369)) ),
inference(clausify,[status(thm)],[f_797_2]) ).
fof(f_798_1,plain,
! [V_i,V_j,V_k] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).
fof(f_798_2,plain,
! [U_2372,U_2371,U_2370] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2372),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2371,U_2370)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2372),U_2371),U_2370)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2370),U_2371)) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
cnf(f_798_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2372),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2371,U_2370)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2372),U_2371),U_2370)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2370),U_2371)) ),
inference(clausify,[status(thm)],[f_798_2]) ).
fof(f_799_1,plain,
! [V_i_2,V_j_2,V_k_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__conv2]) ).
fof(f_799_2,plain,
! [U_2375,U_2374,U_2373] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2375),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2374,U_2373)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2375),U_2373)),U_2374)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2375),U_2373)),U_2374))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2375),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2374,U_2373))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2373),U_2374)) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
cnf(f_799_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2375),U_2373)),U_2374))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2375),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2374,U_2373)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2373),U_2374)) ),
inference(clausify,[status(thm)],[f_799_2]) ).
cnf(f_799_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2375),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2374,U_2373)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2375),U_2373)),U_2374))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2373),U_2374)) ),
inference(clausify,[status(thm)],[f_799_2]) ).
fof(f_800_1,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_n) = V_m
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2]) ).
fof(f_800_2,plain,
! [U_2377,U_2376] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2377,U_2376)),U_2376) = U_2377
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2376),U_2377)) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
cnf(f_800_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2377,U_2376)),U_2376) = U_2377
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2376),U_2377)) ),
inference(clausify,[status(thm)],[f_800_2]) ).
fof(f_801_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 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) )
& ( V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) != V_k_2 ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2),V_j_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add]) ).
fof(f_801_2,plain,
! [U_2380,U_2379,U_2378] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2379,U_2378) = U_2380
| U_2379 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2378) )
& ( U_2379 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2378)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2379,U_2378) != U_2380 ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2378),U_2379)) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
cnf(f_801_3,plain,
( U_2379 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2378)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2379,U_2378) != U_2380
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2378),U_2379)) ),
inference(clausify,[status(thm)],[f_801_2]) ).
cnf(f_801_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2379,U_2378) = U_2380
| U_2379 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2378)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2378),U_2379)) ),
inference(clausify,[status(thm)],[f_801_2]) ).
fof(f_802_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).
fof(f_802_2,plain,
! [U_2383,U_2382,U_2381] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2382),U_2381) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2382,U_2381))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2381),U_2382)) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
cnf(f_802_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2382),U_2381) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2382,U_2381))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2381),U_2382)) ),
inference(clausify,[status(thm)],[f_802_2]) ).
fof(f_803_1,plain,
! [V_i,V_j,V_k] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).
fof(f_803_2,plain,
! [U_2386,U_2385,U_2384] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2385,U_2384)),U_2386) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2386),U_2384)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2384),U_2385)) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
cnf(f_803_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2385,U_2384)),U_2386) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2386),U_2384)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2384),U_2385)) ),
inference(clausify,[status(thm)],[f_803_2]) ).
fof(f_804_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_i)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).
fof(f_804_2,plain,
! [U_2389,U_2388,U_2387] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2388),U_2389),U_2387) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2388,U_2387)),U_2389)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2387),U_2388)) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
cnf(f_804_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2388),U_2389),U_2387) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2388,U_2387)),U_2389)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2387),U_2388)) ),
inference(clausify,[status(thm)],[f_804_2]) ).
fof(f_805_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).
fof(f_805_2,plain,
! [U_2392,U_2391,U_2390] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2391,U_2390)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2392,U_2390)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2391),U_2392)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2391),U_2392))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2391,U_2390)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2392,U_2390))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2390),U_2392))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2390),U_2391)) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
cnf(f_805_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2391),U_2392))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2391,U_2390)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2392,U_2390)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2390),U_2392))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2390),U_2391)) ),
inference(clausify,[status(thm)],[f_805_2]) ).
cnf(f_805_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2391,U_2390)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2392,U_2390)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2391),U_2392))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2390),U_2392))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2390),U_2391)) ),
inference(clausify,[status(thm)],[f_805_2]) ).
fof(f_806_1,plain,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).
fof(f_806_2,plain,
! [U_2395,U_2394,U_2393] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2393,U_2395)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2394,U_2395)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2395),U_2393))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393),U_2394)) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
cnf(f_806_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2393,U_2395)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2394,U_2395)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2395),U_2393))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393),U_2394)) ),
inference(clausify,[status(thm)],[f_806_2]) ).
fof(f_807_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))
| ~ hBOOL(hAPP(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_807_2,plain,
! [U_2398,U_2397,U_2396] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2396),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2397,U_2398)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2396),U_2398)),U_2397)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2396),U_2398)),U_2397))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2396),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2397,U_2398))) ) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
fof(f_807_3,plain,
( ! [U_2404,U_2402,U_2400] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2402,U_2404)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2400),U_2404)),U_2402)) )
& ! [U_2403,U_2401,U_2399] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2399),U_2403)),U_2401))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2399),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2401,U_2403))) ) ),
inference(miniscope,[status(thm)],[f_807_2]) ).
cnf(f_807_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2399),U_2403)),U_2401))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2399),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2401,U_2403))) ),
inference(clausify,[status(thm)],[f_807_3]) ).
cnf(f_807_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2402,U_2404)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2400),U_2404)),U_2402)) ),
inference(clausify,[status(thm)],[f_807_3]) ).
fof(f_808_1,plain,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).
fof(f_808_2,plain,
! [U_2406,U_2405] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2406),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2405,U_2406)) = U_2405
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2405),U_2406)) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
cnf(f_808_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2406),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2405,U_2406)) = U_2405
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2405),U_2406)) ),
inference(clausify,[status(thm)],[f_808_2]) ).
fof(f_809_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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).
fof(f_809_2,plain,
! [U_2408,U_2407] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2408),U_2407) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2408,U_2407))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2407),U_2408)) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
cnf(f_809_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2408),U_2407) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2408,U_2407))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2407),U_2408)) ),
inference(clausify,[status(thm)],[f_809_2]) ).
fof(f_810_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H]) ).
fof(f_810_2,plain,
! [U_2410,U_2409] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2409,U_2410) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2409),U_2410)) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
cnf(f_810_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2409,U_2410) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2409),U_2410)) ),
inference(clausify,[status(thm)],[f_810_2]) ).
fof(f_811_1,plain,
! [V_n_2,V_m_2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),V_n_2))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).
fof(f_811_2,plain,
! [U_2412,U_2411] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2411,U_2412) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2411),U_2412)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2411),U_2412))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2411,U_2412) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
fof(f_811_3,plain,
( ! [U_2416,U_2414] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2414,U_2416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2414),U_2416)) )
& ! [U_2415,U_2413] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413),U_2415))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2413,U_2415) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_811_2]) ).
cnf(f_811_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413),U_2415))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2413,U_2415) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_811_3]) ).
cnf(f_811_5,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2414,U_2416) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2414),U_2416)) ),
inference(clausify,[status(thm)],[f_811_3]) ).
fof(f_812_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_diff__add__0]) ).
fof(f_812_2,plain,
! [U_2418,U_2417] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2417,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2417),U_2418)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_812_1]) ).
cnf(f_812_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2417,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2417),U_2418)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_812_2]) ).
fof(f_813_1,plain,
! [V_n,V_m] : hBOOL(hAPP(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_813_2,plain,
! [U_2420,U_2419] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2419,U_2420)),c_Nat_OSuc(U_2419))),
inference(variable_rename,[status(thm)],[f_813_1]) ).
cnf(f_813_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2419,U_2420)),c_Nat_OSuc(U_2419))),
inference(clausify,[status(thm)],[f_813_2]) ).
fof(f_814_1,plain,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_m))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__less]) ).
fof(f_814_2,plain,
! [U_2422,U_2421] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2422,U_2421)),U_2422))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2422))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2421)) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
cnf(f_814_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2422,U_2421)),U_2422))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2422))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2421)) ),
inference(clausify,[status(thm)],[f_814_2]) ).
fof(f_815_1,plain,
! [V_m_2,V_n_2] :
( ( hBOOL(hAPP(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_m_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),V_n_2))
| ~ hBOOL(hAPP(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_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).
fof(f_815_2,plain,
! [U_2424,U_2423] :
( ( hBOOL(hAPP(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_2423,U_2424)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424),U_2423)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2424),U_2423))
| ~ hBOOL(hAPP(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_2423,U_2424))) ) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
fof(f_815_3,plain,
( ! [U_2428,U_2426] :
( hBOOL(hAPP(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_2426,U_2428)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2428),U_2426)) )
& ! [U_2427,U_2425] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2427),U_2425))
| ~ hBOOL(hAPP(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_2425,U_2427))) ) ),
inference(miniscope,[status(thm)],[f_815_2]) ).
cnf(f_815_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2427),U_2425))
| ~ hBOOL(hAPP(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_2425,U_2427))) ),
inference(clausify,[status(thm)],[f_815_3]) ).
cnf(f_815_5,plain,
( hBOOL(hAPP(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_2426,U_2428)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2428),U_2426)) ),
inference(clausify,[status(thm)],[f_815_3]) ).
fof(f_816_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),hAPP(hAPP(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))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c_2),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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_816_2,plain,
! [U_2434,U_2433,U_2432,U_2431,U_2430,U_2429] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2430),U_2431)),U_2432)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2433),U_2431)),U_2434)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,U_2432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),c_Groups_Ominus__class_Ominus(U_2429,U_2433,U_2430)),U_2431)),U_2434))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,U_2432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),c_Groups_Ominus__class_Ominus(U_2429,U_2433,U_2430)),U_2431)),U_2434)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2430),U_2431)),U_2432)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2433),U_2431)),U_2434))) ) )
| ~ class_Rings_Oordered__ring(U_2429) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
cnf(f_816_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,U_2432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),c_Groups_Ominus__class_Ominus(U_2429,U_2433,U_2430)),U_2431)),U_2434)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2430),U_2431)),U_2432)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2433),U_2431)),U_2434)))
| ~ class_Rings_Oordered__ring(U_2429) ),
inference(clausify,[status(thm)],[f_816_2]) ).
cnf(f_816_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2430),U_2431)),U_2432)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),U_2433),U_2431)),U_2434)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2429,U_2432),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2429),c_Groups_Ominus__class_Ominus(U_2429,U_2433,U_2430)),U_2431)),U_2434)))
| ~ class_Rings_Oordered__ring(U_2429) ),
inference(clausify,[status(thm)],[f_816_2]) ).
fof(f_817_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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_817_2,plain,
! [U_2440,U_2439,U_2438,U_2437,U_2436,U_2435] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2436),U_2437)),U_2438)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2439),U_2437)),U_2440)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),c_Groups_Ominus__class_Ominus(U_2435,U_2436,U_2439)),U_2437)),U_2438)),U_2440)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),c_Groups_Ominus__class_Ominus(U_2435,U_2436,U_2439)),U_2437)),U_2438)),U_2440))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2436),U_2437)),U_2438)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2439),U_2437)),U_2440))) ) )
| ~ class_Rings_Oordered__ring(U_2435) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
cnf(f_817_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),c_Groups_Ominus__class_Ominus(U_2435,U_2436,U_2439)),U_2437)),U_2438)),U_2440))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2436),U_2437)),U_2438)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2439),U_2437)),U_2440)))
| ~ class_Rings_Oordered__ring(U_2435) ),
inference(clausify,[status(thm)],[f_817_2]) ).
cnf(f_817_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2436),U_2437)),U_2438)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),U_2439),U_2437)),U_2440)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2435),c_Groups_Ominus__class_Ominus(U_2435,U_2436,U_2439)),U_2437)),U_2438)),U_2440))
| ~ class_Rings_Oordered__ring(U_2435) ),
inference(clausify,[status(thm)],[f_817_2]) ).
fof(f_818_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(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))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_c_2),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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_818_2,plain,
! [U_2446,U_2445,U_2444,U_2443,U_2442,U_2441] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2442),U_2443)),U_2444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2445),U_2443)),U_2446)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,U_2444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),c_Groups_Ominus__class_Ominus(U_2441,U_2445,U_2442)),U_2443)),U_2446))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,U_2444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),c_Groups_Ominus__class_Ominus(U_2441,U_2445,U_2442)),U_2443)),U_2446)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2442),U_2443)),U_2444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2445),U_2443)),U_2446))) ) )
| ~ class_Rings_Oordered__ring(U_2441) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
cnf(f_818_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,U_2444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),c_Groups_Ominus__class_Ominus(U_2441,U_2445,U_2442)),U_2443)),U_2446)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2442),U_2443)),U_2444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2445),U_2443)),U_2446)))
| ~ class_Rings_Oordered__ring(U_2441) ),
inference(clausify,[status(thm)],[f_818_2]) ).
cnf(f_818_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2442),U_2443)),U_2444)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),U_2445),U_2443)),U_2446)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2441,U_2444),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2441),c_Groups_Ominus__class_Ominus(U_2441,U_2445,U_2442)),U_2443)),U_2446)))
| ~ class_Rings_Oordered__ring(U_2441) ),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(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_819_2,plain,
! [U_2452,U_2451,U_2450,U_2449,U_2448,U_2447] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2448),U_2449)),U_2450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2451),U_2449)),U_2452)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),c_Groups_Ominus__class_Ominus(U_2447,U_2448,U_2451)),U_2449)),U_2450)),U_2452)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),c_Groups_Ominus__class_Ominus(U_2447,U_2448,U_2451)),U_2449)),U_2450)),U_2452))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2448),U_2449)),U_2450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2451),U_2449)),U_2452))) ) )
| ~ class_Rings_Oordered__ring(U_2447) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
cnf(f_819_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),c_Groups_Ominus__class_Ominus(U_2447,U_2448,U_2451)),U_2449)),U_2450)),U_2452))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2448),U_2449)),U_2450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2451),U_2449)),U_2452)))
| ~ class_Rings_Oordered__ring(U_2447) ),
inference(clausify,[status(thm)],[f_819_2]) ).
cnf(f_819_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2448),U_2449)),U_2450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),U_2451),U_2449)),U_2452)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2447,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2447),c_Groups_Ominus__class_Ominus(U_2447,U_2448,U_2451)),U_2449)),U_2450)),U_2452))
| ~ class_Rings_Oordered__ring(U_2447) ),
inference(clausify,[status(thm)],[f_819_2]) ).
fof(f_820_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),hAPP(hAPP(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_820_2,plain,
! [U_2454,U_2453] :
( c_Groups_Ominus__class_Ominus(U_2453,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2454),U_2454),c_Groups_Oone__class_Oone(U_2453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),c_Groups_Oone__class_Oone(U_2453))),c_Groups_Ominus__class_Ominus(U_2453,U_2454,c_Groups_Oone__class_Oone(U_2453)))
| ~ class_Rings_Oring__1(U_2453) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
cnf(f_820_3,plain,
( c_Groups_Ominus__class_Ominus(U_2453,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),U_2454),U_2454),c_Groups_Oone__class_Oone(U_2453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2453),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2453),U_2454),c_Groups_Oone__class_Oone(U_2453))),c_Groups_Ominus__class_Ominus(U_2453,U_2454,c_Groups_Oone__class_Oone(U_2453)))
| ~ class_Rings_Oring__1(U_2453) ),
inference(clausify,[status(thm)],[f_820_2]) ).
fof(f_821_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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))),hAPP(hAPP(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_821_2,plain,
! [U_2457,U_2456,U_2455] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2455,c_Groups_Oabs__class_Oabs(U_2455,c_Groups_Ominus__class_Ominus(U_2455,U_2456,U_2457))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2455),c_Groups_Oabs__class_Oabs(U_2455,U_2456)),c_Groups_Oabs__class_Oabs(U_2455,U_2457))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2455) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
cnf(f_821_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2455,c_Groups_Oabs__class_Oabs(U_2455,c_Groups_Ominus__class_Ominus(U_2455,U_2456,U_2457))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2455),c_Groups_Oabs__class_Oabs(U_2455,U_2456)),c_Groups_Oabs__class_Oabs(U_2455,U_2457))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2455) ),
inference(clausify,[status(thm)],[f_821_2]) ).
fof(f_822_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_822_2,plain,
! [U_2462,U_2461,U_2460,U_2459,U_2458] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458,c_Groups_Oabs__class_Oabs(U_2458,c_Groups_Ominus__class_Ominus(U_2458,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),U_2459),U_2460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),U_2461),U_2462)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),c_Groups_Oabs__class_Oabs(U_2458,c_Groups_Ominus__class_Ominus(U_2458,U_2459,U_2461))),c_Groups_Oabs__class_Oabs(U_2458,c_Groups_Ominus__class_Ominus(U_2458,U_2460,U_2462)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2458) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
cnf(f_822_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458,c_Groups_Oabs__class_Oabs(U_2458,c_Groups_Ominus__class_Ominus(U_2458,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),U_2459),U_2460),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),U_2461),U_2462)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),c_Groups_Oabs__class_Oabs(U_2458,c_Groups_Ominus__class_Ominus(U_2458,U_2459,U_2461))),c_Groups_Oabs__class_Oabs(U_2458,c_Groups_Ominus__class_Ominus(U_2458,U_2460,U_2462)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2458) ),
inference(clausify,[status(thm)],[f_822_2]) ).
fof(f_823_1,plain,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,V_x_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ra_2)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2)),V_x_2)) )
| ~ hBOOL(hAPP(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_823_2,plain,
! [U_2466,U_2465,U_2464,U_2463] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Oabs__class_Oabs(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2464,U_2465))),U_2466))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,U_2464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2463),U_2465),U_2466)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2465,U_2466)),U_2464)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,U_2464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2463),U_2465),U_2466)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2465,U_2466)),U_2464)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Oabs__class_Oabs(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2464,U_2465))),U_2466)) ) )
| ~ class_Rings_Olinordered__idom(U_2463) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
cnf(f_823_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2465,U_2466)),U_2464))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Oabs__class_Oabs(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2464,U_2465))),U_2466))
| ~ class_Rings_Olinordered__idom(U_2463) ),
inference(clausify,[status(thm)],[f_823_2]) ).
cnf(f_823_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,U_2464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2463),U_2465),U_2466)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Oabs__class_Oabs(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2464,U_2465))),U_2466))
| ~ class_Rings_Olinordered__idom(U_2463) ),
inference(clausify,[status(thm)],[f_823_2]) ).
cnf(f_823_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Oabs__class_Oabs(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2464,U_2465))),U_2466))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,U_2464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2463),U_2465),U_2466)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_2463,c_Groups_Ominus__class_Ominus(U_2463,U_2465,U_2466)),U_2464))
| ~ class_Rings_Olinordered__idom(U_2463) ),
inference(clausify,[status(thm)],[f_823_2]) ).
fof(f_824_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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))),hAPP(hAPP(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_824_2,plain,
! [U_2469,U_2468,U_2467] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2467,c_Groups_Ominus__class_Ominus(U_2467,U_2468,U_2469))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2467,U_2468)),c_RealVector_Onorm__class_Onorm(U_2467,U_2469))))
| ~ class_RealVector_Oreal__normed__vector(U_2467) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
cnf(f_824_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2467,c_Groups_Ominus__class_Ominus(U_2467,U_2468,U_2469))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2467,U_2468)),c_RealVector_Onorm__class_Onorm(U_2467,U_2469))))
| ~ class_RealVector_Oreal__normed__vector(U_2467) ),
inference(clausify,[status(thm)],[f_824_2]) ).
fof(f_825_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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).
fof(f_825_2,plain,
! [U_2470] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2470,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2470
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2470)) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
cnf(f_825_3,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2470,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2470
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2470)) ),
inference(clausify,[status(thm)],[f_825_2]) ).
fof(f_826_1,plain,
! [V_i,V_n] :
( hBOOL(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).
fof(f_826_2,plain,
! [U_2472,U_2471] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2471,c_Nat_OSuc(U_2472))),U_2471))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2471)) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
cnf(f_826_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2471,c_Nat_OSuc(U_2472))),U_2471))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2471)) ),
inference(clausify,[status(thm)],[f_826_2]) ).
fof(f_827_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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2)) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(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_827_2,plain,
! [U_2477,U_2476,U_2475] :
( ( hBOOL(hAPP(U_2475,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2476,U_2477)))
| ? [U_2474] :
( ~ hBOOL(hAPP(U_2475,U_2474))
& U_2476 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2477),U_2474) )
| ( ~ hBOOL(hAPP(U_2475,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2476),U_2477)) ) )
& ( ( ! [U_2473] :
( hBOOL(hAPP(U_2475,U_2473))
| U_2476 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2477),U_2473) )
& ( hBOOL(hAPP(U_2475,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2476),U_2477)) ) )
| ~ hBOOL(hAPP(U_2475,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2476,U_2477))) ) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
fof(f_827_3,plain,
( ! [U_2483,U_2481,U_2479] :
( hBOOL(hAPP(U_2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2481,U_2483)))
| ? [U_2474] :
( ~ hBOOL(hAPP(U_2479,U_2474))
& U_2481 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2483),U_2474) )
| ( ~ hBOOL(hAPP(U_2479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2481),U_2483)) ) )
& ! [U_2482,U_2480,U_2478] :
( ( ! [U_2473] :
( hBOOL(hAPP(U_2478,U_2473))
| U_2480 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2482),U_2473) )
& ( hBOOL(hAPP(U_2478,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2480),U_2482)) ) )
| ~ hBOOL(hAPP(U_2478,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2480,U_2482))) ) ),
inference(miniscope,[status(thm)],[f_827_2]) ).
fof(f_827_4,plain,
( ! [U_2483,U_2481,U_2479] :
( hBOOL(hAPP(U_2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2481,U_2483)))
| ( ~ hBOOL(hAPP(U_2479,sK64(U_2483,U_2481,U_2479)))
& U_2481 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2483),sK64(U_2483,U_2481,U_2479)) )
| ( ~ hBOOL(hAPP(U_2479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2481),U_2483)) ) )
& ! [U_2482,U_2480,U_2478] :
( ( ! [U_2473] :
( hBOOL(hAPP(U_2478,U_2473))
| U_2480 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2482),U_2473) )
& ( hBOOL(hAPP(U_2478,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2480),U_2482)) ) )
| ~ hBOOL(hAPP(U_2478,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2480,U_2482))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_2474,sK64(U_2483,U_2481,U_2479))],[f_827_3]) ).
cnf(f_827_5,plain,
( hBOOL(hAPP(U_2478,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2480),U_2482))
| ~ hBOOL(hAPP(U_2478,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2480,U_2482))) ),
inference(clausify,[status(thm)],[f_827_4]) ).
cnf(f_827_6,plain,
( hBOOL(hAPP(U_2478,U_2473))
| U_2480 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2482),U_2473)
| ~ hBOOL(hAPP(U_2478,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2480,U_2482))) ),
inference(clausify,[status(thm)],[f_827_4]) ).
cnf(f_827_7,plain,
( U_2481 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2483),sK64(U_2483,U_2481,U_2479))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2481),U_2483))
| hBOOL(hAPP(U_2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2481,U_2483))) ),
inference(clausify,[status(thm)],[f_827_4]) ).
cnf(f_827_8,plain,
( ~ hBOOL(hAPP(U_2479,sK64(U_2483,U_2481,U_2479)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2481),U_2483))
| hBOOL(hAPP(U_2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2481,U_2483))) ),
inference(clausify,[status(thm)],[f_827_4]) ).
cnf(f_827_9,plain,
( U_2481 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2483),sK64(U_2483,U_2481,U_2479))
| ~ hBOOL(hAPP(U_2479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2481,U_2483))) ),
inference(clausify,[status(thm)],[f_827_4]) ).
cnf(f_827_10,plain,
( ~ hBOOL(hAPP(U_2479,sK64(U_2483,U_2481,U_2479)))
| ~ hBOOL(hAPP(U_2479,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2479,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2481,U_2483))) ),
inference(clausify,[status(thm)],[f_827_4]) ).
fof(f_828_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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2),V_b_2)) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(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_828_2,plain,
! [U_2488,U_2487,U_2486] :
( ( hBOOL(hAPP(U_2486,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2487,U_2488)))
| ? [U_2485] :
( ~ hBOOL(hAPP(U_2486,U_2485))
& U_2487 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2488),U_2485) )
| ( ~ hBOOL(hAPP(U_2486,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2487),U_2488)) ) )
& ( ( ! [U_2484] :
( hBOOL(hAPP(U_2486,U_2484))
| U_2487 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2488),U_2484) )
& ( hBOOL(hAPP(U_2486,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2487),U_2488)) ) )
| ~ hBOOL(hAPP(U_2486,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2487,U_2488))) ) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
fof(f_828_3,plain,
( ! [U_2494,U_2492,U_2490] :
( hBOOL(hAPP(U_2490,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2492,U_2494)))
| ? [U_2485] :
( ~ hBOOL(hAPP(U_2490,U_2485))
& U_2492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2494),U_2485) )
| ( ~ hBOOL(hAPP(U_2490,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2492),U_2494)) ) )
& ! [U_2493,U_2491,U_2489] :
( ( ! [U_2484] :
( hBOOL(hAPP(U_2489,U_2484))
| U_2491 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2493),U_2484) )
& ( hBOOL(hAPP(U_2489,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2491),U_2493)) ) )
| ~ hBOOL(hAPP(U_2489,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2491,U_2493))) ) ),
inference(miniscope,[status(thm)],[f_828_2]) ).
