%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW271+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 09:04:59 AM UTC 2026
% Result : Theorem 228.30s 238.64s
% Output : Proof 228.42s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [V_g_2,V_f_2] :
( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
=> V_f_2 = V_g_2 ),
file('theBenchmark.p',fact_ext) ).
fof(fact_q0,axiom,
v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',fact_q0) ).
fof(fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096,axiom,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)),
file('theBenchmark.p',fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096) ).
fof(fact_one__poly__def,axiom,
! [T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('theBenchmark.p',fact_one__poly__def) ).
fof(fact_pCons__0__0,axiom,
! [T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_pCons__0__0) ).
fof(fact_pCons__eq__0__iff,axiom,
! [V_pb_2,V_aa_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
<=> ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_square__eq__1__iff,axiom,
! [V_x_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_mult__poly__0__left,axiom,
! [V_q,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_mult__poly__0__right,axiom,
! [V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_minus__pCons,axiom,
! [V_p,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ),
file('theBenchmark.p',fact_minus__pCons) ).
fof(fact_minus__poly__code_I2_J,axiom,
! [V_p,V_a,T_b] :
( class_Groups_Oab__group__add(T_b)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)) ),
file('theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(fact_pne,axiom,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('theBenchmark.p',fact_pne) ).
fof(fact_minus__mult__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__mult__right) ).
fof(fact_minus__mult__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) ),
file('theBenchmark.p',fact_minus__mult__left) ).
fof(fact_n0,axiom,
v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_n0) ).
fof(fact_oa,axiom,
c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_oa) ).
fof(fact_dvd__0__right,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_dvd__0__right) ).
fof(fact_a,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_a____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_a) ).
fof(fact_pq0,axiom,
! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_qa____),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('theBenchmark.p',fact_pq0) ).
fof(fact_dvd__refl,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ),
file('theBenchmark.p',fact_dvd__refl) ).
fof(fact_dvd__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_dvd__trans) ).
fof(fact_dvd__0__left,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_dvd__0__left) ).
fof(fact_dvd__mult__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_dvd__mult__left,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvdI,axiom,
! [V_k,V_b,V_a,T_a] :
( class_Rings_Odvd(T_a)
=> ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ),
file('theBenchmark.p',fact_dvdI) ).
fof(fact_mult__dvd__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ),
file('theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_dvd__mult,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_dvd__mult) ).
fof(fact_dvd__mult2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ),
file('theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__triv__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ),
file('theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_dvd__triv__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ),
file('theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_one__dvd,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ),
file('theBenchmark.p',fact_one__dvd) ).
fof(fact_minus__dvd__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_dvd__minus__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [V_b_2,V_c_2,V_aa_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_pCons__eq__iff,axiom,
! [V_qb_2,V_b_2,V_pb_2,V_aa_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Polynomial_OpCons(T_a,V_b_2,V_qb_2)
<=> ( V_pb_2 = V_qb_2
& V_aa_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_divisors__zero,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_mult__eq__0__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_mult__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_mult__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__left) ).
fof(fact_zero__neq__one,axiom,
! [T_a] :
( class_Rings_Ozero__neq__one(T_a)
=> c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [T_a] :
( class_Rings_Ozero__neq__one(T_a)
=> c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_one__neq__zero) ).
fof(fact_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_square__eq__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
<=> ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_aa_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_square__eq__iff) ).
fof(fact_minus__mult__minus,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
file('theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_ap_I1_J,axiom,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)),
file('theBenchmark.p',fact_ap_I1_J) ).
fof(fact_calculation,axiom,
( v_qa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_qa____),v_na____))) ),
file('theBenchmark.p',fact_calculation) ).
fof(fact_mult__left_Ominus,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) ),
file('theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_mult__right_Ominus,axiom,
! [V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)) ),
file('theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_mult_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_neg__equal__zero,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_aa_2
<=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [V_aa_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_assms_I3_J,axiom,
v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_assms_I3_J) ).
fof(fact_assms_I1_J,axiom,
! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('theBenchmark.p',fact_assms_I1_J) ).
fof(fact_dpn,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
file('theBenchmark.p',fact_dpn) ).
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_poly__eq__iff,axiom,
! [V_qb_2,V_pb_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,V_qb_2)
<=> V_pb_2 = V_qb_2 ) ),
file('theBenchmark.p',fact_poly__eq__iff) ).
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_poly__power,axiom,
! [V_x,V_n,V_p,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ),
file('theBenchmark.p',fact_poly__power) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [V_q,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_poly__zero,axiom,
! [V_pb_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
<=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_poly__zero) ).
fof(fact_order__root,axiom,
! [V_aa_2,V_pb_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_order__root) ).
fof(fact_poly__0,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_poly__0) ).
fof(fact_poly__mult,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__mult) ).
fof(fact_poly__minus,axiom,
! [V_x,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
file('theBenchmark.p',fact_poly__minus) ).
fof(fact_poly__1,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_poly__1) ).
fof(fact_zero__reorient,axiom,
! [V_x_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_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_minus__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ),
file('theBenchmark.p',fact_minus__minus) ).
fof(fact_equation__minus__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) ) ),
file('theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_b_2
<=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_aa_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_aa_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_order__1,axiom,
! [V_p,V_a,T_a] :
( class_Rings_Oidom(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)) ),
file('theBenchmark.p',fact_order__1) ).
fof(fact_mult_Ozero__left,axiom,
! [V_b,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__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__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__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_poly__eq__0__iff__dvd,axiom,
! [V_c_2,V_pb_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_c_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2)) ) ),
file('theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
fof(fact_dvd__iff__poly__eq__0,axiom,
! [V_pb_2,V_c_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2))
<=> hAPP(c_Polynomial_Opoly(T_a,V_pb_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
fof(fact_minus__zero,axiom,
! [T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_minus__zero) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [V_aa_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
<=> c_Groups_Ozero__class_Ozero(T_a) = V_aa_2 ) ),
file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_equal__neg__zero,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
<=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_ap_I2_J,axiom,
~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____)),
file('theBenchmark.p',fact_ap_I2_J) ).
fof(fact_oop,axiom,
! [V_a] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,V_a,v_pa____),v_na____),
file('theBenchmark.p',fact_oop) ).
fof(fact_power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__minus) ).
fof(fact_power__0__left,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left) ).
fof(fact_power__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__eq__0__iff,axiom,
! [V_nb_2,V_aa_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_aa_2),V_nb_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_order__2,axiom,
! [V_a,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p)) ) ),
file('theBenchmark.p',fact_order__2) ).
fof(fact_order,axiom,
! [V_a,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)) ) ) ),
file('theBenchmark.p',fact_order) ).
fof(fact_dvd__power__same,axiom,
! [V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ),
file('theBenchmark.p',fact_dvd__power__same) ).
fof(fact_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_assms_I2_J,axiom,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = v_n,
file('theBenchmark.p',fact_assms_I2_J) ).
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_nat__one__le__power,axiom,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ),
file('theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_degree__pCons__le,axiom,
! [V_p,V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))) ),
file('theBenchmark.p',fact_degree__pCons__le) ).
fof(fact_degree__power__le,axiom,
! [V_n,V_p,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),V_n)) ),
file('theBenchmark.p',fact_degree__power__le) ).
fof(fact_power__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> V_a = V_b ) ) ) ),
file('theBenchmark.p',fact_power__inject__base) ).
fof(fact_power__le__imp__le__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_power__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_degree__pCons__eq,axiom,
! [V_a,V_p,T_a] :
( class_Groups_Ozero(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) ) ),
file('theBenchmark.p',fact_degree__pCons__eq) ).
fof(fact_dvd__imp__degree__le,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))
=> ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ),
file('theBenchmark.p',fact_dvd__imp__degree__le) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__decreasing) ).
fof(fact_order__degree,axiom,
! [V_a,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(T_a,V_a,V_p),c_Polynomial_Odegree(T_a,V_p)) ) ),
file('theBenchmark.p',fact_order__degree) ).
fof(fact_le__imp__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ),
file('theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_neg__le__iff__le,axiom,
! [V_aa_2,V_b_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_minus__le__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ),
file('theBenchmark.p',fact_minus__le__iff) ).
fof(fact_le__minus__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ),
file('theBenchmark.p',fact_le__minus__iff) ).
fof(fact_degree__minus,axiom,
! [V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Polynomial_Odegree(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Polynomial_Odegree(T_a,V_p) ),
file('theBenchmark.p',fact_degree__minus) ).