fof(f_828_4,plain,
( ! [U_2494,U_2492,U_2490] :
( hBOOL(hAPP(U_2490,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2492,U_2494)))
| ( ~ hBOOL(hAPP(U_2490,sK65(U_2494,U_2492,U_2490)))
& U_2492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2494),sK65(U_2494,U_2492,U_2490)) )
| ( ~ hBOOL(hAPP(U_2490,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2492),U_2494)) ) )
& ! [U_2493,U_2491,U_2489] :
( ( ! [U_2484] :
( hBOOL(hAPP(U_2489,U_2484))
| U_2491 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2493),U_2484) )
& ( hBOOL(hAPP(U_2489,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2491),U_2493)) ) )
| ~ hBOOL(hAPP(U_2489,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2491,U_2493))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_2485,sK65(U_2494,U_2492,U_2490))],[f_828_3]) ).
cnf(f_828_5,plain,
( hBOOL(hAPP(U_2489,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2491),U_2493))
| ~ hBOOL(hAPP(U_2489,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2491,U_2493))) ),
inference(clausify,[status(thm)],[f_828_4]) ).
cnf(f_828_6,plain,
( hBOOL(hAPP(U_2489,U_2484))
| U_2491 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2493),U_2484)
| ~ hBOOL(hAPP(U_2489,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2491,U_2493))) ),
inference(clausify,[status(thm)],[f_828_4]) ).
cnf(f_828_7,plain,
( U_2492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2494),sK65(U_2494,U_2492,U_2490))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2492),U_2494))
| hBOOL(hAPP(U_2490,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2492,U_2494))) ),
inference(clausify,[status(thm)],[f_828_4]) ).
cnf(f_828_8,plain,
( ~ hBOOL(hAPP(U_2490,sK65(U_2494,U_2492,U_2490)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2492),U_2494))
| hBOOL(hAPP(U_2490,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2492,U_2494))) ),
inference(clausify,[status(thm)],[f_828_4]) ).
cnf(f_828_9,plain,
( U_2492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2494),sK65(U_2494,U_2492,U_2490))
| ~ hBOOL(hAPP(U_2490,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2490,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2492,U_2494))) ),
inference(clausify,[status(thm)],[f_828_4]) ).
cnf(f_828_10,plain,
( ~ hBOOL(hAPP(U_2490,sK65(U_2494,U_2492,U_2490)))
| ~ hBOOL(hAPP(U_2490,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2490,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2492,U_2494))) ),
inference(clausify,[status(thm)],[f_828_4]) ).
fof(f_829_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),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2]) ).
fof(f_829_2,plain,
! [U_2497,U_2496,U_2495] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2496,U_2495)),U_2497) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2496),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2495),U_2497))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2495),U_2496)) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
cnf(f_829_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2496,U_2495)),U_2497) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2496),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2495),U_2497))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2495),U_2496)) ),
inference(clausify,[status(thm)],[f_829_2]) ).
fof(f_830_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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k),c_Nat_OSuc(V_j))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1]) ).
fof(f_830_2,plain,
! [U_2500,U_2499,U_2498] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2500,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2499,U_2498))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2500),U_2498),c_Nat_OSuc(U_2499))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2498),U_2499)) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
cnf(f_830_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2500,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2499,U_2498))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2500),U_2498),c_Nat_OSuc(U_2499))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2498),U_2499)) ),
inference(clausify,[status(thm)],[f_830_2]) ).
fof(f_831_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
| V_m_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2) )
& ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) ) )
| ~ hBOOL(hAPP(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_831_2,plain,
! [U_2505,U_2504,U_2503,U_2502,U_2501] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2504) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2502),U_2503)),U_2505)
| U_2504 != hAPP(hAPP(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_2502,U_2501)),U_2503)),U_2505) )
& ( U_2504 = hAPP(hAPP(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_2502,U_2501)),U_2503)),U_2505)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2504) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2502),U_2503)),U_2505) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2501),U_2502)) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
cnf(f_831_3,plain,
( U_2504 = hAPP(hAPP(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_2502,U_2501)),U_2503)),U_2505)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2504) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2502),U_2503)),U_2505)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2501),U_2502)) ),
inference(clausify,[status(thm)],[f_831_2]) ).
cnf(f_831_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2501),U_2503)),U_2504) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2502),U_2503)),U_2505)
| U_2504 != hAPP(hAPP(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_2502,U_2501)),U_2503)),U_2505)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2501),U_2502)) ),
inference(clausify,[status(thm)],[f_831_2]) ).
fof(f_832_1,plain,
! [V_n,V_m,V_u,V_j,V_i] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u)),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j)) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2]) ).
fof(f_832_2,plain,
! [U_2510,U_2509,U_2508,U_2507,U_2506] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2506),U_2508)),U_2509),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2507),U_2508)),U_2510)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2509,hAPP(hAPP(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_2507,U_2506)),U_2508)),U_2510))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2506),U_2507)) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
cnf(f_832_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2506),U_2508)),U_2509),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2507),U_2508)),U_2510)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2509,hAPP(hAPP(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_2507,U_2506)),U_2508)),U_2510))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2506),U_2507)) ),
inference(clausify,[status(thm)],[f_832_2]) ).
fof(f_833_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
| ~ hBOOL(hAPP(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_833_2,plain,
! [U_2515,U_2514,U_2513,U_2512,U_2511] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2511),U_2513)),U_2514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2512),U_2513)),U_2515)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2514),hAPP(hAPP(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_2512,U_2511)),U_2513)),U_2515))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2514),hAPP(hAPP(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_2512,U_2511)),U_2513)),U_2515)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2511),U_2513)),U_2514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2512),U_2513)),U_2515))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2511),U_2512)) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
cnf(f_833_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2514),hAPP(hAPP(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_2512,U_2511)),U_2513)),U_2515)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2511),U_2513)),U_2514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2512),U_2513)),U_2515)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2511),U_2512)) ),
inference(clausify,[status(thm)],[f_833_2]) ).
cnf(f_833_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2511),U_2513)),U_2514)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2512),U_2513)),U_2515)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2514),hAPP(hAPP(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_2512,U_2511)),U_2513)),U_2515)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2511),U_2512)) ),
inference(clausify,[status(thm)],[f_833_2]) ).
fof(f_834_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2) != V_n_2 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2) = V_n_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) ) )
| ~ hBOOL(hAPP(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_834_2,plain,
! [U_2520,U_2519,U_2518,U_2517,U_2516] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2517),U_2518)),U_2519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2516),U_2518)),U_2520)
| hAPP(hAPP(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_2517,U_2516)),U_2518)),U_2519) != U_2520 )
& ( hAPP(hAPP(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_2517,U_2516)),U_2518)),U_2519) = U_2520
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2517),U_2518)),U_2519) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2516),U_2518)),U_2520) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2516),U_2517)) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
cnf(f_834_3,plain,
( hAPP(hAPP(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_2517,U_2516)),U_2518)),U_2519) = U_2520
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2517),U_2518)),U_2519) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2516),U_2518)),U_2520)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2516),U_2517)) ),
inference(clausify,[status(thm)],[f_834_2]) ).
cnf(f_834_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2517),U_2518)),U_2519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2516),U_2518)),U_2520)
| hAPP(hAPP(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_2517,U_2516)),U_2518)),U_2519) != U_2520
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2516),U_2517)) ),
inference(clausify,[status(thm)],[f_834_2]) ).
fof(f_835_1,plain,
! [V_n,V_m,V_u,V_i,V_j] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u)),V_m),V_n)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_i)) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1]) ).
fof(f_835_2,plain,
! [U_2525,U_2524,U_2523,U_2522,U_2521] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2522),U_2523)),U_2524),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2521),U_2523)),U_2525)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2522,U_2521)),U_2523)),U_2524),U_2525)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2521),U_2522)) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
cnf(f_835_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2522),U_2523)),U_2524),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2521),U_2523)),U_2525)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2522,U_2521)),U_2523)),U_2524),U_2525)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2521),U_2522)) ),
inference(clausify,[status(thm)],[f_835_2]) ).
fof(f_836_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
| ~ hBOOL(hAPP(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_836_2,plain,
! [U_2530,U_2529,U_2528,U_2527,U_2526] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2527),U_2528)),U_2529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2526),U_2528)),U_2530)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2527,U_2526)),U_2528)),U_2529)),U_2530)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2527,U_2526)),U_2528)),U_2529)),U_2530))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2527),U_2528)),U_2529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2526),U_2528)),U_2530))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2526),U_2527)) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
cnf(f_836_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2527,U_2526)),U_2528)),U_2529)),U_2530))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2527),U_2528)),U_2529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2526),U_2528)),U_2530)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2526),U_2527)) ),
inference(clausify,[status(thm)],[f_836_2]) ).
cnf(f_836_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2527),U_2528)),U_2529)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2526),U_2528)),U_2530)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2527,U_2526)),U_2528)),U_2529)),U_2530))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2526),U_2527)) ),
inference(clausify,[status(thm)],[f_836_2]) ).
fof(f_837_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(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_837_2,plain,
! [U_2535,U_2534,U_2533,U_2532,U_2531] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Ominus__class_Ominus(U_2531,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2531),U_2532),U_2533),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2531),U_2534),U_2535)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Ominus__class_Ominus(U_2531,U_2532,U_2534))),c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Ominus__class_Ominus(U_2531,U_2533,U_2535)))))
| ~ class_RealVector_Oreal__normed__vector(U_2531) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
cnf(f_837_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Ominus__class_Ominus(U_2531,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2531),U_2532),U_2533),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2531),U_2534),U_2535)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Ominus__class_Ominus(U_2531,U_2532,U_2534))),c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Ominus__class_Ominus(U_2531,U_2533,U_2535)))))
| ~ class_RealVector_Oreal__normed__vector(U_2531) ),
inference(clausify,[status(thm)],[f_837_2]) ).
fof(f_838_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)
| ~ hBOOL(hAPP(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_838_2,plain,
! [U_2539,U_2538,U_2537,U_2536] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2536),U_2539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2538),U_2537)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2536),hAPP(hAPP(c_Power_Opower__class_Opower(U_2536),U_2539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2538,U_2537))),U_2539)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2537),U_2538))
| ~ class_Groups_Omonoid__mult(U_2536) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
cnf(f_838_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2536),U_2539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2538),U_2537)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2536),hAPP(hAPP(c_Power_Opower__class_Opower(U_2536),U_2539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2538,U_2537))),U_2539)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2537),U_2538))
| ~ class_Groups_Omonoid__mult(U_2536) ),
inference(clausify,[status(thm)],[f_838_2]) ).
fof(f_839_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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred_H]) ).
fof(f_839_2,plain,
! [U_2540] :
( U_2540 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2540,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2540)) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
cnf(f_839_3,plain,
( U_2540 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2540,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2540)) ),
inference(clausify,[status(thm)],[f_839_2]) ).
fof(f_840_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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__1]) ).
fof(f_840_2,plain,
! [U_2541] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2541,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2541
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2541)) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
cnf(f_840_3,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2541,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2541
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2541)) ),
inference(clausify,[status(thm)],[f_840_2]) ).
fof(f_841_1,plain,
! [V_n,V_m] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = c_Nat_OSuc(hAPP(hAPP(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) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__if]) ).
fof(f_841_2,plain,
! [U_2543,U_2542] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2542),U_2543) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2542,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2543))
| U_2542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2542),U_2543) = U_2543
| U_2542 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
fof(f_841_3,plain,
( ! [U_2547,U_2545] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2545),U_2547) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2545,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2547))
| U_2545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2546,U_2544] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2544),U_2546) = U_2546
| U_2544 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_841_2]) ).
cnf(f_841_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2544),U_2546) = U_2546
| U_2544 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_841_3]) ).
cnf(f_841_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2545),U_2547) = c_Nat_OSuc(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2545,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2547))
| U_2545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_841_3]) ).
fof(f_842_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2)),V_m_2)),V_n_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
| ~ hBOOL(hAPP(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_842_2,plain,
! [U_2552,U_2551,U_2550,U_2549,U_2548] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2550)),U_2551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2550)),U_2552)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,U_2548)),U_2550)),U_2551)),U_2552)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,U_2548)),U_2550)),U_2551)),U_2552))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2550)),U_2551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2550)),U_2552))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2548),U_2549)) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
cnf(f_842_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,U_2548)),U_2550)),U_2551)),U_2552))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2550)),U_2551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2550)),U_2552)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2548),U_2549)) ),
inference(clausify,[status(thm)],[f_842_2]) ).
cnf(f_842_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2549),U_2550)),U_2551)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2548),U_2550)),U_2552)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,U_2548)),U_2550)),U_2551)),U_2552))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2548),U_2549)) ),
inference(clausify,[status(thm)],[f_842_2]) ).
fof(f_843_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2)),V_n_2)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
| ~ hBOOL(hAPP(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_843_2,plain,
! [U_2557,U_2556,U_2555,U_2554,U_2553] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2553),U_2555)),U_2556)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2554),U_2555)),U_2557)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2556),hAPP(hAPP(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_2554,U_2553)),U_2555)),U_2557))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2556),hAPP(hAPP(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_2554,U_2553)),U_2555)),U_2557)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2553),U_2555)),U_2556)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2554),U_2555)),U_2557))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2553),U_2554)) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
cnf(f_843_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2556),hAPP(hAPP(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_2554,U_2553)),U_2555)),U_2557)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2553),U_2555)),U_2556)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2554),U_2555)),U_2557)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2553),U_2554)) ),
inference(clausify,[status(thm)],[f_843_2]) ).
cnf(f_843_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2553),U_2555)),U_2556)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2554),U_2555)),U_2557)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2556),hAPP(hAPP(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_2554,U_2553)),U_2555)),U_2557)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2553),U_2554)) ),
inference(clausify,[status(thm)],[f_843_2]) ).
fof(f_844_1,plain,
! [V_n,V_m] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_844_2,plain,
! [U_2559,U_2558] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2559) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2558,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2559))
| U_2558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2558),U_2559) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2558 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
fof(f_844_3,plain,
( ! [U_2563,U_2561] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2561),U_2563) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2561,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2563))
| U_2561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2562,U_2560] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2560 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_844_2]) ).
cnf(f_844_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2560),U_2562) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2560 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_844_3]) ).
cnf(f_844_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2561),U_2563) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2563),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2561,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2563))
| U_2561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_844_3]) ).
fof(f_845_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_845_2,plain,
! [U_2565,U_2564] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2565),U_2564) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2565),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2565),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2564,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2564 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2565),U_2564) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2564 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
fof(f_845_3,plain,
( ! [U_2569,U_2567] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2569),U_2567) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2569),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2567,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2568,U_2566] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2568),U_2566) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2566 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_845_2]) ).
cnf(f_845_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2568),U_2566) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2566 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_845_3]) ).
cnf(f_845_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2569),U_2567) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2569),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2569),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2567,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_845_3]) ).
fof(f_846_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)),hAPP(hAPP(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_846_2,plain,
! [U_2572,U_2571,U_2570] :
( c_Groups_Ominus__class_Ominus(U_2570,hAPP(hAPP(c_Power_Opower__class_Opower(U_2570),U_2571),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2570),U_2572),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2570),c_Groups_Ominus__class_Ominus(U_2570,U_2571,U_2572)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2570),U_2571),U_2572))
| ~ class_Rings_Ocomm__ring__1(U_2570) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
cnf(f_846_3,plain,
( c_Groups_Ominus__class_Ominus(U_2570,hAPP(hAPP(c_Power_Opower__class_Opower(U_2570),U_2571),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2570),U_2572),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2570),c_Groups_Ominus__class_Ominus(U_2570,U_2571,U_2572)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2570),U_2571),U_2572))
| ~ class_Rings_Ocomm__ring__1(U_2570) ),
inference(clausify,[status(thm)],[f_846_2]) ).
fof(f_847_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_847_2,plain,
! [U_2575,U_2574,U_2573] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2573),U_2575),U_2574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2573),U_2575),hAPP(hAPP(c_Power_Opower__class_Opower(U_2573),U_2575),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2574,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2573),U_2575),U_2574) = c_Groups_Oone__class_Oone(U_2573)
| U_2574 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Power_Opower(U_2573) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
cnf(f_847_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2573),U_2575),U_2574) = c_Groups_Oone__class_Oone(U_2573)
| U_2574 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(U_2573) ),
inference(clausify,[status(thm)],[f_847_2]) ).
cnf(f_847_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2573),U_2575),U_2574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2573),U_2575),hAPP(hAPP(c_Power_Opower__class_Opower(U_2573),U_2575),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2574,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(U_2573) ),
inference(clausify,[status(thm)],[f_847_2]) ).
fof(f_848_1,plain,
! [V_r] :
( ? [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r),c_RealDef_Oreal(tc_Nat_Onat,B_n)))
& hBOOL(hAPP(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)) )
| ~ hBOOL(hAPP(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_848_2,plain,
! [U_2577] :
( ? [U_2576] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2577),c_RealDef_Oreal(tc_Nat_Onat,U_2576)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2576,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2577)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2577)) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
! [U_2577] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2577),c_RealDef_Oreal(tc_Nat_Onat,sK66(U_2577))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK66(U_2577),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2577)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2577)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_2576,sK66(U_2577))],[f_848_2]) ).
cnf(f_848_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK66(U_2577),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2577))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2577)) ),
inference(clausify,[status(thm)],[f_848_3]) ).
cnf(f_848_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2577),c_RealDef_Oreal(tc_Nat_Onat,sK66(U_2577))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2577)) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_1,plain,
! [V_X_2,V_M_2,T_a,T_b] :
( ! [B_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n))),hAPP(hAPP(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)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_M_2),B_n)) )
| ? [B_n] :
( ~ hBOOL(hAPP(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)))
& hBOOL(hAPP(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_849_2,plain,
! [U_2583,U_2582,U_2581,U_2580] :
( ! [U_2579] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2579))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2582)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2581,U_2582),U_2579)) )
| ? [U_2578] :
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2580,c_Groups_Ominus__class_Ominus(U_2580,hAPP(U_2583,U_2582),hAPP(U_2583,U_2578)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2581,U_2582),U_2578)) )
| ~ class_Orderings_Oord(U_2581)
| ~ class_RealVector_Oreal__normed__vector(U_2580) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
! [U_2583,U_2582,U_2581,U_2580] :
( ! [U_2579] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2579))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2582)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2581,U_2582),U_2579)) )
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2580,c_Groups_Ominus__class_Ominus(U_2580,hAPP(U_2583,U_2582),hAPP(U_2583,sK67(U_2583,U_2582,U_2581,U_2580))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2581,U_2582),sK67(U_2583,U_2582,U_2581,U_2580))) )
| ~ class_Orderings_Oord(U_2581)
| ~ class_RealVector_Oreal__normed__vector(U_2580) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_2578,sK67(U_2583,U_2582,U_2581,U_2580))],[f_849_2]) ).
cnf(f_849_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2581,U_2582),sK67(U_2583,U_2582,U_2581,U_2580)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2579))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2582)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2581,U_2582),U_2579))
| ~ class_Orderings_Oord(U_2581)
| ~ class_RealVector_Oreal__normed__vector(U_2580) ),
inference(clausify,[status(thm)],[f_849_3]) ).
cnf(f_849_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2580,c_Groups_Ominus__class_Ominus(U_2580,hAPP(U_2583,U_2582),hAPP(U_2583,sK67(U_2583,U_2582,U_2581,U_2580))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2579))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(U_2580,hAPP(U_2583,U_2582)))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_2581,U_2582),U_2579))
| ~ class_Orderings_Oord(U_2581)
| ~ class_RealVector_Oreal__normed__vector(U_2580) ),
inference(clausify,[status(thm)],[f_849_3]) ).
fof(f_850_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),V_y_2))
| ~ hBOOL(hAPP(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))) )
& ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(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_850_2,plain,
! [U_2585,U_2584] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2584),U_2585))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2584,U_2585)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2584,U_2585)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2584),U_2585)) ) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
fof(f_850_3,plain,
( ! [U_2589,U_2587] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2587),U_2589))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2587,U_2589)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) )
& ! [U_2588,U_2586] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2586,U_2588)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2586),U_2588)) ) ),
inference(miniscope,[status(thm)],[f_850_2]) ).
cnf(f_850_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2586,U_2588)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2586),U_2588)) ),
inference(clausify,[status(thm)],[f_850_3]) ).
cnf(f_850_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2587),U_2589))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2587,U_2589)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_850_3]) ).
fof(f_851_1,plain,
! [V_y,V_x] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)),
inference(fof_nnf,[status(thm)],[fact_Im_Odiff]) ).
fof(f_851_2,plain,
! [U_2591,U_2590] : hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2590,U_2591)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_2590),hAPP(c_Complex_OIm,U_2591)),
inference(variable_rename,[status(thm)],[f_851_1]) ).
cnf(f_851_3,plain,
hAPP(c_Complex_OIm,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2590,U_2591)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_2590),hAPP(c_Complex_OIm,U_2591)),
inference(clausify,[status(thm)],[f_851_2]) ).
fof(f_852_1,plain,
! [V_y,V_x] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)),
inference(fof_nnf,[status(thm)],[fact_Re_Odiff]) ).
fof(f_852_2,plain,
! [U_2593,U_2592] : hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2592,U_2593)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_2592),hAPP(c_Complex_ORe,U_2593)),
inference(variable_rename,[status(thm)],[f_852_1]) ).
cnf(f_852_3,plain,
hAPP(c_Complex_ORe,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2592,U_2593)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_2592),hAPP(c_Complex_ORe,U_2593)),
inference(clausify,[status(thm)],[f_852_2]) ).
fof(f_853_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_853_2,plain,
! [U_2596,U_2595,U_2594] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2594),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2595,U_2596)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2594),U_2595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2594),U_2596)),
inference(variable_rename,[status(thm)],[f_853_1]) ).
cnf(f_853_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2594),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2595,U_2596)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2594),U_2595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2594),U_2596)),
inference(clausify,[status(thm)],[f_853_2]) ).
fof(f_854_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_854_2,plain,
! [U_2599,U_2598,U_2597] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2597,U_2598)),U_2599) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2597),U_2599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2598),U_2599)),
inference(variable_rename,[status(thm)],[f_854_1]) ).
cnf(f_854_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2597,U_2598)),U_2599) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2597),U_2599),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2598),U_2599)),
inference(clausify,[status(thm)],[f_854_2]) ).
fof(f_855_1,plain,
! [V_l_2,V_k_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2))
| ~ hBOOL(hAPP(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))) )
& ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).
fof(f_855_2,plain,
! [U_2601,U_2600] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2600),U_2601))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2600,U_2601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2600,U_2601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2600),U_2601)) ) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
fof(f_855_3,plain,
( ! [U_2605,U_2603] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2603),U_2605))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2603,U_2605)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_2604,U_2602] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2602,U_2604)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2602),U_2604)) ) ),
inference(miniscope,[status(thm)],[f_855_2]) ).
cnf(f_855_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2602,U_2604)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2602),U_2604)) ),
inference(clausify,[status(thm)],[f_855_3]) ).
cnf(f_855_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2603),U_2605))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2603,U_2605)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_855_3]) ).
fof(f_856_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(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,hAPP(hAPP(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_856_2,plain,
! [U_2608,U_2607,U_2606] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2606,U_2607),c_RealVector_Onorm__class_Onorm(U_2606,U_2608))),c_RealVector_Onorm__class_Onorm(U_2606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2606),U_2607),U_2608))))
| ~ class_RealVector_Oreal__normed__vector(U_2606) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
cnf(f_856_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2606,U_2607),c_RealVector_Onorm__class_Onorm(U_2606,U_2608))),c_RealVector_Onorm__class_Onorm(U_2606,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2606),U_2607),U_2608))))
| ~ class_RealVector_Oreal__normed__vector(U_2606) ),
inference(clausify,[status(thm)],[f_856_2]) ).
fof(f_857_1,plain,
! [V_y,V_x] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,V_x),hAPP(c_Complex_ORe,V_y)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,V_x),hAPP(c_Complex_OIm,V_y)))))),
inference(fof_nnf,[status(thm)],[fact_metric__bound__lemma]) ).
fof(f_857_2,plain,
! [U_2610,U_2609] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2609,U_2610))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_2609),hAPP(c_Complex_ORe,U_2610)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_2609),hAPP(c_Complex_OIm,U_2610)))))),
inference(variable_rename,[status(thm)],[f_857_1]) ).