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__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ),
file('theBenchmark.p',fact_power__mono) ).
fof(fact_zero__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
file('theBenchmark.p',fact_zero__le__power) ).
fof(fact_one__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
file('theBenchmark.p',fact_one__le__power) ).
fof(fact_power__le__dvd,axiom,
! [V_m,V_b,V_n,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ),
file('theBenchmark.p',fact_power__le__dvd) ).
fof(fact_dvd__power__le,axiom,
! [V_m,V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ),
file('theBenchmark.p',fact_dvd__power__le) ).
fof(fact_le__imp__power__dvd,axiom,
! [V_a,V_n,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_le__imp__power__dvd) ).
fof(fact_degree__pCons__eq__if,axiom,
! [V_a,V_p,T_a] :
( class_Groups_Ozero(T_a)
=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) )
& ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_degree__pCons__eq__if) ).
fof(fact_degree__0,axiom,
! [T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_degree__0) ).
fof(fact_split__mult__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_split__mult__pos__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_comm__mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__comm__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ) ),
file('theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) ) ),
file('theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__le__square,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
file('theBenchmark.p',fact_zero__le__square) ).
fof(fact_zero__le__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_zero__le__one) ).
fof(fact_not__one__le__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_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_minus__le__self__iff,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__0__le__iff__le,axiom,
! [V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_degree__1,axiom,
! [T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_degree__1) ).
fof(fact_degree__pCons__0,axiom,
! [V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_degree__pCons__0) ).
fof(fact_mult__left__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ),
file('theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_mult__right__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ),
file('theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_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_degree__linear__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n ),
file('theBenchmark.p',fact_degree__linear__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_le0,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_le0) ).
fof(fact_dvd__1__left,axiom,
! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)),
file('theBenchmark.p',fact_dvd__1__left) ).
fof(fact_realpow__Suc__le__self,axiom,
! [V_n,V_r,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r) ) ) ),
file('theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_IH,axiom,
! [B_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,v_na____)
=> ! [B_p,B_q] :
( ! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) )
=> ( c_Polynomial_Odegree(tc_Complex_Ocomplex,B_p) = B_m
=> ( B_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B_q),B_m))) ) ) ) ),
file('theBenchmark.p',fact_IH) ).
fof(fact_one__le__mult__iff,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_nb_2)
& 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_realpow__two__disj,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_realpow__two__disj) ).
fof(fact_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_Suc__mult__le__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_nb_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).
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_dvd_Oorder__refl,axiom,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
file('theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_less__zeroE,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_less__zeroE) ).
fof(fact_Suc__mono,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_Suc__mono) ).
fof(fact_lessI,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_lessI) ).
fof(fact_zero__less__Suc,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_dvd_Oeq__iff,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_dvd_Ole__less,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd_Oless__le,axiom,
! [V_y_2,V_x_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [V_b,V_a] :
( V_a != V_b
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Oeq__refl,axiom,
! [V_y,V_x] :
( V_x = V_y
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
file('theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [V_x_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( V_x = V_y
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( V_a != V_b
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_dvd_Oord__eq__le__trans,axiom,
! [V_c,V_b,V_a] :
( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
fof(fact_dvd_Oord__le__eq__trans,axiom,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
fof(fact_dvd__antisym,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oantisym,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
=> V_x = V_y ) ),
file('theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_dvd_Oorder__trans,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ),
file('theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_dvd_Oord__eq__less__trans,axiom,
! [V_c,V_b,V_a] :
( V_a = V_b
=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__less__trans) ).
fof(fact_dvd_Oless__imp__neq,axiom,
! [V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> V_x != V_y ),
file('theBenchmark.p',fact_dvd_Oless__imp__neq) ).
fof(fact_dvd_Oless__not__sym,axiom,
! [V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
file('theBenchmark.p',fact_dvd_Oless__not__sym) ).
fof(fact_dvd_Oless__imp__le,axiom,
! [V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
file('theBenchmark.p',fact_dvd_Oless__imp__le) ).
fof(fact_dvd_Oless__imp__not__less,axiom,
! [V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
fof(fact_dvd_Oless__imp__not__eq,axiom,
! [V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> V_x != V_y ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
fof(fact_dvd_Oless__imp__not__eq2,axiom,
! [V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> V_y != V_x ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
fof(fact_dvd_Oord__less__eq__trans,axiom,
! [V_c,V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
=> ( V_b = V_c
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
fof(fact_dvd_Oless__le__trans,axiom,
! [V_z,V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_dvd_Oless__le__trans) ).
fof(fact_dvd_Oless__asym_H,axiom,
! [V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ),
file('theBenchmark.p',fact_dvd_Oless__asym_H) ).
fof(fact_dvd_Oless__trans,axiom,
! [V_z,V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
file('theBenchmark.p',fact_dvd_Oless__trans) ).
fof(fact_dvd_Oless__asym,axiom,
! [V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
file('theBenchmark.p',fact_dvd_Oless__asym) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_nat__less__cases,axiom,
! [V_P_2,V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
=> ( ( V_m_2 = V_nb_2
=> hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
fof(fact_less__not__refl3,axiom,
! [V_t,V_s] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
=> V_s != V_t ),
file('theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> V_m != V_n ),
file('theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__irrefl__nat,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_linorder__neqE__nat,axiom,
! [V_y,V_x] :
( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_nat__neq__iff,axiom,
! [V_nb_2,V_m_2] :
( V_m_2 != V_nb_2
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_less__not__refl,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__not__refl) ).
fof(fact_not__less0,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_not__less0) ).
fof(fact_neq0__conv,axiom,
! [V_nb_2] :
( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_less__nat__zero__code,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_nat__dvd__not__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ),
file('theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_gr__implies__not0,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_gr0I,axiom,
! [V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
file('theBenchmark.p',fact_gr0I) ).
fof(fact_Suc__less__SucD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__lessD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__lessD) ).
fof(fact_less__SucE,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__SucE) ).
fof(fact_less__trans__Suc,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ),
file('theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_Suc__lessI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Nat_OSuc(V_m) != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ),
file('theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__SucI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_less__SucI) ).
fof(fact_less__antisym,axiom,
! [V_m,V_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [V_m_2,V_nb_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
<=> V_nb_2 = V_m_2 ) ),
file('theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_Suc__less__eq,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_nb_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_less__Suc__eq,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
<=> ( V_m_2 = V_nb_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_not__less__eq,axiom,
! [V_nb_2,V_m_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2)) ),
file('theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__or__eq__imp__le,axiom,
! [V_n,V_m] :
( ( V_m = V_n
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_le__neq__implies__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( V_m != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_less__imp__le__nat,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
<=> ( V_m_2 = V_nb_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
<=> ( V_m_2 != V_nb_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_nat__less__le) ).
fof(fact_power__strict__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_less__minus__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
fof(fact_minus__less__iff,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) ) ),
file('theBenchmark.p',fact_minus__less__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [V_aa_2,V_b_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [V_nb_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_nb_2))
<=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ),
file('theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
<=> ( ? [B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_nb_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_less__Suc0,axiom,
! [V_nb_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_less__Suc0) ).
fof(fact_gr0__conv__Suc,axiom,
! [V_nb_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
<=> ? [B_m] : V_nb_2 = c_Nat_OSuc(B_m) ),
file('theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_dvd__imp__le,axiom,
! [V_n,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ),
file('theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_Suc__le__lessD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_le__less__Suc__eq,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
<=> V_nb_2 = V_m_2 ) ),
file('theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_Suc__leI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
file('theBenchmark.p',fact_Suc__leI) ).
fof(fact_le__imp__less__Suc,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_Suc__le__eq,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_nb_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__Suc__eq__le,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__eq__Suc__le,axiom,
! [V_m_2,V_nb_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ),
file('theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) ),
file('theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_mult__less__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) ),
file('theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [V_nb_2,V_k_2,V_m_2] :
( 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_nb_2),V_k_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) ),
file('theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_mult__less__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ),
file('theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ),
file('theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_dvd__mult__cancel,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_nb_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_power__strict__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_one__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
file('theBenchmark.p',fact_one__less__power) ).
fof(fact_power__strict__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__mono) ).
fof(fact_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_c_2,V_aa_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
& 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_mult__less__cancel__left__disj,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
& 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__left__pos,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_zero__less__mult__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_zero__less__mult__pos2,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__comm__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_not__one__less__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_zero__less__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_zero__less__one) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__less__nonneg,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_less__minus__self__iff,axiom,
! [V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_less__1__mult,axiom,
! [V_n,V_m,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_less__1__mult) ).
fof(fact_zero__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
file('theBenchmark.p',fact_zero__less__power) ).
fof(fact_power__inject__exp,axiom,
! [V_nb_2,V_m_2,V_aa_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_nb_2)
<=> V_m_2 = V_nb_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
fof(fact_one__less__mult,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_one__less__mult) ).
fof(fact_n__less__n__mult__m,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ),
file('theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_mult__le__cancel2,axiom,
! [V_nb_2,V_k_2,V_m_2] :
( 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_nb_2),V_k_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_mult__le__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_dvd__mult__cancel1,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2)),V_m_2))
<=> V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_dvd__mult__cancel2,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_m_2)),V_m_2))
<=> V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel2) ).
fof(fact_power__dvd__imp__le,axiom,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_power__dvd__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__strict__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__less__le__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__right__less__imp__less,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_mult__left__less__imp__less,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__right__le__imp__le,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_power__less__imp__less__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_power__gt1__lemma,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_power__less__power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_power__gt1,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))) ) ),
file('theBenchmark.p',fact_power__gt1) ).
fof(fact_Suc__inject,axiom,
! [V_y,V_x] :
( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
=> V_x = V_y ),
file('theBenchmark.p',fact_Suc__inject) ).
fof(fact_nat_Oinject,axiom,
! [V_nat_H_2,V_nat_2] :
( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
<=> V_nat_2 = V_nat_H_2 ),
file('theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__n__not__n,axiom,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
file('theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [V_n] : V_n != c_Nat_OSuc(V_n),
file('theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_le__antisym,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_le__antisym) ).
fof(fact_le__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ),
file('theBenchmark.p',fact_le__trans) ).
fof(fact_eq__imp__le,axiom,
! [V_n,V_m] :
( V_m = V_n
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_eq__imp__le) ).
fof(fact_nat__le__linear,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_nat__le__linear) ).
fof(fact_le__refl,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_le__refl) ).
fof(fact_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_nat__dvd__1__iff__1,axiom,
! [V_m_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_power__Suc__less,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
file('theBenchmark.p',fact_power__Suc__less) ).
fof(fact_power__Suc__less__one,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ),
file('theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_power__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_dvd__power,axiom,
! [V_x,V_n,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( ( V_x = c_Groups_Oone__class_Oone(T_a)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ),
file('theBenchmark.p',fact_dvd__power) ).
fof(fact_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_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_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_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_dvd__1__iff__1,axiom,
! [V_m_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_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_dvd__1__iff__1) ).