cnf(f_857_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2609,U_2610))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_ORe,U_2609),hAPP(c_Complex_ORe,U_2610)))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(c_Complex_OIm,U_2609),hAPP(c_Complex_OIm,U_2610)))))),
inference(clausify,[status(thm)],[f_857_2]) ).
fof(f_858_1,plain,
! [V_z_2,V_w_2] :
( ( hBOOL(hAPP(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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2),V_z_2))
| ~ hBOOL(hAPP(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_858_2,plain,
! [U_2612,U_2611] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2611),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2612,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2611),U_2612)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2611),U_2612))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2611),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2612,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
fof(f_858_3,plain,
( ! [U_2616,U_2614] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2614),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2616,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2614),U_2616)) )
& ! [U_2615,U_2613] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2613),U_2615))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2613),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2615,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_858_2]) ).
cnf(f_858_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2613),U_2615))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2613),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2615,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_858_3]) ).
cnf(f_858_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2614),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2616,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2614),U_2616)) ),
inference(clausify,[status(thm)],[f_858_3]) ).
fof(f_859_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))
| ~ hBOOL(hAPP(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_859_2,plain,
! [U_2618,U_2617] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2618,U_2617)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2618),c_RealDef_Oreal(tc_Nat_Onat,U_2617))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2617),U_2618)) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
cnf(f_859_3,plain,
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2618,U_2617)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2618),c_RealDef_Oreal(tc_Nat_Onat,U_2617))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2617),U_2618)) ),
inference(clausify,[status(thm)],[f_859_2]) ).
fof(f_860_1,plain,
! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Osin(V_y))),
inference(fof_nnf,[status(thm)],[fact_sin__diff]) ).
fof(f_860_2,plain,
! [U_2620,U_2619] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2619,U_2620)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2619)),c_Transcendental_Ocos(U_2620)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2619)),c_Transcendental_Osin(U_2620))),
inference(variable_rename,[status(thm)],[f_860_1]) ).
cnf(f_860_3,plain,
c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2619,U_2620)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2619)),c_Transcendental_Ocos(U_2620)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2619)),c_Transcendental_Osin(U_2620))),
inference(clausify,[status(thm)],[f_860_2]) ).
fof(f_861_1,plain,
! [V_y,V_x] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Osin(V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Ocos(V_x))),
inference(fof_nnf,[status(thm)],[fact_sin__diff2]) ).
fof(f_861_2,plain,
! [U_2622,U_2621] : c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2621,U_2622)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2622)),c_Transcendental_Osin(U_2621)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2622)),c_Transcendental_Ocos(U_2621))),
inference(variable_rename,[status(thm)],[f_861_1]) ).
cnf(f_861_3,plain,
c_Transcendental_Osin(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2621,U_2622)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2622)),c_Transcendental_Osin(U_2621)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2622)),c_Transcendental_Ocos(U_2621))),
inference(clausify,[status(thm)],[f_861_2]) ).
fof(f_862_1,plain,
! [V_a,V_b] : hBOOL(hAPP(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,hAPP(hAPP(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_862_2,plain,
! [U_2624,U_2623] : hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2623),U_2624)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2623))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2624))),
inference(variable_rename,[status(thm)],[f_862_1]) ).
cnf(f_862_3,plain,
hBOOL(hAPP(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,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2623),U_2624)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2623))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2624))),
inference(clausify,[status(thm)],[f_862_2]) ).
fof(f_863_1,plain,
! [V_y,V_x] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))),
inference(fof_nnf,[status(thm)],[fact_cos__add]) ).
fof(f_863_2,plain,
! [U_2626,U_2625] : c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2625),U_2626)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2625)),c_Transcendental_Ocos(U_2626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2625)),c_Transcendental_Osin(U_2626))),
inference(variable_rename,[status(thm)],[f_863_1]) ).
cnf(f_863_3,plain,
c_Transcendental_Ocos(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2625),U_2626)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2625)),c_Transcendental_Ocos(U_2626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2625)),c_Transcendental_Osin(U_2626))),
inference(clausify,[status(thm)],[f_863_2]) ).
fof(f_864_1,plain,
! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_x)),c_Transcendental_Ocos(V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_x)),c_Transcendental_Osin(V_y))),
inference(fof_nnf,[status(thm)],[fact_cos__diff]) ).
fof(f_864_2,plain,
! [U_2628,U_2627] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2627,U_2628)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2627)),c_Transcendental_Ocos(U_2628))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2627)),c_Transcendental_Osin(U_2628))),
inference(variable_rename,[status(thm)],[f_864_1]) ).
cnf(f_864_3,plain,
c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2627,U_2628)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2627)),c_Transcendental_Ocos(U_2628))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2627)),c_Transcendental_Osin(U_2628))),
inference(clausify,[status(thm)],[f_864_2]) ).
fof(f_865_1,plain,
! [V_y,V_x] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(V_y)),c_Transcendental_Ocos(V_x))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(V_y)),c_Transcendental_Osin(V_x))),
inference(fof_nnf,[status(thm)],[fact_cos__diff2]) ).
fof(f_865_2,plain,
! [U_2630,U_2629] : c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2629,U_2630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2630)),c_Transcendental_Ocos(U_2629))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2630)),c_Transcendental_Osin(U_2629))),
inference(variable_rename,[status(thm)],[f_865_1]) ).
cnf(f_865_3,plain,
c_Transcendental_Ocos(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2629,U_2630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Ocos(U_2630)),c_Transcendental_Ocos(U_2629))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Transcendental_Osin(U_2630)),c_Transcendental_Osin(U_2629))),
inference(clausify,[status(thm)],[f_865_2]) ).
fof(f_866_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)
| ~ hBOOL(hAPP(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_866_2,plain,
! [U_2632,U_2631] :
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2632,c_RealDef_Oreal(tc_Nat_Onat,U_2631))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2632),U_2631)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2631)),U_2632)) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
cnf(f_866_3,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2632,c_RealDef_Oreal(tc_Nat_Onat,U_2631))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2632),U_2631)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2631)),U_2632)) ),
inference(clausify,[status(thm)],[f_866_2]) ).
fof(f_867_1,plain,
! [V_x] : hBOOL(hAPP(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_867_2,plain,
! [U_2633] : hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2633,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2633)))),
inference(variable_rename,[status(thm)],[f_867_1]) ).
cnf(f_867_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2633,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2633)))),
inference(clausify,[status(thm)],[f_867_2]) ).
fof(f_868_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)
| ~ hBOOL(hAPP(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_868_2,plain,
! [U_2635,U_2634] :
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2635,c_RealDef_Oreal(tc_Nat_Onat,U_2634))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2635),U_2634)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2634)),U_2635)) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
cnf(f_868_3,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2635,c_RealDef_Oreal(tc_Nat_Onat,U_2634))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2635),U_2634)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2634)),U_2635)) ),
inference(clausify,[status(thm)],[f_868_2]) ).
fof(f_869_1,plain,
! [V_y,V_x] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),
inference(fof_nnf,[status(thm)],[fact_complex__Re__mult]) ).
fof(f_869_2,plain,
! [U_2637,U_2636] : hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2636),U_2637)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2636)),hAPP(c_Complex_ORe,U_2637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2636)),hAPP(c_Complex_OIm,U_2637))),
inference(variable_rename,[status(thm)],[f_869_1]) ).
cnf(f_869_3,plain,
hAPP(c_Complex_ORe,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2636),U_2637)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2636)),hAPP(c_Complex_ORe,U_2637)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2636)),hAPP(c_Complex_OIm,U_2637))),
inference(clausify,[status(thm)],[f_869_2]) ).
fof(f_870_1,plain,
! [V_z,V_x,V_d] :
( hBOOL(hAPP(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),hAPP(hAPP(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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
inference(fof_nnf,[status(thm)],[fact_decr__lemma]) ).
fof(f_870_2,plain,
! [U_2640,U_2639,U_2638] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(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_2639,U_2640))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2638))),U_2640))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2638)) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
cnf(f_870_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(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_2639,U_2640))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2638))),U_2640))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2638)) ),
inference(clausify,[status(thm)],[f_870_2]) ).
fof(f_871_1,plain,
! [V_x,V_z,V_d] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
inference(fof_nnf,[status(thm)],[fact_incr__lemma]) ).
fof(f_871_2,plain,
! [U_2643,U_2642,U_2641] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(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_2643,U_2642))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2641))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2641)) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
cnf(f_871_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(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_2643,U_2642))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2641))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2641)) ),
inference(clausify,[status(thm)],[f_871_2]) ).
fof(f_872_1,plain,
! [V_z] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_z),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_unimodular__reduce__norm]) ).
fof(f_872_2,plain,
! [U_2644] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2644,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2644),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2644,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2644),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2644) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
cnf(f_872_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2644,c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2644),c_Complex_Oii))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2644,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2644),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2644) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_872_2]) ).
fof(f_873_1,plain,
! [V_x,V_y] :
( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).
fof(f_873_2,plain,
! [U_2646,U_2645] :
( ( c_Nat__Transfer_Otsub(U_2646,U_2645) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2645),U_2646)) )
& ( c_Nat__Transfer_Otsub(U_2646,U_2645) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2646,U_2645)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2645),U_2646)) ) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
fof(f_873_3,plain,
( ! [U_2650,U_2648] :
( c_Nat__Transfer_Otsub(U_2650,U_2648) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2648),U_2650)) )
& ! [U_2649,U_2647] :
( c_Nat__Transfer_Otsub(U_2649,U_2647) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2649,U_2647)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2647),U_2649)) ) ),
inference(miniscope,[status(thm)],[f_873_2]) ).
cnf(f_873_4,plain,
( c_Nat__Transfer_Otsub(U_2649,U_2647) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2649,U_2647)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2647),U_2649)) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_5,plain,
( c_Nat__Transfer_Otsub(U_2650,U_2648) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2648),U_2650)) ),
inference(clausify,[status(thm)],[f_873_3]) ).
fof(f_874_1,plain,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_complex__Re__i]) ).
cnf(f_874_2,plain,
hAPP(c_Complex_ORe,c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_874_1]) ).
fof(f_875_1,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_complex__i__not__zero]) ).
cnf(f_875_2,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_875_1]) ).
fof(f_876_1,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_complex__i__not__one]) ).
cnf(f_876_2,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_876_1]) ).
fof(f_877_1,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_complex__Im__i]) ).
cnf(f_877_2,plain,
hAPP(c_Complex_OIm,c_Complex_Oii) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_877_1]) ).
fof(f_878_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).
fof(f_878_2,plain,
! [U_2652,U_2651] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_2651,U_2652)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2652))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2651)) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
cnf(f_878_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_2651,U_2652)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2652))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2651)) ),
inference(clausify,[status(thm)],[f_878_2]) ).
fof(f_879_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).
fof(f_879_2,plain,
! [U_2654,U_2653] :
( c_Nat__Transfer_Otsub(U_2654,U_2653) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2654,U_2653)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2653),U_2654)) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
cnf(f_879_3,plain,
( c_Nat__Transfer_Otsub(U_2654,U_2653) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2654,U_2653)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2653),U_2654)) ),
inference(clausify,[status(thm)],[f_879_2]) ).
fof(f_880_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))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_int__power__div__base]) ).
fof(f_880_2,plain,
! [U_2656,U_2655] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2656),U_2655),U_2656) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2656),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2655,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2656))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2655)) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
cnf(f_880_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2656),U_2655),U_2656) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2656),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2655,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2656))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2655)) ),
inference(clausify,[status(thm)],[f_880_2]) ).
fof(f_881_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) = hAPP(hAPP(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_881_2,plain,
! [U_2661,U_2660,U_2659,U_2658,U_2657] :
( c_Groups_Ominus__class_Ominus(U_2657,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2657),U_2658),U_2659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2657),U_2660),U_2661)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2657),c_Groups_Ominus__class_Ominus(U_2657,U_2658,U_2660)),c_Groups_Ominus__class_Ominus(U_2657,U_2659,U_2661))
| ~ class_Groups_Oab__group__add(U_2657) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
cnf(f_881_3,plain,
( c_Groups_Ominus__class_Ominus(U_2657,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2657),U_2658),U_2659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2657),U_2660),U_2661)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2657),c_Groups_Ominus__class_Ominus(U_2657,U_2658,U_2660)),c_Groups_Ominus__class_Ominus(U_2657,U_2659,U_2661))
| ~ class_Groups_Oab__group__add(U_2657) ),
inference(clausify,[status(thm)],[f_881_2]) ).
fof(f_882_1,plain,
! [V_k,V_x] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k)),V_x))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_int__div__less__self]) ).
fof(f_882_2,plain,
! [U_2663,U_2662] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2662,U_2663)),U_2662))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2663))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2662)) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
cnf(f_882_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2662,U_2663)),U_2662))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2663))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2662)) ),
inference(clausify,[status(thm)],[f_882_2]) ).
fof(f_883_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq]) ).
fof(f_883_2,plain,
! [U_2666,U_2665,U_2664] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2666),U_2664)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2665,U_2666),U_2664)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2664)) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
cnf(f_883_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2666),U_2664)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2665,U_2666),U_2664)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2664)) ),
inference(clausify,[status(thm)],[f_883_2]) ).
fof(f_884_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_884_2,plain,
! [U_2670,U_2669,U_2668,U_2667] :
( ( ( c_Divides_Odiv__class_Odiv(U_2667,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2670)) = c_Divides_Odiv__class_Odiv(U_2667,U_2669,U_2670)
| U_2668 = c_Groups_Ozero__class_Ozero(U_2667) )
& ( c_Divides_Odiv__class_Odiv(U_2667,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2670)) = c_Groups_Ozero__class_Ozero(U_2667)
| U_2668 != c_Groups_Ozero__class_Ozero(U_2667) ) )
| ~ class_Divides_Osemiring__div(U_2667) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
cnf(f_884_3,plain,
( c_Divides_Odiv__class_Odiv(U_2667,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2670)) = c_Groups_Ozero__class_Ozero(U_2667)
| U_2668 != c_Groups_Ozero__class_Ozero(U_2667)
| ~ class_Divides_Osemiring__div(U_2667) ),
inference(clausify,[status(thm)],[f_884_2]) ).
cnf(f_884_4,plain,
( c_Divides_Odiv__class_Odiv(U_2667,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2667),U_2668),U_2670)) = c_Divides_Odiv__class_Odiv(U_2667,U_2669,U_2670)
| U_2668 = c_Groups_Ozero__class_Ozero(U_2667)
| ~ class_Divides_Osemiring__div(U_2667) ),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_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_885_2,plain,
! [U_2673,U_2672,U_2671] :
( c_Divides_Odiv__class_Odiv(U_2671,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2671),U_2673),U_2672),U_2672) = U_2673
| U_2672 = c_Groups_Ozero__class_Ozero(U_2671)
| ~ class_Divides_Osemiring__div(U_2671) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
cnf(f_885_3,plain,
( c_Divides_Odiv__class_Odiv(U_2671,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2671),U_2673),U_2672),U_2672) = U_2673
| U_2672 = c_Groups_Ozero__class_Ozero(U_2671)
| ~ class_Divides_Osemiring__div(U_2671) ),
inference(clausify,[status(thm)],[f_885_2]) ).
fof(f_886_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_886_2,plain,
! [U_2676,U_2675,U_2674] :
( c_Divides_Odiv__class_Odiv(U_2674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2674),U_2675),U_2676),U_2675) = U_2676
| U_2675 = c_Groups_Ozero__class_Ozero(U_2674)
| ~ class_Divides_Osemiring__div(U_2674) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
cnf(f_886_3,plain,
( c_Divides_Odiv__class_Odiv(U_2674,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2674),U_2675),U_2676),U_2675) = U_2676
| U_2675 = c_Groups_Ozero__class_Ozero(U_2674)
| ~ class_Divides_Osemiring__div(U_2674) ),
inference(clausify,[status(thm)],[f_886_2]) ).
fof(f_887_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_887_2,plain,
! [U_2680,U_2679,U_2678,U_2677] :
( c_Divides_Odiv__class_Odiv(U_2677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2679),U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2680),U_2678)) = c_Divides_Odiv__class_Odiv(U_2677,U_2679,U_2680)
| U_2678 = c_Groups_Ozero__class_Ozero(U_2677)
| ~ class_Divides_Osemiring__div(U_2677) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
cnf(f_887_3,plain,
( c_Divides_Odiv__class_Odiv(U_2677,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2679),U_2678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2677),U_2680),U_2678)) = c_Divides_Odiv__class_Odiv(U_2677,U_2679,U_2680)
| U_2678 = c_Groups_Ozero__class_Ozero(U_2677)
| ~ class_Divides_Osemiring__div(U_2677) ),
inference(clausify,[status(thm)],[f_887_2]) ).
fof(f_888_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_888_2,plain,
! [U_2684,U_2683,U_2682,U_2681] :
( c_Divides_Odiv__class_Odiv(U_2681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2682),U_2683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2682),U_2684)) = c_Divides_Odiv__class_Odiv(U_2681,U_2683,U_2684)
| U_2682 = c_Groups_Ozero__class_Ozero(U_2681)
| ~ class_Divides_Osemiring__div(U_2681) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
cnf(f_888_3,plain,
( c_Divides_Odiv__class_Odiv(U_2681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2682),U_2683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2681),U_2682),U_2684)) = c_Divides_Odiv__class_Odiv(U_2681,U_2683,U_2684)
| U_2682 = c_Groups_Ozero__class_Ozero(U_2681)
| ~ class_Divides_Osemiring__div(U_2681) ),
inference(clausify,[status(thm)],[f_888_2]) ).
fof(f_889_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_889_2,plain,
! [U_2686,U_2685] :
( c_Divides_Odiv__class_Odiv(U_2685,U_2686,U_2686) = c_Groups_Oone__class_Oone(U_2685)
| U_2686 = c_Groups_Ozero__class_Ozero(U_2685)
| ~ class_Divides_Osemiring__div(U_2685) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
cnf(f_889_3,plain,
( c_Divides_Odiv__class_Odiv(U_2685,U_2686,U_2686) = c_Groups_Oone__class_Oone(U_2685)
| U_2686 = c_Groups_Ozero__class_Ozero(U_2685)
| ~ class_Divides_Osemiring__div(U_2685) ),
inference(clausify,[status(thm)],[f_889_2]) ).
fof(f_890_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_890_2,plain,
! [U_2687] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2687) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_890_1]) ).
cnf(f_890_3,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2687) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_890_2]) ).
fof(f_891_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_891_2,plain,
! [U_2689,U_2688] :
( hBOOL(hAPP(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_2688,U_2689)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2689))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2688)) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
cnf(f_891_3,plain,
( hBOOL(hAPP(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_2688,U_2689)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2689))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2688)) ),
inference(clausify,[status(thm)],[f_891_2]) ).
fof(f_892_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_892_2,plain,
! [U_2691,U_2690] :
( c_Divides_Odiv__class_Odiv(U_2690,U_2691,c_Groups_Ozero__class_Ozero(U_2690)) = c_Groups_Ozero__class_Ozero(U_2690)
| ~ class_Divides_Osemiring__div(U_2690) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
cnf(f_892_3,plain,
( c_Divides_Odiv__class_Odiv(U_2690,U_2691,c_Groups_Ozero__class_Ozero(U_2690)) = c_Groups_Ozero__class_Ozero(U_2690)
| ~ class_Divides_Osemiring__div(U_2690) ),
inference(clausify,[status(thm)],[f_892_2]) ).
fof(f_893_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_893_2,plain,
! [U_2693,U_2692] :
( c_Divides_Odiv__class_Odiv(U_2692,c_Groups_Ozero__class_Ozero(U_2692),U_2693) = c_Groups_Ozero__class_Ozero(U_2692)
| ~ class_Divides_Osemiring__div(U_2692) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
cnf(f_893_3,plain,
( c_Divides_Odiv__class_Odiv(U_2692,c_Groups_Ozero__class_Ozero(U_2692),U_2693) = c_Groups_Ozero__class_Ozero(U_2692)
| ~ class_Divides_Osemiring__div(U_2692) ),
inference(clausify,[status(thm)],[f_893_2]) ).
fof(f_894_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0]) ).
fof(f_894_2,plain,
! [U_2695,U_2694] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2694,U_2695)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2695))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2694),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
cnf(f_894_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2694,U_2695)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2695))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2694),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_894_2]) ).
fof(f_895_1,plain,
! [V_a_2,V_b_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff]) ).
fof(f_895_2,plain,
! [U_2697,U_2696] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2697,U_2696)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2697)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2697))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2697,U_2696)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2696),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
cnf(f_895_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2697))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2697,U_2696)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2696),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_895_2]) ).
cnf(f_895_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2697,U_2696)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2697))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2696),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_895_2]) ).
fof(f_896_1,plain,
! [V_a_2,V_b_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff]) ).
fof(f_896_2,plain,
! [U_2699,U_2698] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2699,U_2698)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2699),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2699),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2699,U_2698)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2698)) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
cnf(f_896_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2699),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2699,U_2698)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2698)) ),
inference(clausify,[status(thm)],[f_896_2]) ).
cnf(f_896_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2699,U_2698)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2699),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2698)) ),
inference(clausify,[status(thm)],[f_896_2]) ).
fof(f_897_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_897_2,plain,
! [U_2700] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2700,U_2700) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2700 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
cnf(f_897_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2700,U_2700) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2700 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_897_2]) ).
fof(f_898_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_898_2,plain,
! [U_2702,U_2701] :
( c_Divides_Odiv__class_Odiv(U_2701,U_2702,c_Groups_Oone__class_Oone(U_2701)) = U_2702
| ~ class_Divides_Osemiring__div(U_2701) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
cnf(f_898_3,plain,
( c_Divides_Odiv__class_Odiv(U_2701,U_2702,c_Groups_Oone__class_Oone(U_2701)) = U_2702
| ~ class_Divides_Osemiring__div(U_2701) ),
inference(clausify,[status(thm)],[f_898_2]) ).
fof(f_899_1,plain,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg]) ).
fof(f_899_2,plain,
! [U_2705,U_2704,U_2703] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2704,U_2705)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2703,U_2705)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2705),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2703),U_2704)) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
cnf(f_899_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2704,U_2705)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2703,U_2705)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2705),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2703),U_2704)) ),
inference(clausify,[status(thm)],[f_899_2]) ).
fof(f_900_1,plain,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),V_a_H)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono1]) ).
fof(f_900_2,plain,
! [U_2708,U_2707,U_2706] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2706,U_2708)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2707,U_2708)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2708))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2706),U_2707)) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
cnf(f_900_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2706,U_2708)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2707,U_2708)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2708))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2706),U_2707)) ),
inference(clausify,[status(thm)],[f_900_2]) ).
fof(f_901_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),V_a))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial]) ).
fof(f_901_2,plain,
! [U_2710,U_2709] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2709,U_2710) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2710),U_2709))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2709),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
cnf(f_901_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2709,U_2710) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2710),U_2709))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2709),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_901_2]) ).
fof(f_902_1,plain,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg]) ).
fof(f_902_2,plain,
! [U_2713,U_2712,U_2711] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2711,U_2712)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2711,U_2713)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2712),U_2713))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2712))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
cnf(f_902_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2711,U_2712)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2711,U_2713)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2712),U_2713))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2712))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_902_2]) ).
fof(f_903_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0]) ).
fof(f_903_2,plain,
! [U_2715,U_2714] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2714,U_2715)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2715))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2714),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
cnf(f_903_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2714,U_2715)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2715))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2714),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_903_2]) ).
fof(f_904_1,plain,
! [V_a_2,V_b_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff]) ).
fof(f_904_2,plain,
! [U_2717,U_2716] :
( ( ( hBOOL(hAPP(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_2717,U_2716)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2717),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2717),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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_2717,U_2716))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2716),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
cnf(f_904_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2717),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(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_2717,U_2716)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2716),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_904_2]) ).
cnf(f_904_4,plain,
( hBOOL(hAPP(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_2717,U_2716)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2717),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2716),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_904_2]) ).
fof(f_905_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial]) ).
fof(f_905_2,plain,
! [U_2719,U_2718] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2718,U_2719) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2718),U_2719))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2718)) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
cnf(f_905_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2718,U_2719) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2718),U_2719))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2718)) ),
inference(clausify,[status(thm)],[f_905_2]) ).
fof(f_906_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0]) ).
fof(f_906_2,plain,
! [U_2721,U_2720] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2720,U_2721)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2721),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2720)) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
cnf(f_906_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2720,U_2721)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2721),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2720)) ),
inference(clausify,[status(thm)],[f_906_2]) ).
fof(f_907_1,plain,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2]) ).
fof(f_907_2,plain,
! [U_2724,U_2723,U_2722] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2722,U_2724)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2722,U_2723)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2723),U_2724))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2723))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2722)) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
cnf(f_907_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2722,U_2724)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2722,U_2723)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2723),U_2724))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2723))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2722)) ),
inference(clausify,[status(thm)],[f_907_2]) ).
fof(f_908_1,plain,
! [V_b_2,V_a_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2),V_a_2)) )
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ),
inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff]) ).
fof(f_908_2,plain,
! [U_2726,U_2725] :
( ( ( hBOOL(hAPP(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_2725,U_2726)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2726))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2726),U_2725)) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2726))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2726),U_2725)) )
| ~ hBOOL(hAPP(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_2725,U_2726))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2725)) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
cnf(f_908_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2726),U_2725))
| ~ hBOOL(hAPP(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_2725,U_2726)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2725)) ),
inference(clausify,[status(thm)],[f_908_2]) ).
cnf(f_908_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2726))
| ~ hBOOL(hAPP(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_2725,U_2726)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2725)) ),
inference(clausify,[status(thm)],[f_908_2]) ).
cnf(f_908_5,plain,
( hBOOL(hAPP(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_2725,U_2726)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2726))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2726),U_2725))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2725)) ),
inference(clausify,[status(thm)],[f_908_2]) ).
fof(f_909_1,plain,
! [V_i_2,V_k_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2),V_i_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff]) ).
fof(f_909_2,plain,
! [U_2728,U_2727] :
( ( ( hBOOL(hAPP(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_2728,U_2727)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2727),U_2728)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2727),U_2728))
| ~ hBOOL(hAPP(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_2728,U_2727))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2727)) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
cnf(f_909_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2727),U_2728))
| ~ hBOOL(hAPP(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_2728,U_2727)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2727)) ),
inference(clausify,[status(thm)],[f_909_2]) ).
cnf(f_909_4,plain,
( hBOOL(hAPP(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_2728,U_2727)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2727),U_2728))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2727)) ),
inference(clausify,[status(thm)],[f_909_2]) ).
fof(f_910_1,plain,
! [V_a_2,V_b_2] :
( ( ( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
| ~ hBOOL(hAPP(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))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff]) ).
fof(f_910_2,plain,
! [U_2730,U_2729] :
( ( ( hBOOL(hAPP(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_2730,U_2729)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2730)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2730))
| ~ hBOOL(hAPP(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_2730,U_2729))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2729)) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
cnf(f_910_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2730))
| ~ hBOOL(hAPP(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_2730,U_2729)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2729)) ),
inference(clausify,[status(thm)],[f_910_2]) ).
cnf(f_910_4,plain,
( hBOOL(hAPP(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_2730,U_2729)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2730))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2729)) ),
inference(clausify,[status(thm)],[f_910_2]) ).
fof(f_911_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)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),V_i_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2),V_k_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| 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_911_2,plain,
! [U_2732,U_2731] :
( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2731,U_2732) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2732),U_2731))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2731),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2731),U_2732))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2731)) )
& U_2732 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2732),U_2731))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2731),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2731),U_2732))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2731)) )
| U_2732 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2731,U_2732) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
fof(f_911_3,plain,
( ! [U_2736,U_2734] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2734,U_2736) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2736),U_2734))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2734),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2734),U_2736))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2734)) )
& U_2736 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2735,U_2733] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2735),U_2733))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2733),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2733),U_2735))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2733)) )
| U_2735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2733,U_2735) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_911_2]) ).
cnf(f_911_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2733),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2733))
| U_2735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2733,U_2735) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_911_3]) ).
cnf(f_911_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2735),U_2733))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2733))
| U_2735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2733,U_2735) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_911_3]) ).
cnf(f_911_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2733),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2733),U_2735))
| U_2735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2733,U_2735) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_911_3]) ).
cnf(f_911_7,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2735),U_2733))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2733),U_2735))
| U_2735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2733,U_2735) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_911_3]) ).
cnf(f_911_8,plain,
( U_2736 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2734,U_2736) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_911_3]) ).
cnf(f_911_9,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2734),U_2736))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2734))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2734,U_2736) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_911_3]) ).
cnf(f_911_10,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2736),U_2734))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2734),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2734,U_2736) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_911_3]) ).
fof(f_912_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),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_912_2,plain,
! [U_2740,U_2739,U_2738,U_2737] :
( c_Divides_Odiv__class_Odiv(U_2737,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2737),U_2739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2737),U_2738),U_2740)),U_2738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2737),U_2740),c_Divides_Odiv__class_Odiv(U_2737,U_2739,U_2738))
| U_2738 = c_Groups_Ozero__class_Ozero(U_2737)
| ~ class_Divides_Osemiring__div(U_2737) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
cnf(f_912_3,plain,
( c_Divides_Odiv__class_Odiv(U_2737,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2737),U_2739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2737),U_2738),U_2740)),U_2738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2737),U_2740),c_Divides_Odiv__class_Odiv(U_2737,U_2739,U_2738))
| U_2738 = c_Groups_Ozero__class_Ozero(U_2737)
| ~ class_Divides_Osemiring__div(U_2737) ),
inference(clausify,[status(thm)],[f_912_2]) ).
fof(f_913_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),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_913_2,plain,
! [U_2744,U_2743,U_2742,U_2741] :
( c_Divides_Odiv__class_Odiv(U_2741,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2741),U_2743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2741),U_2744),U_2742)),U_2742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2741),U_2744),c_Divides_Odiv__class_Odiv(U_2741,U_2743,U_2742))
| U_2742 = c_Groups_Ozero__class_Ozero(U_2741)
| ~ class_Divides_Osemiring__div(U_2741) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
cnf(f_913_3,plain,
( c_Divides_Odiv__class_Odiv(U_2741,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2741),U_2743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2741),U_2744),U_2742)),U_2742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2741),U_2744),c_Divides_Odiv__class_Odiv(U_2741,U_2743,U_2742))
| U_2742 = c_Groups_Ozero__class_Ozero(U_2741)
| ~ class_Divides_Osemiring__div(U_2741) ),
inference(clausify,[status(thm)],[f_913_2]) ).
fof(f_914_1,plain,
! [V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_914_2,plain,
! [U_2747,U_2746,U_2745] :
( c_Divides_Odiv__class_Odiv(U_2745,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2745),U_2747),U_2746),U_2746) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2745),c_Divides_Odiv__class_Odiv(U_2745,U_2747,U_2746)),c_Groups_Oone__class_Oone(U_2745))
| U_2746 = c_Groups_Ozero__class_Ozero(U_2745)
| ~ class_Divides_Osemiring__div(U_2745) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
cnf(f_914_3,plain,
( c_Divides_Odiv__class_Odiv(U_2745,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2745),U_2747),U_2746),U_2746) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2745),c_Divides_Odiv__class_Odiv(U_2745,U_2747,U_2746)),c_Groups_Oone__class_Oone(U_2745))
| U_2746 = c_Groups_Ozero__class_Ozero(U_2745)
| ~ class_Divides_Osemiring__div(U_2745) ),
inference(clausify,[status(thm)],[f_914_2]) ).
fof(f_915_1,plain,
! [V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),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_915_2,plain,
! [U_2750,U_2749,U_2748] :
( c_Divides_Odiv__class_Odiv(U_2748,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2748),U_2749),U_2750),U_2749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2748),c_Divides_Odiv__class_Odiv(U_2748,U_2750,U_2749)),c_Groups_Oone__class_Oone(U_2748))
| U_2749 = c_Groups_Ozero__class_Ozero(U_2748)
| ~ class_Divides_Osemiring__div(U_2748) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
cnf(f_915_3,plain,
( c_Divides_Odiv__class_Odiv(U_2748,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2748),U_2749),U_2750),U_2749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2748),c_Divides_Odiv__class_Odiv(U_2748,U_2750,U_2749)),c_Groups_Oone__class_Oone(U_2748))
| U_2749 = c_Groups_Ozero__class_Ozero(U_2748)
| ~ class_Divides_Osemiring__div(U_2748) ),
inference(clausify,[status(thm)],[f_915_2]) ).
fof(f_916_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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& ? [B_j] :
( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [B_i] :
( hBOOL(hAPP(V_P_2,B_i))
| ! [B_j] :
( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),B_j)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [B_i] :
( hBOOL(hAPP(V_P_2,B_i))
| ! [B_j] :
( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j),V_k_2))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_n_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).
fof(f_916_2,plain,
! [U_2761,U_2760,U_2759] :
( ( hBOOL(hAPP(U_2759,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2760,U_2761)))
| ( ? [U_2758] :
( ~ hBOOL(hAPP(U_2759,U_2758))
& ? [U_2757] :
( U_2760 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2761),U_2758)),U_2757)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2761),U_2757)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2761),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_2756] :
( ~ hBOOL(hAPP(U_2759,U_2756))
& ? [U_2755] :
( U_2760 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2761),U_2756)),U_2755)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2755),U_2761))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2755)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2761)) )
| ( ~ hBOOL(hAPP(U_2759,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2761 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_2754] :
( hBOOL(hAPP(U_2759,U_2754))
| ! [U_2753] :
( U_2760 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2761),U_2754)),U_2753)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2761),U_2753)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2761),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2752] :
( hBOOL(hAPP(U_2759,U_2752))
| ! [U_2751] :
( U_2760 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2761),U_2752)),U_2751)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2751),U_2761))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2761)) )
& ( hBOOL(hAPP(U_2759,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2761 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2759,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2760,U_2761))) ) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
fof(f_916_3,plain,
( ! [U_2767,U_2765,U_2763] :
( hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767)))
| ( ? [U_2758] :
( ~ hBOOL(hAPP(U_2763,U_2758))
& ? [U_2757] :
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),U_2758)),U_2757)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),U_2757)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_2756] :
( ~ hBOOL(hAPP(U_2763,U_2756))
& ? [U_2755] :
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),U_2756)),U_2755)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2755),U_2767))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2755)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767)) )
| ( ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2766,U_2764,U_2762] :
( ( ( ! [U_2754] :
( hBOOL(hAPP(U_2762,U_2754))
| ! [U_2753] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2754)),U_2753)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),U_2753)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2752] :
( hBOOL(hAPP(U_2762,U_2752))
| ! [U_2751] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2752)),U_2751)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2751),U_2766))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2766)) )
& ( hBOOL(hAPP(U_2762,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2766 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ) ),
inference(miniscope,[status(thm)],[f_916_2]) ).
fof(f_916_4,plain,
( ! [U_2767,U_2765,U_2763] :
( hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767)))
| ( ? [U_2758] :
( ~ hBOOL(hAPP(U_2763,U_2758))
& ? [U_2757] :
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),U_2758)),U_2757)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),U_2757)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
& ? [U_2755] :
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),U_2755)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2755),U_2767))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2755)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767)) )
| ( ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2766,U_2764,U_2762] :
( ( ( ! [U_2754] :
( hBOOL(hAPP(U_2762,U_2754))
| ! [U_2753] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2754)),U_2753)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),U_2753)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2752] :
( hBOOL(hAPP(U_2762,U_2752))
| ! [U_2751] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2752)),U_2751)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2751),U_2766))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2766)) )
& ( hBOOL(hAPP(U_2762,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2766 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_2756,sK68(U_2767,U_2765,U_2763))],[f_916_3]) ).
fof(f_916_5,plain,
( ! [U_2767,U_2765,U_2763] :
( hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767)))
| ( ? [U_2758] :
( ~ hBOOL(hAPP(U_2763,U_2758))
& ? [U_2757] :
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),U_2758)),U_2757)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),U_2757)) ) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
& U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767)) )
| ( ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2766,U_2764,U_2762] :
( ( ( ! [U_2754] :
( hBOOL(hAPP(U_2762,U_2754))
| ! [U_2753] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2754)),U_2753)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),U_2753)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2752] :
( hBOOL(hAPP(U_2762,U_2752))
| ! [U_2751] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2752)),U_2751)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2751),U_2766))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2766)) )
& ( hBOOL(hAPP(U_2762,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2766 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_2755,sK69(U_2767,U_2765,U_2763))],[f_916_4]) ).
fof(f_916_6,plain,
( ! [U_2767,U_2765,U_2763] :
( hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767)))
| ( ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
& ? [U_2757] :
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),U_2757)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),U_2757)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
& U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767)) )
| ( ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2766,U_2764,U_2762] :
( ( ( ! [U_2754] :
( hBOOL(hAPP(U_2762,U_2754))
| ! [U_2753] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2754)),U_2753)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),U_2753)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2752] :
( hBOOL(hAPP(U_2762,U_2752))
| ! [U_2751] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2752)),U_2751)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2751),U_2766))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2766)) )
& ( hBOOL(hAPP(U_2762,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2766 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_2758,sK70(U_2767,U_2765,U_2763))],[f_916_5]) ).
fof(f_916_7,plain,
( ! [U_2767,U_2765,U_2763] :
( hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767)))
| ( ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
& U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
& U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767)) )
| ( ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2766,U_2764,U_2762] :
( ( ( ! [U_2754] :
( hBOOL(hAPP(U_2762,U_2754))
| ! [U_2753] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2754)),U_2753)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),U_2753)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2752] :
( hBOOL(hAPP(U_2762,U_2752))
| ! [U_2751] :
( U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2752)),U_2751)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2751),U_2766))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2766)) )
& ( hBOOL(hAPP(U_2762,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2766 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_2757,sK71(U_2767,U_2765,U_2763))],[f_916_6]) ).
cnf(f_916_8,plain,
( hBOOL(hAPP(U_2762,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2766 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_9,plain,
( hBOOL(hAPP(U_2762,U_2752))
| U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2752)),U_2751)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2751),U_2766))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2766))
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_10,plain,
( hBOOL(hAPP(U_2762,U_2754))
| U_2764 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2766),U_2754)),U_2753)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2753),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),U_2753))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2766),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2762,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2764,U_2766))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_11,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_12,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_13,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_14,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_15,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_16,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_17,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_18,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_19,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_20,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_21,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_22,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_23,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_24,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_25,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_26,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_27,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_28,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_29,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_30,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_31,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_32,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_33,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_34,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_35,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_36,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_37,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_38,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_39,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_40,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| U_2767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_41,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_42,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_43,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_44,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_45,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2767),sK71(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_46,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_47,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_48,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_49,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_50,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK71(U_2767,U_2765,U_2763)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_51,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_52,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_53,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_54,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_55,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK70(U_2767,U_2765,U_2763))),sK71(U_2767,U_2765,U_2763))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_56,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_57,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK69(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_58,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,sK69(U_2767,U_2765,U_2763)),U_2767))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_59,plain,
( U_2765 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2767),sK68(U_2767,U_2765,U_2763))),sK69(U_2767,U_2765,U_2763))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
cnf(f_916_60,plain,
( ~ hBOOL(hAPP(U_2763,sK68(U_2767,U_2765,U_2763)))
| ~ hBOOL(hAPP(U_2763,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2763,sK70(U_2767,U_2765,U_2763)))
| hBOOL(hAPP(U_2763,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2765,U_2767))) ),
inference(clausify,[status(thm)],[f_916_7]) ).
fof(f_917_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)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1),V_r_1)) )
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1),V_b_1))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
| V_a_1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__eq]) ).
fof(f_917_2,plain,
! [U_2771,U_2770,U_2769,U_2768] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2768,U_2769) = U_2770
| U_2769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2771),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2769),U_2771)) )
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769)) )
| ( ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2771),U_2769))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769)) )
| U_2768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2769),U_2770)),U_2771) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
cnf(f_917_3,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2768,U_2769) = U_2770
| U_2769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2769),U_2770)),U_2771) ),
inference(clausify,[status(thm)],[f_917_2]) ).
cnf(f_917_4,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2771),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2769),U_2771))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2768,U_2769) = U_2770
| U_2769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2769),U_2770)),U_2771) ),
inference(clausify,[status(thm)],[f_917_2]) ).
cnf(f_917_5,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2769))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2771),U_2769))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2768,U_2769) = U_2770
| U_2769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2769),U_2770)),U_2771) ),
inference(clausify,[status(thm)],[f_917_2]) ).
cnf(f_917_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2771),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2769),U_2771))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2771),U_2769))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2771))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2768,U_2769) = U_2770
| U_2769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2768 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2769),U_2770)),U_2771) ),
inference(clausify,[status(thm)],[f_917_2]) ).
fof(f_918_1,plain,
! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_OIm,V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_ORe,V_y)))),
inference(fof_nnf,[status(thm)],[fact_complex__mult__def]) ).
fof(f_918_2,plain,
! [U_2773,U_2772] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2772),U_2773) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2772)),hAPP(c_Complex_ORe,U_2773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2772)),hAPP(c_Complex_OIm,U_2773))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2772)),hAPP(c_Complex_OIm,U_2773))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2772)),hAPP(c_Complex_ORe,U_2773)))),
inference(variable_rename,[status(thm)],[f_918_1]) ).
cnf(f_918_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2772),U_2773) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2772)),hAPP(c_Complex_ORe,U_2773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2772)),hAPP(c_Complex_OIm,U_2773))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2772)),hAPP(c_Complex_OIm,U_2773))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2772)),hAPP(c_Complex_ORe,U_2773)))),
inference(clausify,[status(thm)],[f_918_2]) ).
fof(f_919_1,plain,
! [V_b,V_x,V_a] :
( ? [B_d] :
( ! [B_y] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_y),V_b))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a),B_y)) )
| ~ hBOOL(hAPP(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)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),B_d)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x),V_b))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_lemma__interval]) ).
fof(f_919_2,plain,
! [U_2778,U_2777,U_2776] :
( ? [U_2775] :
( ! [U_2774] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2774),U_2778))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2776),U_2774)) )
| ~ hBOOL(hAPP(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_2777,U_2774))),U_2775)) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2775)) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2777),U_2778))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2776),U_2777)) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
fof(f_919_3,plain,
! [U_2778,U_2777,U_2776] :
( ( ! [U_2774] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2774),U_2778))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2776),U_2774)) )
| ~ hBOOL(hAPP(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_2777,U_2774))),sK72(U_2778,U_2777,U_2776))) )
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK72(U_2778,U_2777,U_2776))) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2777),U_2778))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2776),U_2777)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_2775,sK72(U_2778,U_2777,U_2776))],[f_919_2]) ).
cnf(f_919_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),sK72(U_2778,U_2777,U_2776)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2777),U_2778))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2776),U_2777)) ),
inference(clausify,[status(thm)],[f_919_3]) ).
cnf(f_919_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2776),U_2774))
| ~ hBOOL(hAPP(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_2777,U_2774))),sK72(U_2778,U_2777,U_2776)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2777),U_2778))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2776),U_2777)) ),
inference(clausify,[status(thm)],[f_919_3]) ).
cnf(f_919_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2774),U_2778))
| ~ hBOOL(hAPP(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_2777,U_2774))),sK72(U_2778,U_2777,U_2776)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2777),U_2778))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2776),U_2777)) ),
inference(clausify,[status(thm)],[f_919_3]) ).
fof(f_920_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_920_2,plain,
! [U_2781,U_2780,U_2779] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2779,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2781)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2779,U_2780),U_2781),
inference(variable_rename,[status(thm)],[f_920_1]) ).
cnf(f_920_3,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2779,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2781)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2779,U_2780),U_2781),
inference(clausify,[status(thm)],[f_920_2]) ).
fof(f_921_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__less]) ).
fof(f_921_2,plain,
! [U_2783,U_2782] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2782,U_2783) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2782),U_2783)) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
cnf(f_921_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2782,U_2783) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2782),U_2783)) ),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_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_922_2,plain,
! [U_2784] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2784,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_2784,
inference(variable_rename,[status(thm)],[f_922_1]) ).
cnf(f_922_3,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2784,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_2784,
inference(clausify,[status(thm)],[f_922_2]) ).
fof(f_923_1,plain,
! [V_n,V_m] : hBOOL(hAPP(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_923_2,plain,
! [U_2786,U_2785] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2785,U_2786)),U_2785)),
inference(variable_rename,[status(thm)],[f_923_1]) ).
cnf(f_923_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2785,U_2786)),U_2785)),
inference(clausify,[status(thm)],[f_923_2]) ).
fof(f_924_1,plain,
! [V_k,V_n,V_m] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__le__mono]) ).
fof(f_924_2,plain,
! [U_2789,U_2788,U_2787] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2787,U_2789)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2788,U_2789)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2787),U_2788)) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
cnf(f_924_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2787,U_2789)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2788,U_2789)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2787),U_2788)) ),
inference(clausify,[status(thm)],[f_924_2]) ).
fof(f_925_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_925_2,plain,
! [U_2792,U_2791,U_2790] :
( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2790),U_2791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2790),U_2792)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2791,U_2792)
| U_2790 = 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_2790),U_2791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2790),U_2792)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2790 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
fof(f_925_3,plain,
( ! [U_2798,U_2796,U_2794] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2798)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2796,U_2798)
| U_2794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2797,U_2795,U_2793] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2793),U_2795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2793),U_2797)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2793 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_925_2]) ).
cnf(f_925_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2793),U_2795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2793),U_2797)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2793 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_925_3]) ).
cnf(f_925_5,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2796),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2798)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2796,U_2798)
| U_2794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_925_3]) ).
fof(f_926_1,plain,
! [V_m,V_n] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)),V_m))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__less__dividend]) ).
fof(f_926_2,plain,
! [U_2800,U_2799] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2800,U_2799)),U_2800))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2800))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2799)) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
cnf(f_926_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2800,U_2799)),U_2800))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2800))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2799)) ),
inference(clausify,[status(thm)],[f_926_2]) ).
fof(f_927_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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m]) ).
fof(f_927_2,plain,
! [U_2802,U_2801] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2802),U_2801),U_2801) = U_2802
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2801)) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
cnf(f_927_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2802),U_2801),U_2801) = U_2802
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2801)) ),
inference(clausify,[status(thm)],[f_927_2]) ).
fof(f_928_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
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m]) ).
fof(f_928_2,plain,
! [U_2804,U_2803] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2803),U_2804),U_2803) = U_2804
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2803)) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
cnf(f_928_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2803),U_2804),U_2803) = U_2804
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2803)) ),
inference(clausify,[status(thm)],[f_928_2]) ).
fof(f_929_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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1]) ).
fof(f_929_2,plain,
! [U_2807,U_2806,U_2805] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2805),U_2806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2805),U_2807)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2806,U_2807)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2805)) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
cnf(f_929_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2805),U_2806),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2805),U_2807)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2806,U_2807)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2805)) ),
inference(clausify,[status(thm)],[f_929_2]) ).
fof(f_930_1,plain,
! [V_k,V_n,V_m] :
( hBOOL(hAPP(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)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_div__le__mono2]) ).
fof(f_930_2,plain,
! [U_2810,U_2809,U_2808] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2810,U_2809)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2810,U_2808)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2808),U_2809))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2808)) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
cnf(f_930_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2810,U_2809)),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2810,U_2808)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2808),U_2809))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2808)) ),
inference(clausify,[status(thm)],[f_930_2]) ).
fof(f_931_1,plain,
! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)),
inference(fof_nnf,[status(thm)],[fact_complex__diff]) ).
fof(f_931_2,plain,
! [U_2814,U_2813,U_2812,U_2811] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_2811,U_2812),c_Complex_Ocomplex_OComplex(U_2813,U_2814)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2811,U_2813),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2812,U_2814)),
inference(variable_rename,[status(thm)],[f_931_1]) ).
cnf(f_931_3,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_2811,U_2812),c_Complex_Ocomplex_OComplex(U_2813,U_2814)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2811,U_2813),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2812,U_2814)),
inference(clausify,[status(thm)],[f_931_2]) ).
fof(f_932_1,plain,
! [V_z] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,V_z),hAPP(c_Complex_OIm,V_z)) = V_z,
inference(fof_nnf,[status(thm)],[fact_complex__surj]) ).
fof(f_932_2,plain,
! [U_2815] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,U_2815),hAPP(c_Complex_OIm,U_2815)) = U_2815,
inference(variable_rename,[status(thm)],[f_932_1]) ).
cnf(f_932_3,plain,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,U_2815),hAPP(c_Complex_OIm,U_2815)) = U_2815,
inference(clausify,[status(thm)],[f_932_2]) ).
fof(f_933_1,plain,
! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] :
( ( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)
| V_real2_2 != V_real2_H_2
| V_real1_2 != V_real1_H_2 )
& ( ( V_real2_2 = V_real2_H_2
& V_real1_2 = V_real1_H_2 )
| c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) != c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_complex_Oinject]) ).