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_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_less__eq__nat_Osimps_I1_J,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le__0__eq,axiom,
! [V_nb_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_le__0__eq) ).
fof(fact_Suc__leD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__leD) ).
fof(fact_le__SucE,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> V_m = c_Nat_OSuc(V_n) ) ),
file('theBenchmark.p',fact_le__SucE) ).
fof(fact_le__SucI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_le__SucI) ).
fof(fact_Suc__le__mono,axiom,
! [V_m_2,V_nb_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,V_m_2) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__Suc__eq,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
<=> ( V_m_2 = c_Nat_OSuc(V_nb_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_not__less__eq__eq,axiom,
! [V_nb_2,V_m_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_Suc__n__not__le__n,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
file('theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_mult__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0) ).
fof(fact_mult__0__right,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0__right) ).
fof(fact_mult__is__0,axiom,
! [V_nb_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__cancel1,axiom,
! [V_nb_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_nb_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_nb_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__cancel2,axiom,
! [V_nb_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_nb_2),V_k_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_nb_2 ) ),
file('theBenchmark.p',fact_mult__cancel2) ).
fof(fact_Suc__mult__cancel1,axiom,
! [V_nb_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_nb_2)
<=> V_m_2 = V_nb_2 ),
file('theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_le__square,axiom,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)),
file('theBenchmark.p',fact_le__square) ).
fof(fact_le__cube,axiom,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
file('theBenchmark.p',fact_le__cube) ).
fof(fact_mult__le__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ),
file('theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ),
file('theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_mult__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)) ) ),
file('theBenchmark.p',fact_mult__le__mono) ).
fof(fact_nat__mult__1,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_nat__mult__1) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [V_nb_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_nb_2)
<=> ( V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_nat__mult__1__right,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [V_nb_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_nb_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_mult__eq__1__iff,axiom,
! [V_nb_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_nb_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_nat__mult__le__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2)) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_pow__divides__eq__nat,axiom,
! [V_b_2,V_aa_2,V_nb_2] :
( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_nb_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_aa_2),V_b_2)) ) ),
file('theBenchmark.p',fact_pow__divides__eq__nat) ).
fof(fact_pow__divides__pow__nat,axiom,
! [V_b,V_n,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n)))
=> ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ),
file('theBenchmark.p',fact_pow__divides__pow__nat) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [V_nb_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_nb_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2))
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2)
<=> V_m_2 = V_nb_2 ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_pow__divides__pow__int,axiom,
! [V_b,V_n,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n)))
=> ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)) ) ),
file('theBenchmark.p',fact_pow__divides__pow__int) ).
fof(fact_pow__divides__eq__int,axiom,
! [V_b_2,V_aa_2,V_nb_2] :
( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_nb_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),V_b_2)) ) ),
file('theBenchmark.p',fact_pow__divides__eq__int) ).
fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [V_nb_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_nb_2)
<=> ( V_m_2 = V_nb_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)),
file('theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(fact_dvd__pos__nat,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ) ),
file('theBenchmark.p',fact_dvd__pos__nat) ).
fof(fact_psize__def,axiom,
! [V_p,T_a] :
( class_Groups_Ozero(T_a)
=> ( ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)) )
& ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_psize__def) ).
fof(fact_order__refl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__refl) ).
fof(fact_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_degree__pcompose__le,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q))) ),
file('theBenchmark.p',fact_degree__pcompose__le) ).
fof(fact_pcompose__0,axiom,
! [V_q,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_pcompose__0) ).
fof(fact_poly__pcompose,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__pcompose) ).
fof(fact_power_Opower_Opower__0,axiom,
! [V_aa_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_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_nb_2,V_aa_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Nat_OSuc(V_nb_2)) = hAPP(hAPP(V_times_2,V_aa_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),V_nb_2)),
file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_linorder__le__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_le__funE,axiom,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_xt1_I5_J,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__trans) ).
fof(fact_order__antisym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I4_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I4_J) ).
fof(fact_ord__le__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__le__eq__trans) ).
fof(fact_xt1_I3_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I3_J) ).
fof(fact_ord__eq__le__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__le__trans) ).
fof(fact_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_order__eq__refl,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( V_x = V_y
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__eq__refl) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_x_2 = V_y_2
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_linorder__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__linear) ).
fof(fact_le__fun__def,axiom,
! [V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_linorder__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( V_x != V_y
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__cases) ).
fof(fact_order__less__asym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__asym) ).
fof(fact_xt1_I10_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_order__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I2_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I2_J) ).
fof(fact_ord__less__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__less__eq__trans) ).
fof(fact_xt1_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I1_J) ).
fof(fact_ord__eq__less__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__less__trans) ).
fof(fact_xt1_I9_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_order__less__asym_H,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ),
file('theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_y != V_x ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_x != V_y ) ),
file('theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_order__less__imp__not__less,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_less__imp__neq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> V_x != V_y ) ),
file('theBenchmark.p',fact_less__imp__neq) ).
fof(fact_linorder__neqE,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
file('theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ),
file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__neq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x_2 != V_y_2
<=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_order__less__irrefl,axiom,
! [V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ),
file('theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_psize__eq__0__iff,axiom,
! [V_pb_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__le__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_leI,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_not__leE) ).
fof(fact_linorder__antisym__conv1,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_order__neq__le__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_xt1_I12_J,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a != V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_order__less__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__le__neq__trans,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_a != V_b
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_xt1_I11_J,axiom,
! [V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_a != V_b
=> c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__less__le__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I7_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__le__less__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_xt1_I8_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_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_termination__basic__simps_I5_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_pos__poly__pCons,axiom,
! [V_pb_2,V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
& V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_Polynomial_Opos__poly(T_a,V_pb_2) ) ) ),
file('theBenchmark.p',fact_pos__poly__pCons) ).
fof(fact_compl__le__compl__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_compl__mono,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ),
file('theBenchmark.p',fact_compl__mono) ).
fof(fact_less__fun__def,axiom,
! [V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
fof(fact_not__pos__poly__0,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('theBenchmark.p',fact_not__pos__poly__0) ).
fof(fact_pos__poly__mult,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,V_p)
=> ( c_Polynomial_Opos__poly(T_a,V_q)
=> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ),
file('theBenchmark.p',fact_pos__poly__mult) ).
fof(fact_mult__left__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
file('theBenchmark.p',fact_mult__left__idem) ).
fof(fact_mult__idem,axiom,
! [V_x,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_mult__idem) ).
fof(fact_times_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_times_Oidem) ).
fof(fact_compl__eq__compl__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_uminus__apply,axiom,
! [V_x_2,V_A_2,T_b,T_a] :
( class_Groups_Ouminus(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_uminus__apply) ).
fof(fact_double__compl,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ),
file('theBenchmark.p',fact_double__compl) ).
fof(fact_zdvd__antisym__nonneg,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
=> V_m = V_n ) ) ) ),
file('theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(fact_zdvd__mult__cancel,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))
=> ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ),
file('theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_zdvd__imp__le,axiom,
! [V_n,V_z] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n) ) ),
file('theBenchmark.p',fact_zdvd__imp__le) ).
fof(fact_zdvd__not__zless,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ),
file('theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_pos__poly__total,axiom,
! [V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| c_Polynomial_Opos__poly(T_a,V_p)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_pos__poly__total) ).
fof(fact_poly__replicate__append,axiom,
! [V_x,V_p,V_n,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
file('theBenchmark.p',fact_poly__replicate__append) ).
fof(fact_poly__rec__pCons,axiom,
! [V_pb_2,V_aa_2,T_a,V_z_2,V_f_2,T_b] :
( class_Groups_Ozero(T_b)
=> ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
=> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pb_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pb_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pb_2)) ) ),
file('theBenchmark.p',fact_poly__rec__pCons) ).
fof(fact_synthetic__div__eq__0__iff,axiom,
! [V_c_2,V_pb_2,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> ( c_Polynomial_Osynthetic__div(T_a,V_pb_2,V_c_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
<=> c_Polynomial_Odegree(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_synthetic__div__eq__0__iff) ).
fof(fact_eq__zero__or__degree__less,axiom,
! [V_n,V_p,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
=> ( hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
file('theBenchmark.p',fact_eq__zero__or__degree__less) ).
fof(fact_zle__refl,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
file('theBenchmark.p',fact_zle__refl) ).
fof(fact_zle__linear,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
file('theBenchmark.p',fact_zle__linear) ).
fof(fact_zle__trans,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ),
file('theBenchmark.p',fact_zle__trans) ).
fof(fact_zle__antisym,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
=> V_z = V_w ) ),
file('theBenchmark.p',fact_zle__antisym) ).
fof(fact_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zminus__0) ).
fof(fact_zmult__1,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zmult__1) ).
fof(fact_zmult__1__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zmult__1__right) ).
fof(fact_zmult__commute,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
file('theBenchmark.p',fact_zmult__commute) ).
fof(fact_zmult__zminus,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
file('theBenchmark.p',fact_zmult__zminus) ).
fof(fact_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_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_zless__linear,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
file('theBenchmark.p',fact_zless__linear) ).
fof(fact_zless__le,axiom,
! [V_w_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
<=> ( V_z_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) ) ),
file('theBenchmark.p',fact_zless__le) ).
fof(fact_zmult__zless__mono2,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)) ) ),
file('theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [V_nb_2,V_m_2] :
( 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_nb_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( V_nb_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_int__one__le__iff__zero__less,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ),
file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_int__0__less__1) ).
fof(fact_coeff__monom,axiom,
! [V_a,V_n,V_m,T_a] :
( class_Groups_Ozero(T_a)
=> ( ( V_m != V_n
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_m = V_n
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = V_a ) ) ),
file('theBenchmark.p',fact_coeff__monom) ).
fof(fact_expand__poly__eq,axiom,
! [V_qb_2,V_pb_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( V_pb_2 = V_qb_2
<=> ! [B_n] : hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_a,V_qb_2),B_n) ) ),
file('theBenchmark.p',fact_expand__poly__eq) ).
fof(fact_coeff__inject,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Ocoeff(T_a,V_x_2) = c_Polynomial_Ocoeff(T_a,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_coeff__inject) ).
fof(fact_monom__eq__iff,axiom,
! [V_b_2,V_nb_2,V_aa_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) = c_Polynomial_Omonom(T_a,V_b_2,V_nb_2)
<=> V_aa_2 = V_b_2 ) ),
file('theBenchmark.p',fact_monom__eq__iff) ).
fof(fact_coeff__0,axiom,
! [V_n,T_a] :
( class_Groups_Ozero(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_coeff__0) ).
fof(fact_coeff__pCons__0,axiom,
! [V_p,V_a,T_a] :
( class_Groups_Ozero(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a ),
file('theBenchmark.p',fact_coeff__pCons__0) ).
fof(fact_coeff__pCons__Suc,axiom,
! [V_n,V_p,V_a,T_a] :
( class_Groups_Ozero(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(V_n)) = hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) ),
file('theBenchmark.p',fact_coeff__pCons__Suc) ).
fof(fact_synthetic__div__0,axiom,
! [V_c,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_synthetic__div__0) ).
fof(fact_coeff__minus,axiom,
! [V_n,V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)) ),
file('theBenchmark.p',fact_coeff__minus) ).
fof(fact_poly__dvd__antisym,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) = hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_q),V_p))
=> V_p = V_q ) ) ) ),
file('theBenchmark.p',fact_poly__dvd__antisym) ).
fof(fact_monom__eq__0,axiom,
! [V_n,T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_monom__eq__0) ).
fof(fact_monom__eq__0__iff,axiom,
! [V_nb_2,V_aa_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
<=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_monom__eq__0__iff) ).
fof(fact_degree__monom__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Ozero(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)) = V_n ) ),
file('theBenchmark.p',fact_degree__monom__eq) ).
fof(fact_degree__monom__le,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_n) ),
file('theBenchmark.p',fact_degree__monom__le) ).
fof(fact_minus__monom,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) ),
file('theBenchmark.p',fact_minus__monom) ).
fof(fact_coeff__eq__0,axiom,
! [V_n,V_p,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
=> hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_coeff__eq__0) ).
fof(fact_le__degree,axiom,
! [V_n,V_p,T_a] :
( class_Groups_Ozero(T_a)
=> ( hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) != c_Groups_Ozero__class_Ozero(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p)) ) ),
file('theBenchmark.p',fact_le__degree) ).
fof(fact_leading__coeff__0__iff,axiom,
! [V_pb_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_leading__coeff__0__iff) ).
fof(fact_leading__coeff__neq__0,axiom,
! [V_p,T_a] :
( class_Groups_Ozero(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_leading__coeff__neq__0) ).
fof(fact_monom__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n)) = c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) ),
file('theBenchmark.p',fact_monom__Suc) ).
fof(fact_poly__monom,axiom,
! [V_x,V_n,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ),
file('theBenchmark.p',fact_poly__monom) ).
fof(fact_monom__0,axiom,
! [V_a,T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('theBenchmark.p',fact_monom__0) ).
fof(fact_synthetic__div__pCons,axiom,
! [V_c,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ),
file('theBenchmark.p',fact_synthetic__div__pCons) ).
fof(fact_poly__rec__0,axiom,
! [T_a,V_z_2,V_f_2,T_b] :
( class_Groups_Ozero(T_b)
=> ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
=> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2 ) ),
file('theBenchmark.p',fact_poly__rec__0) ).
fof(fact_coeff__1,axiom,
! [V_n,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_coeff__1) ).
fof(fact_pos__poly__def,axiom,
! [V_pb_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,V_pb_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2))) ) ),
file('theBenchmark.p',fact_pos__poly__def) ).
fof(fact_coeff__linear__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_coeff__linear__power) ).
fof(fact_poly__rec_Osimps,axiom,
! [V_pb_2,V_aa_2,V_f_2,V_z_2,T_a,T_b] :
( class_Groups_Ozero(T_b)
=> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pb_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pb_2),c_If(T_a,c_fequal(V_pb_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pb_2))) ),
file('theBenchmark.p',fact_poly__rec_Osimps) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_zdvd__mono,axiom,
! [V_t_2,V_m_2,V_k_2] :
( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ),
file('theBenchmark.p',fact_zdvd__mono) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_synthetic__div__correct_H,axiom,
! [V_p,V_c,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p ),
file('theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(fact_zminus__zminus,axiom,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
file('theBenchmark.p',fact_zminus__zminus) ).
fof(fact_double__eq__0__iff,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_add__le__cancel__right,axiom,
! [V_b_2,V_c_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ),
file('theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__cancel__left,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) ),
file('theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ),
file('theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ),
file('theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__mono) ).
fof(fact_add__le__imp__le__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_add__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ),
file('theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_mult__poly__add__left,axiom,
! [V_r,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ),
file('theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_add__0__iff,axiom,
! [V_aa_2,V_b_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)
<=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_add__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add__0__right) ).
fof(fact_double__zero__sym,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)
<=> V_aa_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)
=> 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)
=> 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__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__strict__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ),
file('theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ),
file('theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__less__cancel__left,axiom,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_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_aa_2,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) ),
file('theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_crossproduct__eq,axiom,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
<=> ( V_y_2 = V_z_2
| V_w_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_combine__common__factor,axiom,
! [V_c,V_b,V_e,V_a,T_a] :
( class_Rings_Osemiring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ),
file('theBenchmark.p',fact_combine__common__factor) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [V_b,V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_crossproduct__noteq,axiom,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_c_2 != V_d_2
& V_aa_2 != V_b_2 )
<=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mult__left_Oadd,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ),
file('theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_mult__right_Oadd,axiom,
! [V_y,V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ),
file('theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ),
file('theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_minus__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ),
file('theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_add__minus__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ),
file('theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_minus__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ),
file('theBenchmark.p',fact_minus__add) ).
fof(fact_minus__add__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_coeff__add,axiom,
! [V_n,V_q,V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)) ),
file('theBenchmark.p',fact_coeff__add) ).
fof(fact_add__monom,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n) ),
file('theBenchmark.p',fact_add__monom) ).
fof(fact_dvd__add,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))) ) ) ),
file('theBenchmark.p',fact_dvd__add) ).
fof(fact_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__ab__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [V_c_2,V_aa_2,V_b_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_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_aa_2,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_aa_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)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_poly__add,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__add) ).
fof(fact_add__pCons,axiom,
! [V_q,V_b,V_p,V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ),
file('theBenchmark.p',fact_add__pCons) ).
fof(fact_pos__poly__add,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,V_p)
=> ( c_Polynomial_Opos__poly(T_a,V_q)
=> c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ),
file('theBenchmark.p',fact_pos__poly__add) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_add__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_even__less__0__iff,axiom,
! [V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_aa_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_add__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_unity__coeff__ex,axiom,
! [V_l_2,V_P_2,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Rings_Odvd(T_a) )
=> ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l_2),c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))) ) ) ),
file('theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_add__less__le__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__le__less__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__scale__eq__noteq,axiom,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_r != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( V_c != V_d
& V_a = V_b )
=> c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ),
file('theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_less__add__one,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_less__add__one) ).
fof(fact_minus__unique,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ),
file('theBenchmark.p',fact_minus__unique) ).
fof(fact_ab__left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_ab__left__minus) ).
fof(fact_left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_left__minus) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_right__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_right__minus) ).
fof(fact_add__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ),
file('theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [V_a,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_degree__add__less,axiom,
! [V_q,V_n,V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) ) ) ),
file('theBenchmark.p',fact_degree__add__less) ).
fof(fact_degree__add__eq__right,axiom,
! [V_q,V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))
=> c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_q) ) ),
file('theBenchmark.p',fact_degree__add__eq__right) ).
fof(fact_degree__add__eq__left,axiom,
! [V_p,V_q,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))
=> c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_p) ) ),
file('theBenchmark.p',fact_degree__add__eq__left) ).
fof(fact_degree__add__le,axiom,
! [V_q,V_n,V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) ) ) ),
file('theBenchmark.p',fact_degree__add__le) ).