fof(f_933_2,plain,
! [U_2819,U_2818,U_2817,U_2816] :
( ( c_Complex_Ocomplex_OComplex(U_2816,U_2817) = c_Complex_Ocomplex_OComplex(U_2818,U_2819)
| U_2817 != U_2819
| U_2816 != U_2818 )
& ( ( U_2817 = U_2819
& U_2816 = U_2818 )
| c_Complex_Ocomplex_OComplex(U_2816,U_2817) != c_Complex_Ocomplex_OComplex(U_2818,U_2819) ) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
fof(f_933_3,plain,
( ! [U_2827,U_2825,U_2823,U_2821] :
( c_Complex_Ocomplex_OComplex(U_2821,U_2823) = c_Complex_Ocomplex_OComplex(U_2825,U_2827)
| U_2823 != U_2827
| U_2821 != U_2825 )
& ! [U_2826,U_2824,U_2822,U_2820] :
( ( U_2822 = U_2826
& U_2820 = U_2824 )
| c_Complex_Ocomplex_OComplex(U_2820,U_2822) != c_Complex_Ocomplex_OComplex(U_2824,U_2826) ) ),
inference(miniscope,[status(thm)],[f_933_2]) ).
cnf(f_933_4,plain,
( U_2820 = U_2824
| c_Complex_Ocomplex_OComplex(U_2820,U_2822) != c_Complex_Ocomplex_OComplex(U_2824,U_2826) ),
inference(clausify,[status(thm)],[f_933_3]) ).
cnf(f_933_5,plain,
( U_2822 = U_2826
| c_Complex_Ocomplex_OComplex(U_2820,U_2822) != c_Complex_Ocomplex_OComplex(U_2824,U_2826) ),
inference(clausify,[status(thm)],[f_933_3]) ).
cnf(f_933_6,plain,
( c_Complex_Ocomplex_OComplex(U_2821,U_2823) = c_Complex_Ocomplex_OComplex(U_2825,U_2827)
| U_2823 != U_2827
| U_2821 != U_2825 ),
inference(clausify,[status(thm)],[f_933_3]) ).
fof(f_934_1,plain,
! [V_y,V_x] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_y,
inference(fof_nnf,[status(thm)],[fact_Im]) ).
fof(f_934_2,plain,
! [U_2829,U_2828] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(U_2828,U_2829)) = U_2829,
inference(variable_rename,[status(thm)],[f_934_1]) ).
cnf(f_934_3,plain,
hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(U_2828,U_2829)) = U_2829,
inference(clausify,[status(thm)],[f_934_2]) ).
fof(f_935_1,plain,
! [V_y,V_x] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(V_x,V_y)) = V_x,
inference(fof_nnf,[status(thm)],[fact_Re]) ).
fof(f_935_2,plain,
! [U_2831,U_2830] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(U_2830,U_2831)) = U_2830,
inference(variable_rename,[status(thm)],[f_935_1]) ).
cnf(f_935_3,plain,
hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(U_2830,U_2831)) = U_2830,
inference(clausify,[status(thm)],[f_935_2]) ).
fof(f_936_1,plain,
! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),V_b),V_d)),
inference(fof_nnf,[status(thm)],[fact_complex__add]) ).
fof(f_936_2,plain,
! [U_2835,U_2834,U_2833,U_2832] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(U_2832,U_2833)),c_Complex_Ocomplex_OComplex(U_2834,U_2835)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2832),U_2834),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2833),U_2835)),
inference(variable_rename,[status(thm)],[f_936_1]) ).
cnf(f_936_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(U_2832,U_2833)),c_Complex_Ocomplex_OComplex(U_2834,U_2835)) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2832),U_2834),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),U_2833),U_2835)),
inference(clausify,[status(thm)],[f_936_2]) ).
fof(f_937_1,plain,
! [V_b_2,V_a_2] :
( ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| V_b_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(fof_nnf,[status(thm)],[fact_Complex__eq__0]) ).
fof(f_937_2,plain,
! [U_2837,U_2836] :
( ( c_Complex_Ocomplex_OComplex(U_2836,U_2837) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| U_2837 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2836 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_2837 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2836 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_2836,U_2837) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
( ! [U_2841,U_2839] :
( c_Complex_Ocomplex_OComplex(U_2839,U_2841) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| U_2841 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2839 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2840,U_2838] :
( ( U_2840 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2838 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_2838,U_2840) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(miniscope,[status(thm)],[f_937_2]) ).
cnf(f_937_4,plain,
( U_2838 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(U_2838,U_2840) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_937_3]) ).
cnf(f_937_5,plain,
( U_2840 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(U_2838,U_2840) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_937_3]) ).
cnf(f_937_6,plain,
( c_Complex_Ocomplex_OComplex(U_2839,U_2841) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| U_2841 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2839 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_937_3]) ).
fof(f_938_1,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_complex__zero__def]) ).
cnf(f_938_2,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_938_1]) ).
fof(f_939_1,plain,
! [V_y_2,V_x_2] :
( ( c_Complex_Ocomplex_OComplex(V_x_2,V_y_2) = c_Complex_Oii
| V_y_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_y_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(V_x_2,V_y_2) != c_Complex_Oii ) ),
inference(fof_nnf,[status(thm)],[fact_Complex__eq__i]) ).
fof(f_939_2,plain,
! [U_2843,U_2842] :
( ( c_Complex_Ocomplex_OComplex(U_2842,U_2843) = c_Complex_Oii
| U_2843 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_2842 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_2843 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& U_2842 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_2842,U_2843) != c_Complex_Oii ) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
fof(f_939_3,plain,
( ! [U_2847,U_2845] :
( c_Complex_Ocomplex_OComplex(U_2845,U_2847) = c_Complex_Oii
| U_2847 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_2845 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2846,U_2844] :
( ( U_2846 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& U_2844 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_2844,U_2846) != c_Complex_Oii ) ),
inference(miniscope,[status(thm)],[f_939_2]) ).
cnf(f_939_4,plain,
( U_2844 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(U_2844,U_2846) != c_Complex_Oii ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_5,plain,
( U_2846 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(U_2844,U_2846) != c_Complex_Oii ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_6,plain,
( c_Complex_Ocomplex_OComplex(U_2845,U_2847) = c_Complex_Oii
| U_2847 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_2845 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_939_3]) ).
fof(f_940_1,plain,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_i__def]) ).
cnf(f_940_2,plain,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_940_1]) ).
fof(f_941_1,plain,
! [V_b_2,V_a_2] :
( ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| V_b_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(fof_nnf,[status(thm)],[fact_Complex__eq__1]) ).
fof(f_941_2,plain,
! [U_2849,U_2848] :
( ( c_Complex_Ocomplex_OComplex(U_2848,U_2849) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| U_2849 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2848 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( ( U_2849 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2848 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_2848,U_2849) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
fof(f_941_3,plain,
( ! [U_2853,U_2851] :
( c_Complex_Ocomplex_OComplex(U_2851,U_2853) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| U_2853 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2851 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ! [U_2852,U_2850] :
( ( U_2852 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2850 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_2850,U_2852) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(miniscope,[status(thm)],[f_941_2]) ).
cnf(f_941_4,plain,
( U_2850 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(U_2850,U_2852) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_941_3]) ).
cnf(f_941_5,plain,
( U_2852 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(U_2850,U_2852) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_941_3]) ).
cnf(f_941_6,plain,
( c_Complex_Ocomplex_OComplex(U_2851,U_2853) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| U_2853 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2851 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_941_3]) ).
fof(f_942_1,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_complex__one__def]) ).
cnf(f_942_2,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_942_1]) ).
fof(f_943_1,plain,
! [V_a] : c_Complex_Ocis(V_a) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a)),
inference(fof_nnf,[status(thm)],[fact_cis__def]) ).
fof(f_943_2,plain,
! [U_2854] : c_Complex_Ocis(U_2854) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(U_2854),c_Transcendental_Osin(U_2854)),
inference(variable_rename,[status(thm)],[f_943_1]) ).
cnf(f_943_3,plain,
c_Complex_Ocis(U_2854) = c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(U_2854),c_Transcendental_Osin(U_2854)),
inference(clausify,[status(thm)],[f_943_2]) ).
fof(f_944_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))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__geq]) ).
fof(f_944_2,plain,
! [U_2856,U_2855] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2856,U_2855) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2856,U_2855),U_2855))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856),U_2855))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2855)) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
cnf(f_944_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2856,U_2855) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2856,U_2855),U_2855))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2856),U_2855))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2855)) ),
inference(clausify,[status(thm)],[f_944_2]) ).
fof(f_945_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))
| hBOOL(hAPP(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)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m),V_n)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_div__if]) ).
fof(f_945_2,plain,
! [U_2858,U_2857] :
( ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2858,U_2857) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2858,U_2857),U_2857))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2858),U_2857)) )
& ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2858,U_2857) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2858),U_2857)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2857)) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
cnf(f_945_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2858,U_2857) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2858),U_2857))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2857)) ),
inference(clausify,[status(thm)],[f_945_2]) ).
cnf(f_945_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2858,U_2857) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2858,U_2857),U_2857))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2858),U_2857))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2857)) ),
inference(clausify,[status(thm)],[f_945_2]) ).
fof(f_946_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 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
& hBOOL(hAPP(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 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
| ~ hBOOL(hAPP(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_946_2,plain,
! [U_2865,U_2864,U_2863] :
( ( hBOOL(hAPP(U_2863,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2864,U_2865)))
| ( ? [U_2862,U_2861] :
( ~ hBOOL(hAPP(U_2863,U_2862))
& U_2864 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2865),U_2862)),U_2861)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2861),U_2865)) )
& U_2865 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_2863,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_2865 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_2860,U_2859] :
( hBOOL(hAPP(U_2863,U_2860))
| U_2864 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2865),U_2860)),U_2859)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2859),U_2865)) )
| U_2865 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_2863,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2865 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_2863,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2864,U_2865))) ) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
fof(f_946_3,plain,
( ! [U_2871,U_2869,U_2867] :
( hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871)))
| ( ? [U_2862,U_2861] :
( ~ hBOOL(hAPP(U_2867,U_2862))
& U_2869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2871),U_2862)),U_2861)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2861),U_2871)) )
& U_2871 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_2867,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2870,U_2868,U_2866] :
( ( ( ! [U_2860,U_2859] :
( hBOOL(hAPP(U_2866,U_2860))
| U_2868 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2870),U_2860)),U_2859)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2859),U_2870)) )
| U_2870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_2866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2870 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_2866,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2868,U_2870))) ) ),
inference(miniscope,[status(thm)],[f_946_2]) ).
fof(f_946_4,plain,
( ! [U_2871,U_2869,U_2867] :
( hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871)))
| ( ? [U_2861] :
( ~ hBOOL(hAPP(U_2867,sK73(U_2871,U_2869,U_2867)))
& U_2869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2871),sK73(U_2871,U_2869,U_2867))),U_2861)
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2861),U_2871)) )
& U_2871 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_2867,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2870,U_2868,U_2866] :
( ( ( ! [U_2860,U_2859] :
( hBOOL(hAPP(U_2866,U_2860))
| U_2868 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2870),U_2860)),U_2859)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2859),U_2870)) )
| U_2870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_2866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2870 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_2866,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2868,U_2870))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_2862,sK73(U_2871,U_2869,U_2867))],[f_946_3]) ).
fof(f_946_5,plain,
( ! [U_2871,U_2869,U_2867] :
( hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871)))
| ( ~ hBOOL(hAPP(U_2867,sK73(U_2871,U_2869,U_2867)))
& U_2869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2871),sK73(U_2871,U_2869,U_2867))),sK74(U_2871,U_2869,U_2867))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK74(U_2871,U_2869,U_2867)),U_2871))
& U_2871 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_2867,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2870,U_2868,U_2866] :
( ( ( ! [U_2860,U_2859] :
( hBOOL(hAPP(U_2866,U_2860))
| U_2868 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2870),U_2860)),U_2859)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2859),U_2870)) )
| U_2870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_2866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2870 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_2866,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2868,U_2870))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_2861,sK74(U_2871,U_2869,U_2867))],[f_946_4]) ).
cnf(f_946_6,plain,
( hBOOL(hAPP(U_2866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2870 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_2866,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2868,U_2870))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_7,plain,
( hBOOL(hAPP(U_2866,U_2860))
| U_2868 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2870),U_2860)),U_2859)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2859),U_2870))
| U_2870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_2866,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2868,U_2870))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_8,plain,
( U_2871 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_9,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK74(U_2871,U_2869,U_2867)),U_2871))
| U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_10,plain,
( U_2869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2871),sK73(U_2871,U_2869,U_2867))),sK74(U_2871,U_2869,U_2867))
| U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_11,plain,
( ~ hBOOL(hAPP(U_2867,sK73(U_2871,U_2869,U_2867)))
| U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_12,plain,
( U_2871 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_2867,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_13,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK74(U_2871,U_2869,U_2867)),U_2871))
| ~ hBOOL(hAPP(U_2867,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_14,plain,
( U_2869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2871),sK73(U_2871,U_2869,U_2867))),sK74(U_2871,U_2869,U_2867))
| ~ hBOOL(hAPP(U_2867,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
cnf(f_946_15,plain,
( ~ hBOOL(hAPP(U_2867,sK73(U_2871,U_2869,U_2867)))
| ~ hBOOL(hAPP(U_2867,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2867,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2869,U_2871))) ),
inference(clausify,[status(thm)],[f_946_5]) ).
fof(f_947_1,plain,
! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))),
inference(fof_nnf,[status(thm)],[fact_complex__mult]) ).
fof(f_947_2,plain,
! [U_2875,U_2874,U_2873,U_2872] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(U_2872,U_2873)),c_Complex_Ocomplex_OComplex(U_2874,U_2875)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2872),U_2874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2873),U_2875)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2872),U_2875)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2873),U_2874))),
inference(variable_rename,[status(thm)],[f_947_1]) ).
cnf(f_947_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(U_2872,U_2873)),c_Complex_Ocomplex_OComplex(U_2874,U_2875)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2872),U_2874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2873),U_2875)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2872),U_2875)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2873),U_2874))),
inference(clausify,[status(thm)],[f_947_2]) ).
fof(f_948_1,plain,
! [V_a] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(V_a),c_Transcendental_Osin(V_a))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_cmod__unit__one]) ).
fof(f_948_2,plain,
! [U_2876] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(U_2876),c_Transcendental_Osin(U_2876))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(variable_rename,[status(thm)],[f_948_1]) ).
cnf(f_948_3,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Transcendental_Ocos(U_2876),c_Transcendental_Osin(U_2876))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_948_2]) ).
fof(f_949_1,plain,
! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),V_x),V_y) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_x)),hAPP(c_Complex_ORe,V_y)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_x)),hAPP(c_Complex_OIm,V_y))),
inference(fof_nnf,[status(thm)],[fact_complex__add__def]) ).
fof(f_949_2,plain,
! [U_2878,U_2877] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2877),U_2878) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2877)),hAPP(c_Complex_ORe,U_2878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2877)),hAPP(c_Complex_OIm,U_2878))),
inference(variable_rename,[status(thm)],[f_949_1]) ).
cnf(f_949_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex),U_2877),U_2878) = c_Complex_Ocomplex_OComplex(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2877)),hAPP(c_Complex_ORe,U_2878)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2877)),hAPP(c_Complex_OIm,U_2878))),
inference(clausify,[status(thm)],[f_949_2]) ).
fof(f_950_1,plain,
! [V_n_2,V_m_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)))
| ( ! [B_q] :
( ~ hBOOL(hAPP(V_P_2,B_q))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
& ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [B_q] :
( hBOOL(hAPP(V_P_2,B_q))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(B_q))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).
fof(f_950_2,plain,
! [U_2883,U_2882,U_2881] :
( ( hBOOL(hAPP(U_2881,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2882,U_2883)))
| ( ! [U_2880] :
( ~ hBOOL(hAPP(U_2881,U_2880))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2883),c_Nat_OSuc(U_2880))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2883),U_2880)),U_2882)) )
& ( ~ hBOOL(hAPP(U_2881,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2883 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [U_2879] :
( hBOOL(hAPP(U_2881,U_2879))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2883),c_Nat_OSuc(U_2879))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2883),U_2879)),U_2882)) )
| ( hBOOL(hAPP(U_2881,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_2883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_2881,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2882,U_2883))) ) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
fof(f_950_3,plain,
( ! [U_2889,U_2887,U_2885] :
( hBOOL(hAPP(U_2885,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2887,U_2889)))
| ( ! [U_2880] :
( ~ hBOOL(hAPP(U_2885,U_2880))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),c_Nat_OSuc(U_2880))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2880)),U_2887)) )
& ( ~ hBOOL(hAPP(U_2885,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2889 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_2888,U_2886,U_2884] :
( ? [U_2879] :
( hBOOL(hAPP(U_2884,U_2879))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),c_Nat_OSuc(U_2879))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),U_2879)),U_2886)) )
| ( hBOOL(hAPP(U_2884,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_2888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ) ),
inference(miniscope,[status(thm)],[f_950_2]) ).
fof(f_950_4,plain,
( ! [U_2889,U_2887,U_2885] :
( hBOOL(hAPP(U_2885,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2887,U_2889)))
| ( ! [U_2880] :
( ~ hBOOL(hAPP(U_2885,U_2880))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),c_Nat_OSuc(U_2880))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2880)),U_2887)) )
& ( ~ hBOOL(hAPP(U_2885,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2889 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_2888,U_2886,U_2884] :
( ( hBOOL(hAPP(U_2884,sK75(U_2888,U_2886,U_2884)))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),c_Nat_OSuc(sK75(U_2888,U_2886,U_2884)))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),sK75(U_2888,U_2886,U_2884))),U_2886)) )
| ( hBOOL(hAPP(U_2884,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_2888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_2879,sK75(U_2888,U_2886,U_2884))],[f_950_3]) ).
cnf(f_950_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),sK75(U_2888,U_2886,U_2884))),U_2886))
| U_2888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_6,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),c_Nat_OSuc(sK75(U_2888,U_2886,U_2884)))))
| U_2888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_7,plain,
( hBOOL(hAPP(U_2884,sK75(U_2888,U_2886,U_2884)))
| U_2888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_8,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),sK75(U_2888,U_2886,U_2884))),U_2886))
| hBOOL(hAPP(U_2884,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_9,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2888),c_Nat_OSuc(sK75(U_2888,U_2886,U_2884)))))
| hBOOL(hAPP(U_2884,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_10,plain,
( hBOOL(hAPP(U_2884,sK75(U_2888,U_2886,U_2884)))
| hBOOL(hAPP(U_2884,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_2884,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2886,U_2888))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_11,plain,
( ~ hBOOL(hAPP(U_2885,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2889 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_2885,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2887,U_2889))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_12,plain,
( ~ hBOOL(hAPP(U_2885,U_2880))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),c_Nat_OSuc(U_2880))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2889),U_2880)),U_2887))
| hBOOL(hAPP(U_2885,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2887,U_2889))) ),
inference(clausify,[status(thm)],[f_950_4]) ).
fof(f_951_1,plain,
! [V_m_2,V_q_2,V_n_2] :
( ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) )
| V_q_2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2) )
& ( V_q_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_n_2)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),c_Nat_OSuc(V_q_2))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
inference(fof_nnf,[status(thm)],[fact_split__div__lemma]) ).
fof(f_951_2,plain,
! [U_2892,U_2891,U_2890] :
( ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),c_Nat_OSuc(U_2891))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),U_2891)),U_2892)) )
| U_2891 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2892,U_2890) )
& ( U_2891 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2892,U_2890)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),c_Nat_OSuc(U_2891))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),U_2891)),U_2892)) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2890)) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
cnf(f_951_3,plain,
( U_2891 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2892,U_2890)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),c_Nat_OSuc(U_2891))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),U_2891)),U_2892))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2890)) ),
inference(clausify,[status(thm)],[f_951_2]) ).
cnf(f_951_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),U_2891)),U_2892))
| U_2891 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2892,U_2890)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2890)) ),
inference(clausify,[status(thm)],[f_951_2]) ).
cnf(f_951_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2890),c_Nat_OSuc(U_2891))))
| U_2891 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2892,U_2890)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2890)) ),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_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))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__div__geq]) ).
fof(f_952_2,plain,
! [U_2894,U_2893] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2894,U_2893) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2894,U_2893),U_2893))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2893),U_2894))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2893)) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
cnf(f_952_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_2894,U_2893) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2894,U_2893),U_2893))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2893),U_2894))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2893)) ),
inference(clausify,[status(thm)],[f_952_2]) ).
fof(f_953_1,plain,
! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_complex_Osize_I1_J]) ).
fof(f_953_2,plain,
! [U_2896,U_2895] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(U_2895,U_2896)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_953_1]) ).
cnf(f_953_3,plain,
c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(U_2895,U_2896)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_953_2]) ).
fof(f_954_1,plain,
! [V_y] :
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_cos__arg__i__mult__zero__pos]) ).
fof(f_954_2,plain,
! [U_2897] :
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2897))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2897)) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
cnf(f_954_3,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2897))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2897)) ),
inference(clausify,[status(thm)],[f_954_2]) ).
fof(f_955_1,plain,
! [V_y] :
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_cos__arg__i__mult__zero]) ).
fof(f_955_2,plain,
! [U_2898] :
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2898))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2898 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
cnf(f_955_3,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2898))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2898 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_955_2]) ).
fof(f_956_1,plain,
! [V_y] :
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(fof_nnf,[status(thm)],[fact_cos__arg__i__mult__zero__neg]) ).
fof(f_956_2,plain,
! [U_2899] :
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2899))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2899),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
cnf(f_956_3,plain,
( c_Transcendental_Ocos(c_Complex_Oarg(c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2899))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2899),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_956_2]) ).
fof(f_957_1,plain,
! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_complex_Osize_I2_J]) ).
fof(f_957_2,plain,
! [U_2901,U_2900] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_2900,U_2901)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_957_1]) ).
cnf(f_957_3,plain,
c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_2900,U_2901)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_957_2]) ).
fof(f_958_1,plain,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
inference(fof_nnf,[status(thm)],[fact_complex_Orecs]) ).
fof(f_958_2,plain,
! [U_2905,U_2904,U_2903,U_2902] : c_Complex_Ocomplex_Ocomplex__rec(U_2902,U_2903,c_Complex_Ocomplex_OComplex(U_2904,U_2905)) = hAPP(hAPP(U_2903,U_2904),U_2905),
inference(variable_rename,[status(thm)],[f_958_1]) ).
cnf(f_958_3,plain,
c_Complex_Ocomplex_Ocomplex__rec(U_2902,U_2903,c_Complex_Ocomplex_OComplex(U_2904,U_2905)) = hAPP(hAPP(U_2903,U_2904),U_2905),
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_1,plain,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
inference(fof_nnf,[status(thm)],[fact_complex_Osimps_I2_J]) ).
fof(f_959_2,plain,
! [U_2909,U_2908,U_2907,U_2906] : c_Complex_Ocomplex_Ocomplex__case(U_2906,U_2907,c_Complex_Ocomplex_OComplex(U_2908,U_2909)) = hAPP(hAPP(U_2907,U_2908),U_2909),
inference(variable_rename,[status(thm)],[f_959_1]) ).
cnf(f_959_3,plain,
c_Complex_Ocomplex_Ocomplex__case(U_2906,U_2907,c_Complex_Ocomplex_OComplex(U_2908,U_2909)) = hAPP(hAPP(U_2907,U_2908),U_2909),
inference(clausify,[status(thm)],[f_959_2]) ).
fof(f_960_1,plain,
! [V_y,V_x] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_RealDef_Oreal(tc_Nat_Onat,V_y))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_y)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y))
| ~ hBOOL(hAPP(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_natfloor__div__nat]) ).
fof(f_960_2,plain,
! [U_2911,U_2910] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2910),c_RealDef_Oreal(tc_Nat_Onat,U_2911))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(U_2910),U_2911)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2911))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2910)) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
cnf(f_960_3,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2910),c_RealDef_Oreal(tc_Nat_Onat,U_2911))) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_RComplete_Onatfloor(U_2910),U_2911)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2911))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2910)) ),
inference(clausify,[status(thm)],[f_960_2]) ).
fof(f_961_1,plain,
! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),
inference(fof_nnf,[status(thm)],[fact_real__sgn__eq]) ).
fof(f_961_2,plain,
! [U_2912] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_2912) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2912),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2912)),
inference(variable_rename,[status(thm)],[f_961_1]) ).
cnf(f_961_3,plain,
c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_2912) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2912),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2912)),
inference(clausify,[status(thm)],[f_961_2]) ).
fof(f_962_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_ya) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya))
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Oadd]) ).
fof(f_962_2,plain,
! [U_2916,U_2915,U_2914,U_2913] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2913),U_2914),U_2915)),U_2916) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2913),U_2914),U_2916)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2913),U_2915),U_2916))
| ~ class_RealVector_Oreal__normed__field(U_2913) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
cnf(f_962_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2913),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2913),U_2914),U_2915)),U_2916) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2913),U_2914),U_2916)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2913),U_2915),U_2916))
| ~ class_RealVector_Oreal__normed__field(U_2913) ),
inference(clausify,[status(thm)],[f_962_2]) ).
fof(f_963_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__divide__distrib]) ).