fof(fact_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_sum__squares__ge__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))) ),
file('theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_zero__less__two,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_zero__less__two) ).
fof(fact_poly__pCons,axiom,
! [V_x,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ),
file('theBenchmark.p',fact_poly__pCons) ).
fof(fact_uminus__dvd__conv_I2_J,axiom,
! [V_t_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))) ),
file('theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(fact_uminus__dvd__conv_I1_J,axiom,
! [V_t_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2)) ),
file('theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(fact_convex__bound__le,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__le) ).
fof(fact_convex__bound__lt,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_pcompose__pCons,axiom,
! [V_q,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))) ),
file('theBenchmark.p',fact_pcompose__pCons) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_pdivmod__rel__def,axiom,
! [V_r_2,V_qb_2,V_y_2,V_x_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_qb_2,V_r_2)
<=> ( ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2))
| V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
& ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& V_x_2 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_qb_2),V_y_2),V_r_2) ) ) ),
file('theBenchmark.p',fact_pdivmod__rel__def) ).
fof(fact_degree__le,axiom,
! [V_p,V_n,T_a] :
( class_Groups_Ozero(T_a)
=> ( ! [B_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i)
=> hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) = c_Groups_Ozero__class_Ozero(T_a) )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n) ) ),
file('theBenchmark.p',fact_degree__le) ).
fof(fact_poly__gcd__monic,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> ( ( ~ ( V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Oone__class_Oone(T_a) )
& ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_poly__gcd__monic) ).
fof(fact_less__degree__imp,axiom,
! [V_p,V_n,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))
=> ? [B_i] :
( hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) != c_Groups_Ozero__class_Ozero(T_a)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i) ) ) ),
file('theBenchmark.p',fact_less__degree__imp) ).
fof(fact_poly__gcd__dvd2,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_y)) ),
file('theBenchmark.p',fact_poly__gcd__dvd2) ).
fof(fact_poly__gcd__dvd1,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_x)) ),
file('theBenchmark.p',fact_poly__gcd__dvd1) ).
fof(fact_add__leE,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ),
file('theBenchmark.p',fact_add__leE) ).
fof(fact_add__leD1,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
file('theBenchmark.p',fact_add__leD2) ).
fof(fact_add__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
file('theBenchmark.p',fact_add__le__mono) ).
fof(fact_add__le__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_add__le__mono1) ).
fof(fact_trans__le__add2,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
file('theBenchmark.p',fact_trans__le__add2) ).
fof(fact_trans__le__add1,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__le__add1) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_le__iff__add,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
<=> ? [B_k] : V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ),
file('theBenchmark.p',fact_le__iff__add) ).
fof(fact_le__add1,axiom,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
file('theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_le__add2) ).
fof(fact_zadd__left__mono,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ),
file('theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_zadd__0,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
file('theBenchmark.p',fact_zadd__0) ).
fof(fact_zadd__0__right,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zadd__0__right) ).
fof(fact_zminus__zadd__distrib,axiom,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
file('theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
file('theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_zadd__strict__right__mono,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ),
file('theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__eq__self__zero,axiom,
! [V_n,V_m] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
=> V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_add__is__0,axiom,
! [V_nb_2,V_m_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_add__is__0) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
file('theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [V_n] : 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_left__add__mult__distrib,axiom,
! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k),
file('theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_add__mult__distrib2,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
file('theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_not__add__less1,axiom,
! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i),
file('theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i),
file('theBenchmark.p',fact_not__add__less2) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_trans__less__add1,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__less__add1) ).
fof(fact_trans__less__add2,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
file('theBenchmark.p',fact_trans__less__add2) ).
fof(fact_add__less__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_add__less__mono1) ).
fof(fact_add__less__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
file('theBenchmark.p',fact_add__less__mono) ).
fof(fact_less__add__eq__less,axiom,
! [V_n,V_m,V_l,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__lessD1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ),
file('theBenchmark.p',fact_add__lessD1) ).
fof(fact_dvd__reduce,axiom,
! [V_nb_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_nb_2)) ),
file('theBenchmark.p',fact_dvd__reduce) ).
fof(fact_add__Suc__shift,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_add__Suc,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_add__Suc__right) ).
fof(fact_poly__gcd__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_poly__gcd__zero__iff) ).
fof(fact_poly__gcd__0__0,axiom,
! [T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_poly__gcd__0__0) ).
fof(fact_poly__gcd_Ocommute,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,V_a,V_b) = c_Polynomial_Opoly__gcd(T_a,V_b,V_a) ),
file('theBenchmark.p',fact_poly__gcd_Ocommute) ).
fof(fact_poly__gcd_Oleft__commute,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c)) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_poly__gcd_Oleft__commute) ).
fof(fact_poly__gcd_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_poly__gcd_Oassoc) ).
fof(fact_pdivmod__rel__unique__div,axiom,
! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
=> V_q1 = V_q2 ) ) ),
file('theBenchmark.p',fact_pdivmod__rel__unique__div) ).
fof(fact_pdivmod__rel__unique__mod,axiom,
! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
=> V_r1 = V_r2 ) ) ),
file('theBenchmark.p',fact_pdivmod__rel__unique__mod) ).
fof(fact_pdivmod__rel__unique,axiom,
! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
=> ( V_r1 = V_r2
& V_q1 = V_q2 ) ) ) ),
file('theBenchmark.p',fact_pdivmod__rel__unique) ).
fof(fact_pdivmod__rel__0__iff,axiom,
! [V_r_2,V_qb_2,V_y_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_qb_2,V_r_2)
<=> ( V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_pdivmod__rel__0__iff) ).
fof(fact_pdivmod__rel__by__0__iff,axiom,
! [V_r_2,V_qb_2,V_x_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_qb_2,V_r_2)
<=> ( V_r_2 = V_x_2
& V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_pdivmod__rel__by__0__iff) ).
fof(fact_pdivmod__rel__0,axiom,
! [V_y,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('theBenchmark.p',fact_pdivmod__rel__0) ).
fof(fact_pdivmod__rel__by__0,axiom,
! [V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) ),
file('theBenchmark.p',fact_pdivmod__rel__by__0) ).
fof(fact_poly__gcd__greatest,axiom,
! [V_y,V_x,V_k,T_a] :
( class_Fields_Ofield(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_y))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) ) ) ),
file('theBenchmark.p',fact_poly__gcd__greatest) ).
fof(fact_dvd__poly__gcd__iff,axiom,
! [V_y_2,V_x_2,V_k_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_dvd__poly__gcd__iff) ).
fof(fact_poly__gcd__minus__left,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y) ),
file('theBenchmark.p',fact_poly__gcd__minus__left) ).
fof(fact_poly__gcd__minus__right,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y) ),
file('theBenchmark.p',fact_poly__gcd__minus__right) ).
fof(fact_poly__gcd__1__right,axiom,
! [V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_poly__gcd__1__right) ).
fof(fact_poly__gcd__1__left,axiom,
! [V_y,T_a] :
( class_Fields_Ofield(T_a)
=> c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_poly__gcd__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__add) ).
fof(fact_add__is__1,axiom,
! [V_nb_2,V_m_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_nb_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_one__is__add,axiom,
! [V_nb_2,V_m_2] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2)
<=> ( ( V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_nb_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__gr__0,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) ),
file('theBenchmark.p',fact_add__gr__0) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_less__add__Suc1,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
file('theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
file('theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_less__iff__Suc__add,axiom,
! [V_nb_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
<=> ? [B_k] : V_nb_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ),
file('theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_odd__nonzero,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_odd__nonzero) ).
fof(fact_zadd__zless__mono,axiom,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ),
file('theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_mult__Suc__right,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_mult__Suc,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_mult__Suc) ).
fof(fact_zless__add1__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( V_w_2 = V_z_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_Suc__eq__plus1,axiom,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_zdvd__period,axiom,
! [V_c_2,V_t_2,V_x_2,V_d_2,V_aa_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),V_d_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2)),V_t_2))) ) ),
file('theBenchmark.p',fact_zdvd__period) ).
fof(fact_zdvd__reduce,axiom,
! [V_m_2,V_nb_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_nb_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_nb_2)) ),
file('theBenchmark.p',fact_zdvd__reduce) ).
fof(fact_zpower__zadd__distrib,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
file('theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_odd__less__0,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_odd__less__0) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_add1__zle__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ),
file('theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_pdivmod__rel__mult,axiom,
! [V_r_H,V_q_H,V_z,V_r,V_q,V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)
=> c_Polynomial_Opdivmod__rel(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z),V_q_H,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H),V_r)) ) ) ),
file('theBenchmark.p',fact_pdivmod__rel__mult) ).
fof(fact_degree__mult__le,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))) ),
file('theBenchmark.p',fact_degree__mult__le) ).
fof(fact_degree__mult__eq,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ( V_q != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)) ) ) ),
file('theBenchmark.p',fact_degree__mult__eq) ).
fof(fact_mult__monom,axiom,
! [V_n,V_b,V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ),
file('theBenchmark.p',fact_mult__monom) ).
fof(fact_le__imp__0__less,axiom,
! [V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ),
file('theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_coeff__mult__degree__sum,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))) ),
file('theBenchmark.p',fact_coeff__mult__degree__sum) ).