fof(f_963_2,plain,
! [U_2920,U_2919,U_2918,U_2917] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2917),U_2918),U_2919)),U_2920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2917),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2917),U_2918),U_2920)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2917),U_2919),U_2920))
| ~ class_Rings_Odivision__ring(U_2917) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
cnf(f_963_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2917),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2917),U_2918),U_2919)),U_2920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2917),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2917),U_2918),U_2920)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2917),U_2919),U_2920))
| ~ class_Rings_Odivision__ring(U_2917) ),
inference(clausify,[status(thm)],[f_963_2]) ).
fof(f_964_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__1]) ).
fof(f_964_2,plain,
! [U_2922,U_2921] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2921),U_2922),c_Groups_Oone__class_Oone(U_2921)) = U_2922
| ~ class_Rings_Odivision__ring(U_2921) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
cnf(f_964_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2921),U_2922),c_Groups_Oone__class_Oone(U_2921)) = U_2922
| ~ class_Rings_Odivision__ring(U_2921) ),
inference(clausify,[status(thm)],[f_964_2]) ).
fof(f_965_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) != c_Groups_Oone__class_Oone(T_a) ) )
| V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).
fof(f_965_2,plain,
! [U_2925,U_2924,U_2923] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2923),U_2925),U_2924) = c_Groups_Oone__class_Oone(U_2923)
| U_2925 != U_2924 )
& ( U_2925 = U_2924
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2923),U_2925),U_2924) != c_Groups_Oone__class_Oone(U_2923) ) )
| U_2924 = c_Groups_Ozero__class_Ozero(U_2923)
| ~ class_Rings_Odivision__ring(U_2923) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
cnf(f_965_3,plain,
( U_2925 = U_2924
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2923),U_2925),U_2924) != c_Groups_Oone__class_Oone(U_2923)
| U_2924 = c_Groups_Ozero__class_Ozero(U_2923)
| ~ class_Rings_Odivision__ring(U_2923) ),
inference(clausify,[status(thm)],[f_965_2]) ).
cnf(f_965_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2923),U_2925),U_2924) = c_Groups_Oone__class_Oone(U_2923)
| U_2925 != U_2924
| U_2924 = c_Groups_Ozero__class_Ozero(U_2923)
| ~ class_Rings_Odivision__ring(U_2923) ),
inference(clausify,[status(thm)],[f_965_2]) ).
fof(f_966_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self]) ).
fof(f_966_2,plain,
! [U_2927,U_2926] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2926),U_2927),U_2927) = c_Groups_Oone__class_Oone(U_2926)
| U_2927 = c_Groups_Ozero__class_Ozero(U_2926)
| ~ class_Rings_Odivision__ring(U_2926) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
cnf(f_966_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2926),U_2927),U_2927) = c_Groups_Oone__class_Oone(U_2926)
| U_2927 = c_Groups_Ozero__class_Ozero(U_2926)
| ~ class_Rings_Odivision__ring(U_2926) ),
inference(clausify,[status(thm)],[f_966_2]) ).
fof(f_967_1,plain,
! [V_a,T_a] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| V_a != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self__if]) ).
fof(f_967_2,plain,
! [U_2929,U_2928] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2928),U_2929),U_2929) = c_Groups_Oone__class_Oone(U_2928)
| U_2929 = c_Groups_Ozero__class_Ozero(U_2928) )
& ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2928),U_2929),U_2929) = c_Groups_Ozero__class_Ozero(U_2928)
| U_2929 != c_Groups_Ozero__class_Ozero(U_2928) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_2928) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
cnf(f_967_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2928),U_2929),U_2929) = c_Groups_Ozero__class_Ozero(U_2928)
| U_2929 != c_Groups_Ozero__class_Ozero(U_2928)
| ~ class_Rings_Odivision__ring__inverse__zero(U_2928) ),
inference(clausify,[status(thm)],[f_967_2]) ).
cnf(f_967_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2928),U_2929),U_2929) = c_Groups_Oone__class_Oone(U_2928)
| U_2929 = c_Groups_Ozero__class_Ozero(U_2928)
| ~ class_Rings_Odivision__ring__inverse__zero(U_2928) ),
inference(clausify,[status(thm)],[f_967_2]) ).
fof(f_968_1,plain,
! [V_n,V_a,V_b,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide]) ).
fof(f_968_2,plain,
! [U_2933,U_2932,U_2931,U_2930] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2930),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2930),U_2932),U_2931)),U_2933) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2930),hAPP(hAPP(c_Power_Opower__class_Opower(U_2930),U_2932),U_2933)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2930),U_2931),U_2933))
| U_2931 = c_Groups_Ozero__class_Ozero(U_2930)
| ~ class_Fields_Ofield(U_2930) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
cnf(f_968_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2930),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2930),U_2932),U_2931)),U_2933) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2930),hAPP(hAPP(c_Power_Opower__class_Opower(U_2930),U_2932),U_2933)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2930),U_2931),U_2933))
| U_2931 = c_Groups_Ozero__class_Ozero(U_2930)
| ~ class_Fields_Ofield(U_2930) ),
inference(clausify,[status(thm)],[f_968_2]) ).
fof(f_969_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one__over]) ).
fof(f_969_2,plain,
! [U_2936,U_2935,U_2934] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2934),c_Groups_Oone__class_Oone(U_2934)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2934),U_2935),U_2936)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2934),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2934),c_Groups_Oone__class_Oone(U_2934)),U_2935)),U_2936)
| ~ class_Fields_Ofield__inverse__zero(U_2934) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
cnf(f_969_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2934),c_Groups_Oone__class_Oone(U_2934)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2934),U_2935),U_2936)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2934),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2934),c_Groups_Oone__class_Oone(U_2934)),U_2935)),U_2936)
| ~ class_Fields_Ofield__inverse__zero(U_2934) ),
inference(clausify,[status(thm)],[f_969_2]) ).
fof(f_970_1,plain,
! [V_y_2,V_X_2,T_a] :
( c_SEQ_Oconvergent(T_a,c_COMBC(tc_Nat_Onat,T_a,T_a,c_COMBB(T_a,tc_fun(T_a,T_a),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(T_a),V_X_2),V_y_2))
| ~ c_SEQ_Oconvergent(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Oconvergent]) ).
fof(f_970_2,plain,
! [U_2939,U_2938,U_2937] :
( c_SEQ_Oconvergent(U_2937,c_COMBC(tc_Nat_Onat,U_2937,U_2937,c_COMBB(U_2937,tc_fun(U_2937,U_2937),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(U_2937),U_2938),U_2939))
| ~ c_SEQ_Oconvergent(U_2937,U_2938)
| ~ class_RealVector_Oreal__normed__field(U_2937) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
cnf(f_970_3,plain,
( c_SEQ_Oconvergent(U_2937,c_COMBC(tc_Nat_Onat,U_2937,U_2937,c_COMBB(U_2937,tc_fun(U_2937,U_2937),tc_Nat_Onat,c_Rings_Oinverse__class_Odivide(U_2937),U_2938),U_2939))
| ~ c_SEQ_Oconvergent(U_2937,U_2938)
| ~ class_RealVector_Oreal__normed__field(U_2937) ),
inference(clausify,[status(thm)],[f_970_2]) ).
fof(f_971_1,plain,
! [V_b,V_a,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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__field(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__divide]) ).
fof(f_971_2,plain,
! [U_2942,U_2941,U_2940] :
( c_RealVector_Onorm__class_Onorm(U_2940,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2940),U_2941),U_2942)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2940,U_2941)),c_RealVector_Onorm__class_Onorm(U_2940,U_2942))
| ~ class_RealVector_Oreal__normed__field(U_2940)
| ~ class_Fields_Ofield__inverse__zero(U_2940) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
cnf(f_971_3,plain,
( c_RealVector_Onorm__class_Onorm(U_2940,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2940),U_2941),U_2942)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2940,U_2941)),c_RealVector_Onorm__class_Onorm(U_2940,U_2942))
| ~ class_RealVector_Oreal__normed__field(U_2940)
| ~ class_Fields_Ofield__inverse__zero(U_2940) ),
inference(clausify,[status(thm)],[f_971_2]) ).
fof(f_972_1,plain,
! [V_b,V_a,V_c,T_a] :
( V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) != V_b
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__imp]) ).
fof(f_972_2,plain,
! [U_2946,U_2945,U_2944,U_2943] :
( U_2945 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2943),U_2946),U_2944)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2943),U_2945),U_2944) != U_2946
| U_2944 = c_Groups_Ozero__class_Ozero(U_2943)
| ~ class_Rings_Odivision__ring(U_2943) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
cnf(f_972_3,plain,
( U_2945 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2943),U_2946),U_2944)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2943),U_2945),U_2944) != U_2946
| U_2944 = c_Groups_Ozero__class_Ozero(U_2943)
| ~ class_Rings_Odivision__ring(U_2943) ),
inference(clausify,[status(thm)],[f_972_2]) ).
fof(f_973_1,plain,
! [V_a,V_b,V_c,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a
| V_b != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__imp]) ).
fof(f_973_2,plain,
! [U_2950,U_2949,U_2948,U_2947] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2947),U_2949),U_2948) = U_2950
| U_2949 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2947),U_2950),U_2948)
| U_2948 = c_Groups_Ozero__class_Ozero(U_2947)
| ~ class_Rings_Odivision__ring(U_2947) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
cnf(f_973_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2947),U_2949),U_2948) = U_2950
| U_2949 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2947),U_2950),U_2948)
| U_2948 = c_Groups_Ozero__class_Ozero(U_2947)
| ~ class_Rings_Odivision__ring(U_2947) ),
inference(clausify,[status(thm)],[f_973_2]) ).
fof(f_974_1,plain,
! [V_a_2,V_b_2,V_c_2,T_a] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2
| V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) != V_a_2 ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).
fof(f_974_2,plain,
! [U_2954,U_2953,U_2952,U_2951] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2951),U_2953),U_2952) = U_2954
| U_2953 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2954),U_2952) )
& ( U_2953 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2954),U_2952)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2951),U_2953),U_2952) != U_2954 ) )
| U_2952 = c_Groups_Ozero__class_Ozero(U_2951)
| ~ class_Rings_Odivision__ring(U_2951) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
cnf(f_974_3,plain,
( U_2953 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2954),U_2952)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2951),U_2953),U_2952) != U_2954
| U_2952 = c_Groups_Ozero__class_Ozero(U_2951)
| ~ class_Rings_Odivision__ring(U_2951) ),
inference(clausify,[status(thm)],[f_974_2]) ).
cnf(f_974_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2951),U_2953),U_2952) = U_2954
| U_2953 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2954),U_2952)
| U_2952 = c_Groups_Ozero__class_Ozero(U_2951)
| ~ class_Rings_Odivision__ring(U_2951) ),
inference(clausify,[status(thm)],[f_974_2]) ).
fof(f_975_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) != V_b_2 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).
fof(f_975_2,plain,
! [U_2958,U_2957,U_2956,U_2955] :
( ( ( U_2957 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2955),U_2958),U_2956)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2955),U_2957),U_2956) != U_2958 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2955),U_2957),U_2956) = U_2958
| U_2957 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2955),U_2958),U_2956) ) )
| U_2956 = c_Groups_Ozero__class_Ozero(U_2955)
| ~ class_Rings_Odivision__ring(U_2955) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
cnf(f_975_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2955),U_2957),U_2956) = U_2958
| U_2957 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2955),U_2958),U_2956)
| U_2956 = c_Groups_Ozero__class_Ozero(U_2955)
| ~ class_Rings_Odivision__ring(U_2955) ),
inference(clausify,[status(thm)],[f_975_2]) ).
cnf(f_975_4,plain,
( U_2957 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2955),U_2958),U_2956)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2955),U_2957),U_2956) != U_2958
| U_2956 = c_Groups_Ozero__class_Ozero(U_2955)
| ~ class_Rings_Odivision__ring(U_2955) ),
inference(clausify,[status(thm)],[f_975_2]) ).
fof(f_976_1,plain,
! [V_a,V_b,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_a)),c_RealVector_Onorm__class_Onorm(T_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__norm__divide]) ).
fof(f_976_2,plain,
! [U_2961,U_2960,U_2959] :
( c_RealVector_Onorm__class_Onorm(U_2959,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2959),U_2961),U_2960)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2959,U_2961)),c_RealVector_Onorm__class_Onorm(U_2959,U_2960))
| U_2960 = c_Groups_Ozero__class_Ozero(U_2959)
| ~ class_RealVector_Oreal__normed__field(U_2959) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
cnf(f_976_3,plain,
( c_RealVector_Onorm__class_Onorm(U_2959,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2959),U_2961),U_2960)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2959,U_2961)),c_RealVector_Onorm__class_Onorm(U_2959,U_2960))
| U_2960 = c_Groups_Ozero__class_Ozero(U_2959)
| ~ class_RealVector_Oreal__normed__field(U_2959) ),
inference(clausify,[status(thm)],[f_976_2]) ).
fof(f_977_1,plain,
! [V_y,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Ozero]) ).
fof(f_977_2,plain,
! [U_2963,U_2962] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2962),c_Groups_Ozero__class_Ozero(U_2962)),U_2963) = c_Groups_Ozero__class_Ozero(U_2962)
| ~ class_RealVector_Oreal__normed__field(U_2962) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
cnf(f_977_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2962),c_Groups_Ozero__class_Ozero(U_2962)),U_2963) = c_Groups_Ozero__class_Ozero(U_2962)
| ~ class_RealVector_Oreal__normed__field(U_2962) ),
inference(clausify,[status(thm)],[f_977_2]) ).
fof(f_978_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero__left]) ).
fof(f_978_2,plain,
! [U_2965,U_2964] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2964),c_Groups_Ozero__class_Ozero(U_2964)),U_2965) = c_Groups_Ozero__class_Ozero(U_2964)
| ~ class_Rings_Odivision__ring(U_2964) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
cnf(f_978_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2964),c_Groups_Ozero__class_Ozero(U_2964)),U_2965) = c_Groups_Ozero__class_Ozero(U_2964)
| ~ class_Rings_Odivision__ring(U_2964) ),
inference(clausify,[status(thm)],[f_978_2]) ).
fof(f_979_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero]) ).
fof(f_979_2,plain,
! [U_2967,U_2966] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2966),U_2967),c_Groups_Ozero__class_Ozero(U_2966)) = c_Groups_Ozero__class_Ozero(U_2966)
| ~ class_Rings_Odivision__ring__inverse__zero(U_2966) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
cnf(f_979_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2966),U_2967),c_Groups_Ozero__class_Ozero(U_2966)) = c_Groups_Ozero__class_Ozero(U_2966)
| ~ class_Rings_Odivision__ring__inverse__zero(U_2966) ),
inference(clausify,[status(thm)],[f_979_2]) ).
fof(f_980_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right]) ).
fof(f_980_2,plain,
! [U_2971,U_2970,U_2969,U_2968] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),U_2969),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2968),U_2970),U_2971)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),U_2969),U_2970)),U_2971)
| ~ class_Rings_Odivision__ring(U_2968) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
cnf(f_980_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),U_2969),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2968),U_2970),U_2971)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),U_2969),U_2970)),U_2971)
| ~ class_Rings_Odivision__ring(U_2968) ),
inference(clausify,[status(thm)],[f_980_2]) ).
fof(f_981_1,plain,
! [V_a,V_r] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_r)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_a),V_r),
inference(fof_nnf,[status(thm)],[fact_real__divide__square__eq]) ).
fof(f_981_2,plain,
! [U_2973,U_2972] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2972),U_2973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2972),U_2972)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2973),U_2972),
inference(variable_rename,[status(thm)],[f_981_1]) ).
cnf(f_981_3,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2972),U_2973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2972),U_2972)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2973),U_2972),
inference(clausify,[status(thm)],[f_981_2]) ).
fof(f_982_1,plain,
! [V_n,V_b,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__divide]) ).
fof(f_982_2,plain,
! [U_2977,U_2976,U_2975,U_2974] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2974),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2974),U_2975),U_2976)),U_2977) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2974),hAPP(hAPP(c_Power_Opower__class_Opower(U_2974),U_2975),U_2977)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2974),U_2976),U_2977))
| ~ class_Fields_Ofield__inverse__zero(U_2974) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
cnf(f_982_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2974),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2974),U_2975),U_2976)),U_2977) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2974),hAPP(hAPP(c_Power_Opower__class_Opower(U_2974),U_2975),U_2977)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2974),U_2976),U_2977))
| ~ class_Fields_Ofield__inverse__zero(U_2974) ),
inference(clausify,[status(thm)],[f_982_2]) ).
fof(f_983_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x_2),V_y_2)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) )
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
& ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_x_2)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y_2))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x_2),V_y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff]) ).
fof(f_983_2,plain,
! [U_2979,U_2978] :
( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2978),U_2979)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2979),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2978)) )
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2979))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2978),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
& ( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2979),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2978)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2979))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2978),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2978),U_2979))) ) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
fof(f_983_3,plain,
( ! [U_2983,U_2981] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2981),U_2983)))
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2983),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2981)) )
| ( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2983))
& ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2981),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
& ! [U_2982,U_2980] :
( ( ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2982),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2980)) )
& ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2982))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2980),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) ) )
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2980),U_2982))) ) ),
inference(miniscope,[status(thm)],[f_983_2]) ).
cnf(f_983_4,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2982))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2980),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2980),U_2982))) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_5,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2982),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2980))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2980),U_2982))) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_6,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2981))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2981),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2981),U_2983))) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_7,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2983),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2981),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2981),U_2983))) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_8,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2981))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2983))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2981),U_2983))) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_9,plain,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2983),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_2983))
| hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_2981),U_2983))) ),
inference(clausify,[status(thm)],[f_983_3]) ).
fof(f_984_1,plain,
! [V_z] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)),
inference(fof_nnf,[status(thm)],[fact_Im__sgn]) ).
fof(f_984_2,plain,
! [U_2984] : hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,U_2984)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2984)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2984)),
inference(variable_rename,[status(thm)],[f_984_1]) ).
cnf(f_984_3,plain,
hAPP(c_Complex_OIm,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,U_2984)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_OIm,U_2984)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2984)),
inference(clausify,[status(thm)],[f_984_2]) ).
fof(f_985_1,plain,
! [V_z] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z)),
inference(fof_nnf,[status(thm)],[fact_Re__sgn]) ).
fof(f_985_2,plain,
! [U_2985] : hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,U_2985)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2985)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2985)),
inference(variable_rename,[status(thm)],[f_985_1]) ).
cnf(f_985_3,plain,
hAPP(c_Complex_ORe,c_Groups_Osgn__class_Osgn(tc_Complex_Ocomplex,U_2985)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),hAPP(c_Complex_ORe,U_2985)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2985)),
inference(clausify,[status(thm)],[f_985_2]) ).
fof(f_986_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(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_Rings_Oinverse__class_Odivide(T_a),V_x),V_ya),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_ya))
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Odiff]) ).
fof(f_986_2,plain,
! [U_2989,U_2988,U_2987,U_2986] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2986),c_Groups_Ominus__class_Ominus(U_2986,U_2987,U_2988)),U_2989) = c_Groups_Ominus__class_Ominus(U_2986,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2986),U_2987),U_2989),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2986),U_2988),U_2989))
| ~ class_RealVector_Oreal__normed__field(U_2986) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
cnf(f_986_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2986),c_Groups_Ominus__class_Ominus(U_2986,U_2987,U_2988)),U_2989) = c_Groups_Ominus__class_Ominus(U_2986,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2986),U_2987),U_2989),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2986),U_2988),U_2989))
| ~ class_RealVector_Oreal__normed__field(U_2986) ),
inference(clausify,[status(thm)],[f_986_2]) ).
fof(f_987_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),V_c) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib]) ).
fof(f_987_2,plain,
! [U_2993,U_2992,U_2991,U_2990] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2990),c_Groups_Ominus__class_Ominus(U_2990,U_2991,U_2992)),U_2993) = c_Groups_Ominus__class_Ominus(U_2990,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2990),U_2991),U_2993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2990),U_2992),U_2993))
| ~ class_Rings_Odivision__ring(U_2990) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
cnf(f_987_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2990),c_Groups_Ominus__class_Ominus(U_2990,U_2991,U_2992)),U_2993) = c_Groups_Ominus__class_Ominus(U_2990,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2990),U_2991),U_2993),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2990),U_2992),U_2993))
| ~ class_Rings_Odivision__ring(U_2990) ),
inference(clausify,[status(thm)],[f_987_2]) ).
fof(f_988_1,plain,
! [V_h,V_d,V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),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_c),V_d))),V_h) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)),V_h))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),V_h)),V_d))
| ~ class_RealVector_Oreal__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__mult__lemma]) ).
fof(f_988_2,plain,
! [U_2999,U_2998,U_2997,U_2996,U_2995,U_2994] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2994),c_Groups_Ominus__class_Ominus(U_2994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),U_2995),U_2996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),U_2997),U_2998))),U_2999) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),U_2995),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2994),c_Groups_Ominus__class_Ominus(U_2994,U_2996,U_2998)),U_2999))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2994),c_Groups_Ominus__class_Ominus(U_2994,U_2995,U_2997)),U_2999)),U_2998))
| ~ class_RealVector_Oreal__field(U_2994) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
cnf(f_988_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2994),c_Groups_Ominus__class_Ominus(U_2994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),U_2995),U_2996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),U_2997),U_2998))),U_2999) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),U_2995),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2994),c_Groups_Ominus__class_Ominus(U_2994,U_2996,U_2998)),U_2999))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2994),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_2994),c_Groups_Ominus__class_Ominus(U_2994,U_2995,U_2997)),U_2999)),U_2998))
| ~ class_RealVector_Oreal__field(U_2994) ),
inference(clausify,[status(thm)],[f_988_2]) ).
fof(f_989_1,plain,
! [V_b_2,V_a_2,V_fa_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_a_2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_fa_2,V_b_2),hAPP(V_fa_2,V_a_2))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b_2,V_a_2))),V_b_2)),
inference(fof_nnf,[status(thm)],[fact_lemma__MVT]) ).
fof(f_989_2,plain,
! [U_3002,U_3001,U_3000] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3002),hAPP(U_3000,U_3001))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3002,U_3001))),U_3001)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3002),hAPP(U_3000,U_3001))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3002,U_3001))),U_3002)),
inference(variable_rename,[status(thm)],[f_989_1]) ).
cnf(f_989_3,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3002),hAPP(U_3000,U_3001))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3002,U_3001))),U_3001)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3002),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_3000,U_3002),hAPP(U_3000,U_3001))),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3002,U_3001))),U_3002)),
inference(clausify,[status(thm)],[f_989_2]) ).
fof(f_990_1,plain,
! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)))),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__div4]) ).
fof(f_990_2,plain,
! [U_3004,U_3003] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3003,U_3004))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3003)),c_RealDef_Oreal(tc_Nat_Onat,U_3004)))),
inference(variable_rename,[status(thm)],[f_990_1]) ).
cnf(f_990_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3003,U_3004))),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3003)),c_RealDef_Oreal(tc_Nat_Onat,U_3004)))),
inference(clausify,[status(thm)],[f_990_2]) ).
fof(f_991_1,plain,
! [V_m,V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__diff]) ).
fof(f_991_2,plain,
! [U_3008,U_3007,U_3006,U_3005] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3005),U_3006),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3008,U_3007)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3005),hAPP(hAPP(c_Power_Opower__class_Opower(U_3005),U_3006),U_3008)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3005),U_3006),U_3007))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3007),U_3008))
| U_3006 = c_Groups_Ozero__class_Ozero(U_3005)
| ~ class_Fields_Ofield(U_3005) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
cnf(f_991_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3005),U_3006),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3008,U_3007)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3005),hAPP(hAPP(c_Power_Opower__class_Opower(U_3005),U_3006),U_3008)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3005),U_3006),U_3007))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3007),U_3008))
| U_3006 = c_Groups_Ozero__class_Ozero(U_3005)
| ~ class_Fields_Ofield(U_3005) ),
inference(clausify,[status(thm)],[f_991_2]) ).
fof(f_992_1,plain,
! [V_y,V_x] :
( c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),V_x),V_y)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),V_y))
| ~ hBOOL(hAPP(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__div]) ).
fof(f_992_2,plain,
! [U_3010,U_3009] :
( c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_3009),U_3010)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(U_3009),c_Transcendental_Oln(U_3010))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_3010))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_3009)) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
cnf(f_992_3,plain,
( c_Transcendental_Oln(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),U_3009),U_3010)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Transcendental_Oln(U_3009),c_Transcendental_Oln(U_3010))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_3010))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),U_3009)) ),
inference(clausify,[status(thm)],[f_992_2]) ).
fof(f_993_1,plain,
! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x))))),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__div2]) ).
fof(f_993_2,plain,
! [U_3012,U_3011] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3011)),c_RealDef_Oreal(tc_Nat_Onat,U_3012)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3011,U_3012))))),
inference(variable_rename,[status(thm)],[f_993_1]) ).
cnf(f_993_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3011)),c_RealDef_Oreal(tc_Nat_Onat,U_3012)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3011,U_3012))))),
inference(clausify,[status(thm)],[f_993_2]) ).
fof(f_994_1,plain,
! [V_x,V_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),c_RealDef_Oreal(tc_Nat_Onat,V_x)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_x)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__div3]) ).
fof(f_994_2,plain,
! [U_3014,U_3013] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3013)),c_RealDef_Oreal(tc_Nat_Onat,U_3014)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3013,U_3014)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_994_1]) ).
cnf(f_994_3,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3013)),c_RealDef_Oreal(tc_Nat_Onat,U_3014)),c_RealDef_Oreal(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3013,U_3014)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_994_2]) ).
fof(f_995_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_c),c_Groups_Ozero__class_Ozero(T_a)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_a),V_b))
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg]) ).
fof(f_995_2,plain,
! [U_3018,U_3017,U_3016,U_3015] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3015,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3015),U_3018),U_3016)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3015),U_3018),U_3017)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_3015,c_Groups_Ozero__class_Ozero(U_3015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3015),U_3016),U_3017)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3015,U_3018),c_Groups_Ozero__class_Ozero(U_3015)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3015,U_3016),U_3017))
| ~ class_Fields_Olinordered__field__inverse__zero(U_3015) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
cnf(f_995_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3015,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3015),U_3018),U_3016)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3015),U_3018),U_3017)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_3015,c_Groups_Ozero__class_Ozero(U_3015)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3015),U_3016),U_3017)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3015,U_3018),c_Groups_Ozero__class_Ozero(U_3015)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3015,U_3016),U_3017))
| ~ class_Fields_Olinordered__field__inverse__zero(U_3015) ),
inference(clausify,[status(thm)],[f_995_2]) ).
fof(f_996_1,plain,
! [V_c,V_a,V_b,T_a] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a)),V_c))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(T_a,V_b),V_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono]) ).
fof(f_996_2,plain,
! [U_3022,U_3021,U_3020,U_3019] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3019,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3019),U_3022),U_3021)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3019),U_3022),U_3020)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_3019,c_Groups_Ozero__class_Ozero(U_3019)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3019),U_3021),U_3020)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3019,c_Groups_Ozero__class_Ozero(U_3019)),U_3022))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3019,U_3020),U_3021))
| ~ class_Fields_Olinordered__field(U_3019) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
cnf(f_996_3,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3019,hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3019),U_3022),U_3021)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_3019),U_3022),U_3020)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(U_3019,c_Groups_Ozero__class_Ozero(U_3019)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3019),U_3021),U_3020)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3019,c_Groups_Ozero__class_Ozero(U_3019)),U_3022))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(U_3019,U_3020),U_3021))
| ~ class_Fields_Olinordered__field(U_3019) ),
inference(clausify,[status(thm)],[f_996_2]) ).
fof(f_997_1,plain,
! [V_b,V_a] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(V_a)),c_Complex_Ocis(V_b)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_b)),
inference(fof_nnf,[status(thm)],[fact_cis__divide]) ).
fof(f_997_2,plain,
! [U_3024,U_3023] : hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(U_3023)),c_Complex_Ocis(U_3024)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3023,U_3024)),
inference(variable_rename,[status(thm)],[f_997_1]) ).
cnf(f_997_3,plain,
hAPP(hAPP(c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Complex_Ocis(U_3023)),c_Complex_Ocis(U_3024)) = c_Complex_Ocis(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3023,U_3024)),
inference(clausify,[status(thm)],[f_997_2]) ).
fof(f_998_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_998_2,plain,
! [U_3025] :
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3025))
| ~ class_Rings_Oidom(U_3025) ),
inference(variable_rename,[status(thm)],[f_998_1]) ).
cnf(f_998_3,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3025))
| ~ class_Rings_Oidom(U_3025) ),
inference(clausify,[status(thm)],[f_998_2]) ).
fof(f_999_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_999_2,plain,
! [U_3026] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3026))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3026) ),
inference(variable_rename,[status(thm)],[f_999_1]) ).
cnf(f_999_3,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3026))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3026) ),
inference(clausify,[status(thm)],[f_999_2]) ).
fof(f_1000_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_1000_2,plain,
! [U_3027] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3027))
| ~ class_Rings_Ocomm__semiring__0(U_3027) ),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
cnf(f_1000_3,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3027))
| ~ class_Rings_Ocomm__semiring__0(U_3027) ),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_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_1001_2,plain,
! [U_3028] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3028))
| ~ class_Rings_Ocomm__ring(U_3028) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
cnf(f_1001_3,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3028))
| ~ class_Rings_Ocomm__ring(U_3028) ),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_1,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(f_1002_2,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1002_1]) ).
fof(f_1003_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_1003_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1003_1]) ).
fof(f_1004_1,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(f_1004_2,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1004_1]) ).
fof(f_1005_1,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]) ).
cnf(f_1005_2,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1005_1]) ).
fof(f_1006_1,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]) ).
cnf(f_1006_2,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1006_1]) ).
fof(f_1007_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_1007_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1007_1]) ).
fof(f_1008_1,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]) ).
cnf(f_1008_2,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1008_1]) ).
fof(f_1009_1,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]) ).
cnf(f_1009_2,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1009_1]) ).
fof(f_1010_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_1010_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1010_1]) ).
fof(f_1011_1,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]) ).
cnf(f_1011_2,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1011_1]) ).
fof(f_1012_1,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).
cnf(f_1012_2,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1012_1]) ).
fof(f_1013_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]) ).
cnf(f_1013_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1013_1]) ).
fof(f_1014_1,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]) ).
cnf(f_1014_2,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1014_1]) ).
fof(f_1015_1,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).
cnf(f_1015_2,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1015_1]) ).
fof(f_1016_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_1016_2,plain,
! [U_3030,U_3029] :
( class_Orderings_Opreorder(tc_fun(U_3030,U_3029))
| ~ class_Orderings_Opreorder(U_3029) ),
inference(variable_rename,[status(thm)],[f_1016_1]) ).
cnf(f_1016_3,plain,
( class_Orderings_Opreorder(tc_fun(U_3030,U_3029))
| ~ class_Orderings_Opreorder(U_3029) ),
inference(clausify,[status(thm)],[f_1016_2]) ).
fof(f_1017_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_1017_2,plain,
! [U_3032,U_3031] :
( class_Orderings_Oorder(tc_fun(U_3032,U_3031))
| ~ class_Orderings_Oorder(U_3031) ),
inference(variable_rename,[status(thm)],[f_1017_1]) ).
cnf(f_1017_3,plain,
( class_Orderings_Oorder(tc_fun(U_3032,U_3031))
| ~ class_Orderings_Oorder(U_3031) ),
inference(clausify,[status(thm)],[f_1017_2]) ).
fof(f_1018_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_1018_2,plain,
! [U_3034,U_3033] :
( class_Orderings_Oord(tc_fun(U_3034,U_3033))
| ~ class_Orderings_Oord(U_3033) ),
inference(variable_rename,[status(thm)],[f_1018_1]) ).
cnf(f_1018_3,plain,
( class_Orderings_Oord(tc_fun(U_3034,U_3033))
| ~ class_Orderings_Oord(U_3033) ),
inference(clausify,[status(thm)],[f_1018_2]) ).
fof(f_1019_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]) ).
cnf(f_1019_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1019_1]) ).
fof(f_1020_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]) ).
cnf(f_1020_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1020_1]) ).
fof(f_1021_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]) ).
cnf(f_1021_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1021_1]) ).
fof(f_1022_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1022_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1022_1]) ).
fof(f_1023_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).
cnf(f_1023_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1023_1]) ).
fof(f_1024_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).
cnf(f_1024_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1024_1]) ).
fof(f_1025_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1025_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1025_1]) ).
fof(f_1026_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]) ).
cnf(f_1026_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1026_1]) ).
fof(f_1027_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1027_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1027_1]) ).
fof(f_1028_1,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).
cnf(f_1028_2,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1028_1]) ).
fof(f_1029_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1029_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1029_1]) ).
fof(f_1030_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]) ).
cnf(f_1030_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1030_1]) ).
fof(f_1031_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).
cnf(f_1031_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1031_1]) ).
fof(f_1032_1,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).
cnf(f_1032_2,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1032_1]) ).
fof(f_1033_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).
cnf(f_1033_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1033_1]) ).
fof(f_1034_1,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).
cnf(f_1034_2,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1034_1]) ).
fof(f_1035_1,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).
cnf(f_1035_2,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1035_1]) ).
fof(f_1036_1,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).
cnf(f_1036_2,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1036_1]) ).
fof(f_1037_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).
cnf(f_1037_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1037_1]) ).
fof(f_1038_1,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).
cnf(f_1038_2,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1038_1]) ).
fof(f_1039_1,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).
cnf(f_1039_2,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1039_1]) ).
fof(f_1040_1,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).
cnf(f_1040_2,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1040_1]) ).
fof(f_1041_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).
cnf(f_1041_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1041_1]) ).
fof(f_1042_1,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).
cnf(f_1042_2,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1042_1]) ).
fof(f_1043_1,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).
cnf(f_1043_2,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1043_1]) ).
fof(f_1044_1,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).
cnf(f_1044_2,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1044_1]) ).
fof(f_1045_1,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).
cnf(f_1045_2,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1045_1]) ).
fof(f_1046_1,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).
cnf(f_1046_2,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1046_1]) ).
fof(f_1047_1,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).
cnf(f_1047_2,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1047_1]) ).
fof(f_1048_1,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).
cnf(f_1048_2,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1048_1]) ).
fof(f_1049_1,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).
cnf(f_1049_2,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1049_1]) ).
fof(f_1050_1,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).
cnf(f_1050_2,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1050_1]) ).
fof(f_1051_1,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).
cnf(f_1051_2,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1051_1]) ).
fof(f_1052_1,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).
cnf(f_1052_2,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1052_1]) ).
fof(f_1053_1,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).
cnf(f_1053_2,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1053_1]) ).
fof(f_1054_1,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).
cnf(f_1054_2,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1054_1]) ).
fof(f_1055_1,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).
cnf(f_1055_2,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1055_1]) ).
fof(f_1056_1,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
cnf(f_1056_2,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1056_1]) ).
fof(f_1057_1,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).
cnf(f_1057_2,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1057_1]) ).
fof(f_1058_1,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).
cnf(f_1058_2,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1058_1]) ).
fof(f_1059_1,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).
cnf(f_1059_2,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1059_1]) ).
fof(f_1060_1,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).
cnf(f_1060_2,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1060_1]) ).
fof(f_1061_1,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).
cnf(f_1061_2,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1061_1]) ).
fof(f_1062_1,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).
cnf(f_1062_2,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1062_1]) ).
fof(f_1063_1,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).
cnf(f_1063_2,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1063_1]) ).
fof(f_1064_1,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).
cnf(f_1064_2,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1064_1]) ).
fof(f_1065_1,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).
cnf(f_1065_2,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1065_1]) ).
fof(f_1066_1,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).
cnf(f_1066_2,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1066_1]) ).
fof(f_1067_1,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).
cnf(f_1067_2,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1067_1]) ).
fof(f_1068_1,plain,
class_Power_Opower(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).
cnf(f_1068_2,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1068_1]) ).
fof(f_1069_1,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).
cnf(f_1069_2,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1069_1]) ).
fof(f_1070_1,plain,
class_Rings_Oring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).
cnf(f_1070_2,plain,
class_Rings_Oring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1070_1]) ).
fof(f_1071_1,plain,
class_Groups_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).
cnf(f_1071_2,plain,
class_Groups_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1071_1]) ).
fof(f_1072_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]) ).
cnf(f_1072_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1072_1]) ).
fof(f_1073_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]) ).
cnf(f_1073_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1073_1]) ).
fof(f_1074_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]) ).
cnf(f_1074_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1074_1]) ).
fof(f_1075_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1075_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1075_1]) ).
fof(f_1076_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).
cnf(f_1076_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1076_1]) ).
fof(f_1077_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1077_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1077_1]) ).
fof(f_1078_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1078_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1078_1]) ).
fof(f_1079_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1079_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1079_1]) ).
fof(f_1080_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).
cnf(f_1080_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1080_1]) ).
fof(f_1081_1,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).
cnf(f_1081_2,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1081_1]) ).
fof(f_1082_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
cnf(f_1082_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1082_1]) ).
fof(f_1083_1,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).
cnf(f_1083_2,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1083_1]) ).
fof(f_1084_1,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
cnf(f_1084_2,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1084_1]) ).
fof(f_1085_1,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).
cnf(f_1085_2,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1085_1]) ).
fof(f_1086_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).
cnf(f_1086_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1086_1]) ).
fof(f_1087_1,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).
cnf(f_1087_2,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1087_1]) ).
fof(f_1088_1,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).
cnf(f_1088_2,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1088_1]) ).
fof(f_1089_1,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).
cnf(f_1089_2,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1089_1]) ).
fof(f_1090_1,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).
cnf(f_1090_2,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1090_1]) ).
fof(f_1091_1,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
cnf(f_1091_2,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1091_1]) ).
fof(f_1092_1,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).
cnf(f_1092_2,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1092_1]) ).
fof(f_1093_1,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).
cnf(f_1093_2,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1093_1]) ).
fof(f_1094_1,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).
cnf(f_1094_2,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1094_1]) ).
fof(f_1095_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(f_1095_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1095_1]) ).
fof(f_1096_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
cnf(f_1096_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1096_1]) ).
fof(f_1097_1,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).
cnf(f_1097_2,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1097_1]) ).
fof(f_1098_1,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).
cnf(f_1098_2,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1098_1]) ).
fof(f_1099_1,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).
cnf(f_1099_2,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1099_1]) ).
fof(f_1100_1,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).
cnf(f_1100_2,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1100_1]) ).
fof(f_1101_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
cnf(f_1101_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1101_1]) ).
fof(f_1102_1,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).
cnf(f_1102_2,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1102_1]) ).
fof(f_1103_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
cnf(f_1103_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1103_1]) ).
fof(f_1104_1,plain,
class_Power_Opower(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).
cnf(f_1104_2,plain,
class_Power_Opower(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1104_1]) ).
fof(f_1105_1,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).
cnf(f_1105_2,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1105_1]) ).
fof(f_1106_1,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).
cnf(f_1106_2,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1106_1]) ).
fof(f_1107_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
cnf(f_1107_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1107_1]) ).
fof(f_1108_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
cnf(f_1108_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1108_1]) ).
fof(f_1109_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
cnf(f_1109_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1109_1]) ).
fof(f_1110_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]) ).
cnf(f_1110_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1110_1]) ).
fof(f_1111_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]) ).
cnf(f_1111_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1111_1]) ).
fof(f_1112_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]) ).
cnf(f_1112_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1112_1]) ).
fof(f_1113_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1113_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1113_1]) ).
fof(f_1114_1,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(f_1114_2,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1114_1]) ).
fof(f_1115_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]) ).
cnf(f_1115_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1115_1]) ).
fof(f_1116_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]) ).
cnf(f_1116_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1116_1]) ).
fof(f_1117_1,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).
cnf(f_1117_2,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1117_1]) ).
fof(f_1118_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).
cnf(f_1118_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1118_1]) ).
fof(f_1119_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]) ).
cnf(f_1119_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1119_1]) ).
fof(f_1120_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1120_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1120_1]) ).
fof(f_1121_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]) ).
cnf(f_1121_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1121_1]) ).
fof(f_1122_1,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(f_1122_2,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1122_1]) ).
fof(f_1123_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1123_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1123_1]) ).
fof(f_1124_1,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
cnf(f_1124_2,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1124_1]) ).
fof(f_1125_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1125_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1125_1]) ).
fof(f_1126_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]) ).
cnf(f_1126_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1126_1]) ).
fof(f_1127_1,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).
cnf(f_1127_2,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1127_1]) ).
fof(f_1128_1,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(f_1128_2,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1128_1]) ).
fof(f_1129_1,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
cnf(f_1129_2,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1129_1]) ).
fof(f_1130_1,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__field]) ).
cnf(f_1130_2,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1130_1]) ).
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]) ).
cnf(f_1131_2,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1131_1]) ).
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]) ).
cnf(f_1132_2,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1132_1]) ).
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]) ).
cnf(f_1133_2,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1133_1]) ).
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]) ).
cnf(f_1134_2,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1134_1]) ).
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]) ).
cnf(f_1135_2,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1135_1]) ).
fof(f_1136_1,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]) ).
cnf(f_1136_2,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1136_1]) ).
fof(f_1137_1,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(f_1137_2,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1137_1]) ).
fof(f_1138_1,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(f_1138_2,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1138_1]) ).
fof(f_1139_1,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).
cnf(f_1139_2,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1139_1]) ).
fof(f_1140_1,plain,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Ometric__space]) ).
cnf(f_1140_2,plain,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1140_1]) ).
fof(f_1141_1,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).
cnf(f_1141_2,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1141_1]) ).
fof(f_1142_1,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).
cnf(f_1142_2,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1142_1]) ).
fof(f_1143_1,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
cnf(f_1143_2,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1143_1]) ).
fof(f_1144_1,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).
cnf(f_1144_2,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1144_1]) ).
fof(f_1145_1,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]) ).
cnf(f_1145_2,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1145_1]) ).
fof(f_1146_1,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).
cnf(f_1146_2,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1146_1]) ).
fof(f_1147_1,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
cnf(f_1147_2,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1147_1]) ).
fof(f_1148_1,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).
cnf(f_1148_2,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1148_1]) ).
fof(f_1149_1,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(f_1149_2,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1149_1]) ).
fof(f_1150_1,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(f_1150_2,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1150_1]) ).
fof(f_1151_1,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__field]) ).
cnf(f_1151_2,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1151_1]) ).
fof(f_1152_1,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
cnf(f_1152_2,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1152_1]) ).
fof(f_1153_1,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).
cnf(f_1153_2,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1153_1]) ).
fof(f_1154_1,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).
cnf(f_1154_2,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1154_1]) ).
fof(f_1155_1,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).
cnf(f_1155_2,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1155_1]) ).
fof(f_1156_1,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
cnf(f_1156_2,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1156_1]) ).
fof(f_1157_1,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(f_1157_2,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1157_1]) ).
fof(f_1158_1,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(f_1158_2,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1158_1]) ).
fof(f_1159_1,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
cnf(f_1159_2,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1159_1]) ).
fof(f_1160_1,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).
cnf(f_1160_2,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1160_1]) ).
fof(f_1161_1,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
cnf(f_1161_2,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1161_1]) ).
fof(f_1162_1,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).
cnf(f_1162_2,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1162_1]) ).
fof(f_1163_1,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(f_1163_2,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1163_1]) ).
fof(f_1164_1,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).
cnf(f_1164_2,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1164_1]) ).
fof(f_1165_1,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(f_1165_2,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1165_1]) ).
fof(f_1166_1,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).
cnf(f_1166_2,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1166_1]) ).
fof(f_1167_1,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).
cnf(f_1167_2,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1167_1]) ).
fof(f_1168_1,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]) ).
cnf(f_1168_2,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1168_1]) ).
fof(f_1169_1,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).
cnf(f_1169_2,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1169_1]) ).
fof(f_1170_1,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]) ).
cnf(f_1170_2,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1170_1]) ).
fof(f_1171_1,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).
cnf(f_1171_2,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1171_1]) ).
fof(f_1172_1,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).
cnf(f_1172_2,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1172_1]) ).
fof(f_1173_1,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).
cnf(f_1173_2,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1173_1]) ).
fof(f_1174_1,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).
cnf(f_1174_2,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1174_1]) ).
fof(f_1175_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]) ).
cnf(f_1175_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1175_1]) ).
fof(f_1176_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
cnf(f_1176_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1176_1]) ).
fof(f_1177_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]) ).
cnf(f_1177_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1177_1]) ).
fof(f_1178_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).
cnf(f_1178_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1178_1]) ).
fof(f_1179_1,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
cnf(f_1179_2,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1179_1]) ).
fof(f_1180_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1180_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1180_1]) ).
fof(f_1181_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]) ).
cnf(f_1181_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1181_1]) ).
fof(f_1182_1,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(f_1182_2,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1182_1]) ).
fof(f_1183_1,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__field]) ).
cnf(f_1183_2,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1183_1]) ).
fof(f_1184_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]) ).
cnf(f_1184_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1184_1]) ).
fof(f_1185_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).
cnf(f_1185_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1185_1]) ).
fof(f_1186_1,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield__inverse__zero]) ).
cnf(f_1186_2,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1186_1]) ).
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]) ).
cnf(f_1187_2,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1187_1]) ).
fof(f_1188_1,plain,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Ometric__space]) ).
cnf(f_1188_2,plain,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1188_1]) ).
fof(f_1189_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).
cnf(f_1189_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1189_1]) ).
fof(f_1190_1,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).
cnf(f_1190_2,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1190_1]) ).
fof(f_1191_1,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
cnf(f_1191_2,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1191_1]) ).
fof(f_1192_1,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
cnf(f_1192_2,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1192_1]) ).
fof(f_1193_1,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(f_1193_2,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1193_1]) ).
fof(f_1194_1,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__field]) ).
cnf(f_1194_2,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1194_1]) ).
fof(f_1195_1,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]) ).
cnf(f_1195_2,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1195_1]) ).
fof(f_1196_1,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).
cnf(f_1196_2,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1196_1]) ).
fof(f_1197_1,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
cnf(f_1197_2,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1197_1]) ).
fof(f_1198_1,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
cnf(f_1198_2,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1198_1]) ).
fof(f_1199_1,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
cnf(f_1199_2,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1199_1]) ).
fof(f_1200_1,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
cnf(f_1200_2,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1200_1]) ).
fof(f_1201_1,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).
cnf(f_1201_2,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1201_1]) ).
fof(f_1202_1,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).
cnf(f_1202_2,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1202_1]) ).
fof(f_1203_1,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(f_1203_2,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1203_1]) ).
fof(f_1204_1,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
cnf(f_1204_2,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1204_1]) ).
fof(f_1205_1,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).
cnf(f_1205_2,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1205_1]) ).
fof(f_1206_1,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).
cnf(f_1206_2,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1206_1]) ).
fof(f_1207_1,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
cnf(f_1207_2,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1207_1]) ).
fof(f_1208_1,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
cnf(f_1208_2,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1208_1]) ).
fof(f_1209_1,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
cnf(f_1209_2,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1209_1]) ).
fof(f_1210_1,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).
cnf(f_1210_2,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1210_1]) ).
fof(f_1211_1,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).
cnf(f_1211_2,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1211_1]) ).
fof(f_1212_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_1212_2,plain,
! [U_3035] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3035))
| ~ class_Rings_Oidom(U_3035) ),
inference(variable_rename,[status(thm)],[f_1212_1]) ).
cnf(f_1212_3,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3035))
| ~ class_Rings_Oidom(U_3035) ),
inference(clausify,[status(thm)],[f_1212_2]) ).
fof(f_1213_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_1213_2,plain,
! [U_3036] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3036))
| ~ class_Rings_Olinordered__idom(U_3036) ),
inference(variable_rename,[status(thm)],[f_1213_1]) ).
cnf(f_1213_3,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3036))
| ~ class_Rings_Olinordered__idom(U_3036) ),
inference(clausify,[status(thm)],[f_1213_2]) ).
fof(f_1214_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_1214_2,plain,
! [U_3037] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3037))
| ~ class_Rings_Olinordered__idom(U_3037) ),
inference(variable_rename,[status(thm)],[f_1214_1]) ).
cnf(f_1214_3,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3037))
| ~ class_Rings_Olinordered__idom(U_3037) ),
inference(clausify,[status(thm)],[f_1214_2]) ).
fof(f_1215_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_1215_2,plain,
! [U_3038] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3038))
| ~ class_Rings_Olinordered__idom(U_3038) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
cnf(f_1215_3,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3038))
| ~ class_Rings_Olinordered__idom(U_3038) ),
inference(clausify,[status(thm)],[f_1215_2]) ).
fof(f_1216_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_1216_2,plain,
! [U_3039] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3039))
| ~ class_Rings_Olinordered__idom(U_3039) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
cnf(f_1216_3,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3039))
| ~ class_Rings_Olinordered__idom(U_3039) ),
inference(clausify,[status(thm)],[f_1216_2]) ).
fof(f_1217_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_1217_2,plain,
! [U_3040] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3040))
| ~ class_Rings_Olinordered__idom(U_3040) ),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
cnf(f_1217_3,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3040))
| ~ class_Rings_Olinordered__idom(U_3040) ),
inference(clausify,[status(thm)],[f_1217_2]) ).
fof(f_1218_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_1218_2,plain,
! [U_3041] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3041))
| ~ class_Rings_Olinordered__idom(U_3041) ),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
cnf(f_1218_3,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3041))
| ~ class_Rings_Olinordered__idom(U_3041) ),
inference(clausify,[status(thm)],[f_1218_2]) ).