fof(fact_self__quotient__aux1,axiom,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_self__quotient__aux2,axiom,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_nat__add__right__cancel,axiom,
! [V_nb_2,V_k_2,V_m_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2)
<=> V_m_2 = V_nb_2 ),
file('theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2)
<=> V_m_2 = V_nb_2 ),
file('theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_nat__add__assoc,axiom,
! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
file('theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
file('theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_nat__add__commute,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
file('theBenchmark.p',fact_nat__add__commute) ).
fof(fact_zadd__assoc,axiom,
! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
file('theBenchmark.p',fact_zadd__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
file('theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_zadd__commute,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_q__pos__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ),
file('theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_q__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_unique__quotient__lemma,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_poly__gcd__unique,axiom,
! [V_y,V_x,V_d,T_a] :
( class_Fields_Ofield(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))
=> ( ! [B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_y))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_d)) ) )
=> ( ( ( ~ ( V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) = c_Groups_Oone__class_Oone(T_a) )
& ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
=> hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) = c_Groups_Ozero__class_Ozero(T_a) ) )
=> c_Polynomial_Opoly__gcd(T_a,V_x,V_y) = V_d ) ) ) ) ),
file('theBenchmark.p',fact_poly__gcd__unique) ).
fof(fact_le__Suc__ex__iff,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
<=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ),
file('theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_incr__mult__lemma,axiom,
! [V_k_2,V_P_2,V_d_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
=> ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
=> ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
file('theBenchmark.p',fact_incr__mult__lemma) ).
fof(fact_ex__least__nat__less,axiom,
! [V_nb_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(V_P_2,V_nb_2))
=> ? [B_k] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
=> ~ hBOOL(hAPP(V_P_2,B_i)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_nb_2) ) ) ),
file('theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_realpow__minus__mult,axiom,
! [V_x,V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ),
file('theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_dvd_OmonoD,axiom,
! [V_y_2,V_x_2,V_f_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_a,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2)) ) ) ),
file('theBenchmark.p',fact_dvd_OmonoD) ).
fof(fact_diff__diff__right,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ),
file('theBenchmark.p',fact_diff__diff__right) ).
fof(fact_le__diff__conv,axiom,
! [V_i_2,V_k_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) ),
file('theBenchmark.p',fact_le__diff__conv) ).
fof(fact_le__add__diff,axiom,
! [V_m,V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ),
file('theBenchmark.p',fact_le__add__diff) ).
fof(fact_le__add__diff__inverse,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_add__diff__assoc,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_le__diff__conv2,axiom,
! [V_i_2,V_j_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ),
file('theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_le__add__diff__inverse2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_le__imp__diff__is__add,axiom,
! [V_k_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
<=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ),
file('theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_diff__add__assoc,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_add__diff__assoc2,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [V_i,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ),
file('theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_add__diff__inverse,axiom,
! [V_n,V_m] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__diff__conv,axiom,
! [V_k_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ),
file('theBenchmark.p',fact_less__diff__conv) ).
fof(fact_diff__add__0,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__cancel2,axiom,
! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__cancel,axiom,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
file('theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__diff__left,axiom,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
file('theBenchmark.p',fact_diff__diff__left) ).
fof(fact_diff__add__inverse,axiom,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_add__diff__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ),
file('theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ),
file('theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_mult__diff__mult,axiom,
! [V_b,V_a,V_y,V_x,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ),
file('theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( class_Rings_Oring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
<=> V_c_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2) ) ),
file('theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( class_Rings_Oring(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
<=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [V_b,V_a,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ),
file('theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_diff__minus__eq__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_ab__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_diff__def) ).
fof(fact_zero__less__diff,axiom,
! [V_m_2,V_nb_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_m_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_zero__less__diff) ).
fof(fact_diff__less,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ),
file('theBenchmark.p',fact_diff__less) ).
fof(fact_diff__less__Suc,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
file('theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_diff__is__0__eq,axiom,
! [V_nb_2,V_m_2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_diff__is__0__eq_H,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_Suc__diff__le,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
file('theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_less__diff__iff,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
=> ( 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_nb_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ),
file('theBenchmark.p',fact_less__diff__iff) ).
fof(fact_diff__less__mono,axiom,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ),
file('theBenchmark.p',fact_diff__less__mono) ).
fof(fact_dvd__diffD1,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ),
file('theBenchmark.p',fact_dvd__diffD1) ).
fof(fact_dvd__diffD,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ),
file('theBenchmark.p',fact_dvd__diffD) ).
fof(fact_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_minus__diff__eq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ),
file('theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( class_Groups_Ominus(T_a)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_minus__apply) ).
fof(fact_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_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__pCons,axiom,
! [V_q,V_b,V_p,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ),
file('theBenchmark.p',fact_diff__pCons) ).
fof(fact_poly__diff,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__diff) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( class_Groups_Oab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
=> ( V_aa_2 = V_b_2
<=> V_c_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
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_dvd__diff__nat,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) ) ),
file('theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_dvd__diff,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))) ) ) ),
file('theBenchmark.p',fact_dvd__diff) ).
fof(fact_diff__monom,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n) ),
file('theBenchmark.p',fact_diff__monom) ).
fof(fact_coeff__diff,axiom,
! [V_n,V_q,V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)) ),
file('theBenchmark.p',fact_coeff__diff) ).
fof(fact_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_diff__less__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ),
file('theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_less__imp__diff__less,axiom,
! [V_n,V_k,V_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ),
file('theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_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_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_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__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_mult_Odiff__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ),
file('theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [V_y,V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ),
file('theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult_Odiff__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ),
file('theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_diff__eq__diff__less,axiom,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
=> ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
<=> 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__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_aa_2,T_a] :
( class_Groups_Oab__group__add(T_a)
=> ( V_aa_2 = V_b_2
<=> c_Groups_Ominus__class_Ominus(T_a,V_aa_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_aa_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_aa_2 = V_b_2 ) ),
file('theBenchmark.p',fact_right__minus__eq) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
<=> 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__le__self,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m),
file('theBenchmark.p',fact_diff__le__self) ).
fof(fact_diff__le__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ),
file('theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_diff__le__mono,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ),
file('theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__diff__cancel,axiom,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ),
file('theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_eq__diff__iff,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_k_2)
<=> V_m_2 = V_nb_2 ) ) ),
file('theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [V_n,V_m,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_le__diff__iff,axiom,
! [V_nb_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
=> ( 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_nb_2,V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ) ),
file('theBenchmark.p',fact_le__diff__iff) ).
fof(fact_diff__0,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ),
file('theBenchmark.p',fact_diff__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_le__iff__diff__le__0,axiom,
! [V_b_2,V_aa_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)) ) ),
file('theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2) ) ),
file('theBenchmark.p',fact_less__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)) ) ),
file('theBenchmark.p',fact_less__add__iff2) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [V_x,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_inf__period_I4_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ( class_Rings_Odvd(T_a)
& class_Rings_Ocomm__ring(T_a) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))) ) ) ),
file('theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_inf__period_I3_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ( class_Rings_Odvd(T_a)
& class_Rings_Ocomm__ring(T_a) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))) ) ) ),
file('theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_diff__Suc__less,axiom,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n) ),
file('theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_Suc__pred,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
file('theBenchmark.p',fact_Suc__pred) ).
fof(fact_nat__diff__split__asm,axiom,
! [V_b_2,V_aa_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
<=> ~ ( ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_nat__diff__split,axiom,
! [V_b_2,V_aa_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
<=> ( ! [B_d] :
( V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
=> hBOOL(hAPP(V_P_2,B_d)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_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] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [V_m,V_j,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_nat__le__add__iff1,axiom,
! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_nb_2) ) ),
file('theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__diff__add__eq1,axiom,
! [V_n,V_m,V_u,V_i,V_j] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n) ),
file('theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__eq__add__iff1,axiom,
! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_nb_2 ) ),
file('theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__le__add__iff2,axiom,
! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2)) ) ),
file('theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__diff__add__eq2,axiom,
! [V_n,V_m,V_u,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ),
file('theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_nat__eq__add__iff2,axiom,
! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)
<=> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2) ) ),
file('theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_degree__synthetic__div,axiom,
! [V_c,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_degree__synthetic__div) ).
fof(fact_Suc__pred_H,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_Suc__diff__1,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ),
file('theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_add__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) )
& ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n ) ),
file('theBenchmark.p',fact_add__eq__if) ).
fof(fact_nat__less__add__iff2,axiom,
! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2)) ) ),
file('theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_nat__less__add__iff1,axiom,
! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_nb_2) ) ),
file('theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_mult__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) )
& ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__eq__if) ).
fof(fact_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)),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_lemma__realpow__diff,axiom,
! [V_y,V_n,V_p,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ),
file('theBenchmark.p',fact_lemma__realpow__diff) ).
fof(fact_diff__int__def__symmetric,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
file('theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_diff__int__def) ).
fof(fact_less__bin__lemma,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_degree__diff__less,axiom,
! [V_q,V_n,V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) ) ) ),
file('theBenchmark.p',fact_degree__diff__less) ).
fof(fact_degree__diff__le,axiom,
! [V_q,V_n,V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) ) ) ),
file('theBenchmark.p',fact_degree__diff__le) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ),
file('theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_zdvd__zdiffD,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ),
file('theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_less__eq__poly__def,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
<=> ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_less__eq__poly__def) ).