fof(f_1219_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_1219_2,plain,
! [U_3042] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3042))
| ~ class_Rings_Olinordered__idom(U_3042) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
cnf(f_1219_3,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3042))
| ~ class_Rings_Olinordered__idom(U_3042) ),
inference(clausify,[status(thm)],[f_1219_2]) ).
fof(f_1220_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_1220_2,plain,
! [U_3043] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3043))
| ~ class_Rings_Olinordered__idom(U_3043) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
cnf(f_1220_3,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3043))
| ~ class_Rings_Olinordered__idom(U_3043) ),
inference(clausify,[status(thm)],[f_1220_2]) ).
fof(f_1221_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_1221_2,plain,
! [U_3044] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3044))
| ~ class_Rings_Olinordered__idom(U_3044) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
cnf(f_1221_3,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3044))
| ~ class_Rings_Olinordered__idom(U_3044) ),
inference(clausify,[status(thm)],[f_1221_2]) ).
fof(f_1222_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_1222_2,plain,
! [U_3045] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3045))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3045) ),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
cnf(f_1222_3,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3045))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3045) ),
inference(clausify,[status(thm)],[f_1222_2]) ).
fof(f_1223_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_1223_2,plain,
! [U_3046] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3046))
| ~ class_Rings_Oidom(U_3046) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
cnf(f_1223_3,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3046))
| ~ class_Rings_Oidom(U_3046) ),
inference(clausify,[status(thm)],[f_1223_2]) ).
fof(f_1224_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_1224_2,plain,
! [U_3047] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3047))
| ~ class_Rings_Olinordered__idom(U_3047) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
cnf(f_1224_3,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3047))
| ~ class_Rings_Olinordered__idom(U_3047) ),
inference(clausify,[status(thm)],[f_1224_2]) ).
fof(f_1225_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_1225_2,plain,
! [U_3048] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3048))
| ~ class_Rings_Olinordered__idom(U_3048) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
cnf(f_1225_3,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3048))
| ~ class_Rings_Olinordered__idom(U_3048) ),
inference(clausify,[status(thm)],[f_1225_2]) ).
fof(f_1226_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_1226_2,plain,
! [U_3049] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3049))
| ~ class_Rings_Oidom(U_3049) ),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
cnf(f_1226_3,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3049))
| ~ class_Rings_Oidom(U_3049) ),
inference(clausify,[status(thm)],[f_1226_2]) ).
fof(f_1227_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_1227_2,plain,
! [U_3050] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3050))
| ~ class_Rings_Olinordered__idom(U_3050) ),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
cnf(f_1227_3,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3050))
| ~ class_Rings_Olinordered__idom(U_3050) ),
inference(clausify,[status(thm)],[f_1227_2]) ).
fof(f_1228_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_1228_2,plain,
! [U_3051] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3051))
| ~ class_Rings_Olinordered__idom(U_3051) ),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
cnf(f_1228_3,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3051))
| ~ class_Rings_Olinordered__idom(U_3051) ),
inference(clausify,[status(thm)],[f_1228_2]) ).
fof(f_1229_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_1229_2,plain,
! [U_3052] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3052))
| ~ class_Rings_Olinordered__idom(U_3052) ),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
cnf(f_1229_3,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3052))
| ~ class_Rings_Olinordered__idom(U_3052) ),
inference(clausify,[status(thm)],[f_1229_2]) ).
fof(f_1230_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_1230_2,plain,
! [U_3053] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3053))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3053) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
cnf(f_1230_3,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3053))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3053) ),
inference(clausify,[status(thm)],[f_1230_2]) ).
fof(f_1231_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_1231_2,plain,
! [U_3054] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3054))
| ~ class_Rings_Olinordered__idom(U_3054) ),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
cnf(f_1231_3,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3054))
| ~ class_Rings_Olinordered__idom(U_3054) ),
inference(clausify,[status(thm)],[f_1231_2]) ).
fof(f_1232_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_1232_2,plain,
! [U_3055] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3055))
| ~ class_Rings_Olinordered__idom(U_3055) ),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
cnf(f_1232_3,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3055))
| ~ class_Rings_Olinordered__idom(U_3055) ),
inference(clausify,[status(thm)],[f_1232_2]) ).
fof(f_1233_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_1233_2,plain,
! [U_3056] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3056))
| ~ class_Rings_Ocomm__semiring__0(U_3056) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
cnf(f_1233_3,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3056))
| ~ class_Rings_Ocomm__semiring__0(U_3056) ),
inference(clausify,[status(thm)],[f_1233_2]) ).
fof(f_1234_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_1234_2,plain,
! [U_3057] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3057))
| ~ class_Rings_Ocomm__semiring__1(U_3057) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
cnf(f_1234_3,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3057))
| ~ class_Rings_Ocomm__semiring__1(U_3057) ),
inference(clausify,[status(thm)],[f_1234_2]) ).
fof(f_1235_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_1235_2,plain,
! [U_3058] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3058))
| ~ class_Groups_Ocomm__monoid__add(U_3058) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
cnf(f_1235_3,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3058))
| ~ class_Groups_Ocomm__monoid__add(U_3058) ),
inference(clausify,[status(thm)],[f_1235_2]) ).
fof(f_1236_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_1236_2,plain,
! [U_3059] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3059))
| ~ class_Rings_Olinordered__idom(U_3059) ),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
cnf(f_1236_3,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3059))
| ~ class_Rings_Olinordered__idom(U_3059) ),
inference(clausify,[status(thm)],[f_1236_2]) ).
fof(f_1237_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_1237_2,plain,
! [U_3060] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3060))
| ~ class_Rings_Olinordered__idom(U_3060) ),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
cnf(f_1237_3,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3060))
| ~ class_Rings_Olinordered__idom(U_3060) ),
inference(clausify,[status(thm)],[f_1237_2]) ).
fof(f_1238_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_1238_2,plain,
! [U_3061] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3061))
| ~ class_Rings_Oidom(U_3061) ),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
cnf(f_1238_3,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3061))
| ~ class_Rings_Oidom(U_3061) ),
inference(clausify,[status(thm)],[f_1238_2]) ).
fof(f_1239_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_1239_2,plain,
! [U_3062] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3062))
| ~ class_Groups_Ocomm__monoid__add(U_3062) ),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
cnf(f_1239_3,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3062))
| ~ class_Groups_Ocomm__monoid__add(U_3062) ),
inference(clausify,[status(thm)],[f_1239_2]) ).
fof(f_1240_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_1240_2,plain,
! [U_3063] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3063))
| ~ class_Rings_Olinordered__idom(U_3063) ),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
cnf(f_1240_3,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3063))
| ~ class_Rings_Olinordered__idom(U_3063) ),
inference(clausify,[status(thm)],[f_1240_2]) ).
fof(f_1241_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_1241_2,plain,
! [U_3064] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3064))
| ~ class_Rings_Olinordered__idom(U_3064) ),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
cnf(f_1241_3,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3064))
| ~ class_Rings_Olinordered__idom(U_3064) ),
inference(clausify,[status(thm)],[f_1241_2]) ).
fof(f_1242_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_1242_2,plain,
! [U_3065] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3065))
| ~ class_Rings_Ocomm__semiring__1(U_3065) ),
inference(variable_rename,[status(thm)],[f_1242_1]) ).
cnf(f_1242_3,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3065))
| ~ class_Rings_Ocomm__semiring__1(U_3065) ),
inference(clausify,[status(thm)],[f_1242_2]) ).
fof(f_1243_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_1243_2,plain,
! [U_3066] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3066))
| ~ class_Fields_Ofield(U_3066) ),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
cnf(f_1243_3,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3066))
| ~ class_Fields_Ofield(U_3066) ),
inference(clausify,[status(thm)],[f_1243_2]) ).
fof(f_1244_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_1244_2,plain,
! [U_3067] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3067))
| ~ class_Rings_Ocomm__semiring__0(U_3067) ),
inference(variable_rename,[status(thm)],[f_1244_1]) ).
cnf(f_1244_3,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3067))
| ~ class_Rings_Ocomm__semiring__0(U_3067) ),
inference(clausify,[status(thm)],[f_1244_2]) ).
fof(f_1245_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_1245_2,plain,
! [U_3068] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3068))
| ~ class_Groups_Oab__group__add(U_3068) ),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
cnf(f_1245_3,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3068))
| ~ class_Groups_Oab__group__add(U_3068) ),
inference(clausify,[status(thm)],[f_1245_2]) ).
fof(f_1246_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_1246_2,plain,
! [U_3069] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3069))
| ~ class_Rings_Ocomm__semiring__1(U_3069) ),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
cnf(f_1246_3,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3069))
| ~ class_Rings_Ocomm__semiring__1(U_3069) ),
inference(clausify,[status(thm)],[f_1246_2]) ).
fof(f_1247_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_1247_2,plain,
! [U_3070] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3070))
| ~ class_Rings_Olinordered__idom(U_3070) ),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
cnf(f_1247_3,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3070))
| ~ class_Rings_Olinordered__idom(U_3070) ),
inference(clausify,[status(thm)],[f_1247_2]) ).
fof(f_1248_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_1248_2,plain,
! [U_3071] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3071))
| ~ class_Rings_Olinordered__idom(U_3071) ),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
cnf(f_1248_3,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3071))
| ~ class_Rings_Olinordered__idom(U_3071) ),
inference(clausify,[status(thm)],[f_1248_2]) ).
fof(f_1249_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_1249_2,plain,
! [U_3072] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3072))
| ~ class_Rings_Olinordered__idom(U_3072) ),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
cnf(f_1249_3,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3072))
| ~ class_Rings_Olinordered__idom(U_3072) ),
inference(clausify,[status(thm)],[f_1249_2]) ).
fof(f_1250_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_1250_2,plain,
! [U_3073] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3073))
| ~ class_Rings_Ocomm__semiring__1(U_3073) ),
inference(variable_rename,[status(thm)],[f_1250_1]) ).
cnf(f_1250_3,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3073))
| ~ class_Rings_Ocomm__semiring__1(U_3073) ),
inference(clausify,[status(thm)],[f_1250_2]) ).
fof(f_1251_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_1251_2,plain,
! [U_3074] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3074))
| ~ class_Rings_Ocomm__ring__1(U_3074) ),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
cnf(f_1251_3,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3074))
| ~ class_Rings_Ocomm__ring__1(U_3074) ),
inference(clausify,[status(thm)],[f_1251_2]) ).
fof(f_1252_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_1252_2,plain,
! [U_3075] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3075))
| ~ class_Groups_Ocomm__monoid__add(U_3075) ),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
cnf(f_1252_3,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3075))
| ~ class_Groups_Ocomm__monoid__add(U_3075) ),
inference(clausify,[status(thm)],[f_1252_2]) ).
fof(f_1253_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_1253_2,plain,
! [U_3076] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3076))
| ~ class_Rings_Ocomm__semiring__0(U_3076) ),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
cnf(f_1253_3,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3076))
| ~ class_Rings_Ocomm__semiring__0(U_3076) ),
inference(clausify,[status(thm)],[f_1253_2]) ).
fof(f_1254_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_1254_2,plain,
! [U_3077] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3077))
| ~ class_Groups_Oab__group__add(U_3077) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
cnf(f_1254_3,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3077))
| ~ class_Groups_Oab__group__add(U_3077) ),
inference(clausify,[status(thm)],[f_1254_2]) ).
fof(f_1255_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_1255_2,plain,
! [U_3078] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3078))
| ~ class_Rings_Ocomm__semiring__0(U_3078) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
cnf(f_1255_3,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3078))
| ~ class_Rings_Ocomm__semiring__0(U_3078) ),
inference(clausify,[status(thm)],[f_1255_2]) ).
fof(f_1256_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_1256_2,plain,
! [U_3079] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3079))
| ~ class_Rings_Olinordered__idom(U_3079) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
cnf(f_1256_3,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3079))
| ~ class_Rings_Olinordered__idom(U_3079) ),
inference(clausify,[status(thm)],[f_1256_2]) ).
fof(f_1257_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_1257_2,plain,
! [U_3080] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3080))
| ~ class_Rings_Ocomm__semiring__0(U_3080) ),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
cnf(f_1257_3,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3080))
| ~ class_Rings_Ocomm__semiring__0(U_3080) ),
inference(clausify,[status(thm)],[f_1257_2]) ).
fof(f_1258_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_1258_2,plain,
! [U_3081] :
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3081))
| ~ class_Rings_Olinordered__idom(U_3081) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
cnf(f_1258_3,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3081))
| ~ class_Rings_Olinordered__idom(U_3081) ),
inference(clausify,[status(thm)],[f_1258_2]) ).
fof(f_1259_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_1259_2,plain,
! [U_3082] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3082))
| ~ class_Rings_Olinordered__idom(U_3082) ),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
cnf(f_1259_3,plain,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3082))
| ~ class_Rings_Olinordered__idom(U_3082) ),
inference(clausify,[status(thm)],[f_1259_2]) ).
fof(f_1260_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_1260_2,plain,
! [U_3083] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3083))
| ~ class_Rings_Ocomm__ring__1(U_3083) ),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
cnf(f_1260_3,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3083))
| ~ class_Rings_Ocomm__ring__1(U_3083) ),
inference(clausify,[status(thm)],[f_1260_2]) ).
fof(f_1261_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_1261_2,plain,
! [U_3084] :
( class_Power_Opower(tc_Polynomial_Opoly(U_3084))
| ~ class_Rings_Ocomm__semiring__1(U_3084) ),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
cnf(f_1261_3,plain,
( class_Power_Opower(tc_Polynomial_Opoly(U_3084))
| ~ class_Rings_Ocomm__semiring__1(U_3084) ),
inference(clausify,[status(thm)],[f_1261_2]) ).
fof(f_1262_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_1262_2,plain,
! [U_3085] :
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3085))
| ~ class_Groups_Ozero(U_3085) ),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
cnf(f_1262_3,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3085))
| ~ class_Groups_Ozero(U_3085) ),
inference(clausify,[status(thm)],[f_1262_2]) ).
fof(f_1263_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_1263_2,plain,
! [U_3086] :
( class_Rings_Oring(tc_Polynomial_Opoly(U_3086))
| ~ class_Rings_Ocomm__ring(U_3086) ),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
cnf(f_1263_3,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(U_3086))
| ~ class_Rings_Ocomm__ring(U_3086) ),
inference(clausify,[status(thm)],[f_1263_2]) ).
fof(f_1264_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_1264_2,plain,
! [U_3087] :
( class_Groups_Oone(tc_Polynomial_Opoly(U_3087))
| ~ class_Rings_Ocomm__semiring__1(U_3087) ),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
cnf(f_1264_3,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(U_3087))
| ~ class_Rings_Ocomm__semiring__1(U_3087) ),
inference(clausify,[status(thm)],[f_1264_2]) ).
fof(f_1265_1,plain,
! [V_Q,V_P,T_b,T_a] : hAPP(c_COMBK(T_a,T_b,V_P),V_Q) = V_P,
inference(fof_nnf,[status(thm)],[help_c__COMBK__1]) ).
fof(f_1265_2,plain,
! [U_3091,U_3090,U_3089,U_3088] : hAPP(c_COMBK(U_3088,U_3089,U_3090),U_3091) = U_3090,
inference(variable_rename,[status(thm)],[f_1265_1]) ).
cnf(f_1265_3,plain,
hAPP(c_COMBK(U_3088,U_3089,U_3090),U_3091) = U_3090,
inference(clausify,[status(thm)],[f_1265_2]) ).
fof(f_1266_1,plain,
! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
inference(fof_nnf,[status(thm)],[help_c__COMBB__1]) ).
fof(f_1266_2,plain,
! [U_3097,U_3096,U_3095,U_3094,U_3093,U_3092] : hAPP(c_COMBB(U_3092,U_3093,U_3094,U_3095,U_3096),U_3097) = hAPP(U_3095,hAPP(U_3096,U_3097)),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
cnf(f_1266_3,plain,
hAPP(c_COMBB(U_3092,U_3093,U_3094,U_3095,U_3096),U_3097) = hAPP(U_3095,hAPP(U_3096,U_3097)),
inference(clausify,[status(thm)],[f_1266_2]) ).
fof(f_1267_1,plain,
! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBC(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
inference(fof_nnf,[status(thm)],[help_c__COMBC__1]) ).
fof(f_1267_2,plain,
! [U_3103,U_3102,U_3101,U_3100,U_3099,U_3098] : hAPP(c_COMBC(U_3098,U_3099,U_3100,U_3101,U_3102),U_3103) = hAPP(hAPP(U_3101,U_3103),U_3102),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
cnf(f_1267_3,plain,
hAPP(c_COMBC(U_3098,U_3099,U_3100,U_3101,U_3102),U_3103) = hAPP(hAPP(U_3101,U_3103),U_3102),
inference(clausify,[status(thm)],[f_1267_2]) ).
fof(f_1268_1,plain,
! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
inference(fof_nnf,[status(thm)],[help_c__COMBS__1]) ).
fof(f_1268_2,plain,
! [U_3109,U_3108,U_3107,U_3106,U_3105,U_3104] : hAPP(c_COMBS(U_3104,U_3105,U_3106,U_3107,U_3108),U_3109) = hAPP(hAPP(U_3107,U_3109),hAPP(U_3108,U_3109)),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
cnf(f_1268_3,plain,
hAPP(c_COMBS(U_3104,U_3105,U_3106,U_3107,U_3108),U_3109) = hAPP(hAPP(U_3107,U_3109),hAPP(U_3108,U_3109)),
inference(clausify,[status(thm)],[f_1268_2]) ).
fof(f_1269_1,negated_conjecture,
~ ( ! [B_n] : hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
& hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_1269_2,negated_conjecture,
( ? [B_n] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,B_n)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(fof_nnf,[status(thm)],[f_1269_1]) ).
fof(f_1269_3,negated_conjecture,
( ? [U_3110] : ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,U_3110)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(variable_rename,[status(thm)],[f_1269_2]) ).
fof(f_1269_4,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sK76)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3110,sK76)],[f_1269_3]) ).
cnf(f_1269_5,negated_conjecture,
( ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_Complex_OIm,hAPP(v_s,hAPP(v_f____,hAPP(v_ga____,sK76)))))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),v_r),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))) ),
inference(clausify,[status(thm)],[f_1269_4]) ).
cnf(f_206_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_206_4]) ).
cnf(f_206_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_206_5]) ).
cnf(f_206_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_206_6]) ).
cnf(f_206_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_206_7]) ).
cnf(f_206_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_206_8]) ).
cnf(f_206_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_206_9]) ).
cnf(f_206_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_206_10]) ).
cnf(f_917_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_917_3]) ).
cnf(f_946_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_946_8]) ).
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_Orderings_Oord__class_Oless__eq(Eq_x_0,Eq_x_1) = c_Orderings_Oord__class_Oless__eq(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_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_8,axiom,
( c_Groups_Oplus__class_Oplus(Eq_x_0) = c_Groups_Oplus__class_Oplus(Eq_y_0)
| 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_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_11,axiom,
( c_Orderings_Oord__class_Oless(Eq_x_0,Eq_x_1) = c_Orderings_Oord__class_Oless(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_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_13,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_14,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_x_0,Eq_x_1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,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_17,axiom,
( c_COMBB(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_COMBB(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_18,axiom,
( c_COMBK(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBK(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_COMBC(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_COMBC(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_20,axiom,
( c_COMBS(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_COMBS(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_21,axiom,
( c_Complex_Oexpi(Eq_x_0) = c_Complex_Oexpi(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,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_24,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_25,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_26,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_27,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_28,axiom,
( c_Complex_Orcis(Eq_x_0,Eq_x_1) = c_Complex_Orcis(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_Complex_Ocis(Eq_x_0) = c_Complex_Ocis(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_30,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_31,axiom,
( c_Transcendental_Ocos(Eq_x_0) = c_Transcendental_Ocos(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( c_Transcendental_Osin(Eq_x_0) = c_Transcendental_Osin(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,axiom,
( c_Transcendental_Oarccos(Eq_x_0) = c_Transcendental_Oarccos(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_34,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_35,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_36,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_37,axiom,
( c_Complex_Ocomplex_OComplex(Eq_x_0,Eq_x_1) = c_Complex_Ocomplex_OComplex(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_38,axiom,
( c_Complex_Ocomplex_Ocomplex__size(Eq_x_0) = c_Complex_Ocomplex_Ocomplex__size(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( c_Complex_Oarg(Eq_x_0) = c_Complex_Oarg(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( c_Nat_Osize__class_Osize(Eq_x_0,Eq_x_1) = c_Nat_Osize__class_Osize(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,
( c_Complex_Ocomplex_Ocomplex__rec(Eq_x_0,Eq_x_1,Eq_x_2) = c_Complex_Ocomplex_Ocomplex__rec(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,
( c_Complex_Ocomplex_Ocomplex__case(Eq_x_0,Eq_x_1,Eq_x_2) = c_Complex_Ocomplex_Ocomplex__case(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,
( c_Rings_Oinverse__class_Odivide(Eq_x_0) = c_Rings_Oinverse__class_Odivide(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,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_45,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK2(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_46,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( 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_48,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_49,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,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_51,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_52,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK16(Eq_x_0,Eq_x_1) = sK16(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,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(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,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(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,
( 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_60,axiom,
( sK24(Eq_x_0) = sK24(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK25(Eq_x_0,Eq_x_1) = sK25(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,
( 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_63,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_64,axiom,
( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(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,
( 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_66,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_67,axiom,
( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(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,
( 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_69,axiom,
( sK33(Eq_x_0) = sK33(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK34(Eq_x_0) = sK34(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_71,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK35(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_72,axiom,
( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(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,
( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK38(Eq_x_0,Eq_x_1,Eq_x_2) = sK38(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,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,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_77,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_78,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(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_79,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_80,axiom,
( sK44(Eq_x_0) = sK44(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,axiom,
( sK45(Eq_x_0,Eq_x_1) = sK45(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_82,axiom,
( sK46(Eq_x_0,Eq_x_1) = sK46(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,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_84,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(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,
( sK49(Eq_x_0) = sK49(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_86,axiom,
( sK50(Eq_x_0,Eq_x_1) = sK50(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,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(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_88,axiom,
( sK52(Eq_x_0,Eq_x_1) = sK52(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,
( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(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,
( sK54(Eq_x_0,Eq_x_1) = sK54(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,
( sK55(Eq_x_0) = sK55(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_92,axiom,
( sK56(Eq_x_0,Eq_x_1) = sK56(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,
( 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_94,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_95,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_96,axiom,
( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_97,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_98,axiom,
( sK62(Eq_x_0,Eq_x_1) = sK62(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_99,axiom,
( sK63(Eq_x_0) = sK63(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_100,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_101,axiom,
( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(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_102,axiom,
( sK66(Eq_x_0) = sK66(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_103,axiom,
( sK67(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK67(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_104,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_105,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_106,axiom,
( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(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_107,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_108,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_109,axiom,
( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(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_110,axiom,
( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(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_111,axiom,
( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(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_112,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_113,axiom,
( c_SEQ_Osubseq(Eq_y_0)
| ~ c_SEQ_Osubseq(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_114,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_115,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_116,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_117,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_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,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_128,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_129,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_130,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_131,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_132,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_133,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_134,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_135,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_136,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_137,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_138,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_139,axiom,
( c_SEQ_Omonoseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_Omonoseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_140,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_141,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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,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_150,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_151,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_152,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_153,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_154,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_155,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_156,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_157,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_158,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_159,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_160,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_161,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_162,axiom,
( c_SEQ_Oconvergent(Eq_y_0,Eq_y_1)
| ~ c_SEQ_Oconvergent(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_163,axiom,
( class_RealVector_Ometric__space(Eq_y_0)
| ~ class_RealVector_Ometric__space(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_164,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_165,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_166,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_167,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_168,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_169,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_170,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_171,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_172,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_173,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_174,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_175,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_176,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_177,axiom,
( class_RealVector_Oreal__normed__field(Eq_y_0)
| ~ class_RealVector_Oreal__normed__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_178,axiom,
( class_Rings_Odivision__ring(Eq_y_0)
| ~ class_Rings_Odivision__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_179,axiom,
( class_Rings_Odivision__ring__inverse__zero(Eq_y_0)
| ~ class_Rings_Odivision__ring__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_180,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_181,axiom,
( class_Fields_Ofield__inverse__zero(Eq_y_0)
| ~ class_Fields_Ofield__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_182,axiom,
( class_RealVector_Oreal__field(Eq_y_0)
| ~ class_RealVector_Oreal__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_183,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_184,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_185,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_186,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_187,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_188,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW208+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % 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 : n013.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 05:09:50 UTC 2026
% 0.09/0.36 % CPUTime :
% 228.23/228.60 % SZS status Theorem for theBenchmark
% 228.23/228.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------