fof(fact_less__poly__def,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
<=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ),
file('theBenchmark.p',fact_less__poly__def) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_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_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_zle__diff1__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) ),
file('theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_int__power__div__base,axiom,
! [V_k,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
file('theBenchmark.p',fact_int__power__div__base) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [V_k_2,V_i_2] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [V_aa_2,V_b_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [V_i_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [V_b_2,V_aa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_aa_2) ) ) ),
file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_zdiv__mono2,axiom,
! [V_b,V_b_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_div__pos__pos__trivial,axiom,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [V_aa_2,V_b_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_zdiv__mono2__neg,axiom,
! [V_b,V_b_H,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_div__neg__neg__trivial,axiom,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_zdiv__mono1,axiom,
! [V_b,V_a_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)) ) ),
file('theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_zdiv__mono1__neg,axiom,
! [V_b,V_a_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ),
file('theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_int__div__less__self,axiom,
! [V_k,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ),
file('theBenchmark.p',fact_int__div__less__self) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [V_b,V_a,V_c] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c) ),
file('theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_div__add,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)) ) ) ),
file('theBenchmark.p',fact_div__add) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_div__mult__mult1,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_div__mult__mult1) ).
fof(fact_div__mult__mult2,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_div__mult__mult2) ).
fof(fact_div__mult__self1__is__id,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = V_a ) ),
file('theBenchmark.p',fact_div__mult__self1__is__id) ).
fof(fact_div__mult__self2__is__id,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = V_a ) ),
file('theBenchmark.p',fact_div__mult__self2__is__id) ).
fof(fact_div__mult__mult1__if,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Divides_Odiv__class_Odiv(T_a,V_a,V_b) )
& ( V_c = c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_div__mult__mult1__if) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ),
file('theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_div__mult__swap,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ),
file('theBenchmark.p',fact_div__mult__swap) ).
fof(fact_dvd__div__mult__self,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b ) ),
file('theBenchmark.p',fact_dvd__div__mult__self) ).
fof(fact_dvd__div__mult,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a) ) ),
file('theBenchmark.p',fact_dvd__div__mult) ).
fof(fact_div__mult__div__if__dvd,axiom,
! [V_w,V_z,V_x,V_y,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_div__mult__div__if__dvd) ).
fof(fact_div__neg__pos__less0,axiom,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('theBenchmark.p',fact_div__neg__pos__less0) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [V_aa_2,V_b_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_pos__imp__zdiv__neg__iff,axiom,
! [V_aa_2,V_b_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_zdiv__zero,axiom,
! [V_b] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zdiv__zero) ).
fof(fact_div__by__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_div__by__0) ).
fof(fact_div__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_div__0) ).
fof(fact_zdvd__mult__div__cancel,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_zdvd__mult__div__cancel) ).
fof(fact_div__power,axiom,
! [V_n,V_x,V_y,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ),
file('theBenchmark.p',fact_div__power) ).
fof(fact_div__dvd__div,axiom,
! [V_c_2,V_b_2,V_aa_2,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2)),c_Divides_Odiv__class_Odiv(T_a,V_c_2,V_aa_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b_2),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_div__dvd__div) ).
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_dvd__div__neg,axiom,
! [V_x,V_y,T_a] :
( class_Divides_Oring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ),
file('theBenchmark.p',fact_dvd__div__neg) ).
fof(fact_dvd__neg__div,axiom,
! [V_x,V_y,T_a] :
( class_Divides_Oring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ),
file('theBenchmark.p',fact_dvd__neg__div) ).
fof(fact_zdiv__zminus__zminus,axiom,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),
file('theBenchmark.p',fact_zdiv__zminus__zminus) ).
fof(fact_zdiv__zminus2,axiom,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b),
file('theBenchmark.p',fact_zdiv__zminus2) ).
fof(fact_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__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_div__mult__self2,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ),
file('theBenchmark.p',fact_div__mult__self2) ).
fof(fact_div__mult__self1,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ),
file('theBenchmark.p',fact_div__mult__self1) ).
fof(fact_div__add__self2,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_div__add__self2) ).
fof(fact_div__add__self1,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_div__add__self1) ).
fof(fact_dvd__div__div__eq__mult,axiom,
! [V_d_2,V_b_2,V_c_2,V_aa_2,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c_2),V_d_2))
=> ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) = c_Divides_Odiv__class_Odiv(T_a,V_d_2,V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__div__eq__mult) ).
fof(fact_dvd__div__eq__mult,axiom,
! [V_c_2,V_b_2,V_aa_2,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_aa_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
=> ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) = V_c_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__eq__mult) ).
fof(fact_split__zdiv,axiom,
! [V_k_2,V_nb_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [B_i] :
( ? [B_j] :
( V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) )
=> hBOOL(hAPP(V_P_2,B_i)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
=> ! [B_i] :
( ? [B_j] :
( V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) )
=> hBOOL(hAPP(V_P_2,B_i)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('theBenchmark.p',fact_split__zdiv) ).
fof(fact_divmod__int__rel__div__eq,axiom,
! [V_r_1,V_y,V_b_1,V_a_1] :
( V_a_1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y),V_r_1)
=> ( ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1) ) ) )
=> ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ),
file('theBenchmark.p',fact_divmod__int__rel__div__eq) ).
fof(fact_z3div__def,axiom,
! [V_k,V_l] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
=> c_SMT_Oz3div(V_k,V_l) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l)
=> c_SMT_Oz3div(V_k,V_l) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l) ) ),
file('theBenchmark.p',fact_z3div__def) ).
fof(fact_tsub__def,axiom,
! [V_x,V_y] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ),
file('theBenchmark.p',fact_tsub__def) ).
fof(fact_div__le__mono2,axiom,
! [V_k,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m)) ) ),
file('theBenchmark.p',fact_div__le__mono2) ).
fof(fact_div__mult__self1__is__m,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m ),
file('theBenchmark.p',fact_div__mult__self1__is__m) ).
fof(fact_div__mult__self__is__m,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m ),
file('theBenchmark.p',fact_div__mult__self__is__m) ).
fof(fact_nat__mult__div__cancel1,axiom,
! [V_n,V_m,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_nat__mult__div__cancel1) ).
fof(fact_div__less__dividend,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m) ) ),
file('theBenchmark.p',fact_div__less__dividend) ).
fof(fact_div__le__dividend,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m),
file('theBenchmark.p',fact_div__le__dividend) ).
fof(fact_div__le__mono,axiom,
! [V_k,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k)) ),
file('theBenchmark.p',fact_div__le__mono) ).
fof(fact_div__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__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_div__less) ).
fof(fact_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_poly__div__minus__right,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ),
file('theBenchmark.p',fact_poly__div__minus__right) ).
fof(fact_poly__div__minus__left,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y)) ),
file('theBenchmark.p',fact_poly__div__minus__left) ).
fof(fact_poly__div__mult__right,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z) ),
file('theBenchmark.p',fact_poly__div__mult__right) ).
fof(fact_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__poly__eq,axiom,
! [V_r,V_q,V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = V_q ) ),
file('theBenchmark.p',fact_div__poly__eq) ).
fof(fact_div__poly__less,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Ofield(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))
=> c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_div__poly__less) ).
fof(fact_div__if,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_div__if) ).
fof(fact_div__geq,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)) ) ),
file('theBenchmark.p',fact_div__geq) ).
fof(fact_split__div,axiom,
! [V_k_2,V_nb_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_nb_2,V_k_2)))
<=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ! [B_i,B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)
=> ( V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
=> hBOOL(hAPP(V_P_2,B_i)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_split__div) ).
fof(fact_split__div_H,axiom,
! [V_nb_2,V_m_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_nb_2)))
<=> ( ? [B_q] :
( hBOOL(hAPP(V_P_2,B_q))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(B_q)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),B_q),V_m_2) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_nb_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_qb_2,V_nb_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(V_qb_2)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_qb_2),V_m_2) )
<=> V_qb_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
file('theBenchmark.p',fact_split__div__lemma) ).
fof(fact_le__div__geq,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless__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_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_tsub__eq,axiom,
! [V_x,V_y] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ),
file('theBenchmark.p',fact_tsub__eq) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ),
file('theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_sgn__poly__def,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_sgn__poly__def) ).
fof(fact_sgn__minus,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ),
file('theBenchmark.p',fact_sgn__minus) ).
fof(fact_sgn__one,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_sgn__one) ).
fof(fact_sgn__sgn,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ),
file('theBenchmark.p',fact_sgn__sgn) ).
fof(fact_sgn__mult,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ),
file('theBenchmark.p',fact_sgn__mult) ).
fof(fact_sgn__times,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ),
file('theBenchmark.p',fact_sgn__times) ).
fof(fact_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,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__zero__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_sgn__zero__iff) ).
fof(fact_sgn__0__0,axiom,
! [V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_sgn__0__0) ).
fof(fact_sgn__greater,axiom,
! [V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_sgn__greater) ).
fof(fact_sgn__less,axiom,
! [V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_sgn__less) ).
fof(fact_sgn__1__pos,axiom,
! [V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Oone__class_Oone(T_a)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
file('theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_sgn__pos,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__if,axiom,
! [V_x,T_a] :
( class_Groups_Osgn__if(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sgn__if) ).
fof(fact_sgn__1__neg,axiom,
! [V_aa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__neg,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_sgn__neg) ).
fof(fact_decr__mult__lemma,axiom,
! [V_k_2,V_P_2,V_d_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
=> ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
=> ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
file('theBenchmark.p',fact_decr__mult__lemma) ).
fof(fact_split__neg__lemma,axiom,
! [V_nb_2,V_P_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_nb_2,V_k_2)))
<=> ! [B_i,B_j] :
( ( V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) )
=> hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
file('theBenchmark.p',fact_split__neg__lemma) ).
fof(fact_div__mod__equality,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) ),
file('theBenchmark.p',fact_div__mod__equality) ).
fof(fact_div__mod__equality2,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) ),
file('theBenchmark.p',fact_div__mod__equality2) ).
fof(fact_mod__div__equality,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
file('theBenchmark.p',fact_mod__div__equality) ).
fof(fact_mod__div__equality2,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
file('theBenchmark.p',fact_mod__div__equality2) ).
fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)) = V_a ),
file('theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).
fof(fact_zdiv__zadd1__eq,axiom,
! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)),
file('theBenchmark.p',fact_zdiv__zadd1__eq) ).
fof(fact_zmod__zdiv__trivial,axiom,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(fact_mod__div__trivial,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_DIVISION__BY__ZERO,axiom,
! [V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
& c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_zmod__zdiv__equality,axiom,
! [V_b,V_a] : V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
file('theBenchmark.p',fact_zmod__zdiv__equality) ).
fof(fact_zdiv__zmult1__eq,axiom,
! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)),
file('theBenchmark.p',fact_zdiv__zmult1__eq) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(T_1)
=> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [T_2,T_1] :
( class_Orderings_Opreorder(T_1)
=> class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [T_2,T_1] :
( class_Orderings_Oorder(T_1)
=> class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [T_2,T_1] :
( class_Orderings_Oord(T_1)
=> class_Orderings_Oord(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [T_2,T_1] :
( class_Groups_Ouminus(T_1)
=> class_Groups_Ouminus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [T_2,T_1] :
( class_Groups_Ominus(T_1)
=> class_Groups_Ominus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__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_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Osgn__if,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
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__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_Ono__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
! [T_1] :
( class_Fields_Ofield(T_1)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
! [T_1] :
( class_Fields_Ofield(T_1)
=> class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [T_1] :
( class_Groups_Ozero(T_1)
=> class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(help_c__fequal__1,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(c_fequal(V_x_2,V_y_2)) ),
file('theBenchmark.p',help_c__fequal__1) ).
fof(help_c__fequal__2,axiom,
! [V_y_2,V_x_2] :
( hBOOL(c_fequal(V_x_2,V_y_2))
| V_x_2 != V_y_2 ),
file('theBenchmark.p',help_c__fequal__2) ).
fof(conj_0,hypothesis,
( ? [B_r] : v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r)
=> v_thesis____ ),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
v_thesis____,
file('theBenchmark.p',conj_1) ).
fof(f_1_1,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
inference(fof_nnf,[status(thm)],[fact_ext]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = U_2
| ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_nnf,[status(thm)],[fact_q0]) ).
cnf(f_2_2,plain,
v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[f_2_1]) ).
fof(f_3_1,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)),
inference(fof_nnf,[status(thm)],[fact__096_091_058_N_Aa_M_A1_058_093_Advd_Aq_096]) ).
cnf(f_3_2,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),v_qa____)),
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
! [T_a] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__poly__def]) ).
fof(f_4_2,plain,
! [U_3] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_3)) = c_Polynomial_OpCons(U_3,c_Groups_Oone__class_Oone(U_3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3)))
| ~ class_Rings_Ocomm__semiring__1(U_3) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_3)) = c_Polynomial_OpCons(U_3,c_Groups_Oone__class_Oone(U_3),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3)))
| ~ class_Rings_Ocomm__semiring__1(U_3) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [T_a] :
( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pCons__0__0]) ).
fof(f_5_2,plain,
! [U_4] :
( c_Polynomial_OpCons(U_4,c_Groups_Ozero__class_Ozero(U_4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_4))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_4))
| ~ class_Groups_Ozero(U_4) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( c_Polynomial_OpCons(U_4,c_Groups_Ozero__class_Ozero(U_4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_4))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_4))
| ~ class_Groups_Ozero(U_4) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [V_pb_2,V_aa_2,T_a] :
( ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff]) ).
fof(f_6_2,plain,
! [U_7,U_6,U_5] :
( ( ( c_Polynomial_OpCons(U_5,U_6,U_7) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
| U_7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
| U_6 != c_Groups_Ozero__class_Ozero(U_5) )
& ( ( U_7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
& U_6 = c_Groups_Ozero__class_Ozero(U_5) )
| c_Polynomial_OpCons(U_5,U_6,U_7) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5)) ) )
| ~ class_Groups_Ozero(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( U_6 = c_Groups_Ozero__class_Ozero(U_5)
| c_Polynomial_OpCons(U_5,U_6,U_7) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
| ~ class_Groups_Ozero(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( U_7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
| c_Polynomial_OpCons(U_5,U_6,U_7) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
| ~ class_Groups_Ozero(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( c_Polynomial_OpCons(U_5,U_6,U_7) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
| U_7 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_5))
| U_6 != c_Groups_Ozero__class_Ozero(U_5)
| ~ class_Groups_Ozero(U_5) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x)
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J]) ).
fof(f_7_2,plain,
! [U_9,U_8] :
( c_Groups_Ouminus__class_Ouminus(U_8,U_9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8),c_Groups_Ouminus__class_Ouminus(U_8,c_Groups_Oone__class_Oone(U_8))),U_9)
| ~ class_Rings_Ocomm__ring__1(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_8,U_9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8),c_Groups_Ouminus__class_Ouminus(U_8,c_Groups_Oone__class_Oone(U_8))),U_9)
| ~ class_Rings_Ocomm__ring__1(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [V_x_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
& V_x_2 != c_Groups_Oone__class_Oone(T_a) ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).
fof(f_8_2,plain,
! [U_11,U_10] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_11) = c_Groups_Oone__class_Oone(U_10)
| ( U_11 != c_Groups_Ouminus__class_Ouminus(U_10,c_Groups_Oone__class_Oone(U_10))
& U_11 != c_Groups_Oone__class_Oone(U_10) ) )
& ( U_11 = c_Groups_Ouminus__class_Ouminus(U_10,c_Groups_Oone__class_Oone(U_10))
| U_11 = c_Groups_Oone__class_Oone(U_10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_11) != c_Groups_Oone__class_Oone(U_10) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( U_11 = c_Groups_Ouminus__class_Ouminus(U_10,c_Groups_Oone__class_Oone(U_10))
| U_11 = c_Groups_Oone__class_Oone(U_10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_11) != c_Groups_Oone__class_Oone(U_10)
| ~ class_Rings_Oring__1__no__zero__divisors(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_11 != c_Groups_Oone__class_Oone(U_10)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_11) = c_Groups_Oone__class_Oone(U_10)
| ~ class_Rings_Oring__1__no__zero__divisors(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( U_11 != c_Groups_Ouminus__class_Ouminus(U_10,c_Groups_Oone__class_Oone(U_10))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10),U_11),U_11) = c_Groups_Oone__class_Oone(U_10)
| ~ class_Rings_Oring__1__no__zero__divisors(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [V_q,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left]) ).
fof(f_9_2,plain,
! [U_13,U_12] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_12)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_12))),U_13) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_12))
| ~ class_Rings_Ocomm__semiring__0(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_12)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_12))),U_13) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_12))
| ~ class_Rings_Ocomm__semiring__0(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [V_p,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right]) ).
fof(f_10_2,plain,
! [U_15,U_14] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_14)),U_15),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_14))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_14))
| ~ class_Rings_Ocomm__semiring__0(U_14) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_14)),U_15),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_14))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_14))
| ~ class_Rings_Ocomm__semiring__0(U_14) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [V_p,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__pCons]) ).
fof(f_11_2,plain,
! [U_18,U_17,U_16] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_16),c_Polynomial_OpCons(U_16,U_17,U_18)) = c_Polynomial_OpCons(U_16,c_Groups_Ouminus__class_Ouminus(U_16,U_17),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_16),U_18))
| ~ class_Groups_Oab__group__add(U_16) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_16),c_Polynomial_OpCons(U_16,U_17,U_18)) = c_Polynomial_OpCons(U_16,c_Groups_Ouminus__class_Ouminus(U_16,U_17),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_16),U_18))
| ~ class_Groups_Oab__group__add(U_16) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [V_p,V_a,T_b] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J]) ).
fof(f_12_2,plain,
! [U_21,U_20,U_19] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_19),c_Polynomial_OpCons(U_19,U_20,U_21)) = c_Polynomial_OpCons(U_19,c_Groups_Ouminus__class_Ouminus(U_19,U_20),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_19),U_21))
| ~ class_Groups_Oab__group__add(U_19) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_19),c_Polynomial_OpCons(U_19,U_20,U_21)) = c_Polynomial_OpCons(U_19,c_Groups_Ouminus__class_Ouminus(U_19,U_20),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_19),U_21))
| ~ class_Groups_Oab__group__add(U_19) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(fof_nnf,[status(thm)],[fact_pne]) ).
cnf(f_13_2,plain,
v_pa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__right]) ).
fof(f_14_2,plain,
! [U_24,U_23,U_22] :
( c_Groups_Ouminus__class_Ouminus(U_22,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_22),U_23),U_24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_22),U_23),c_Groups_Ouminus__class_Ouminus(U_22,U_24))
| ~ class_Rings_Oring(U_22) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_22,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_22),U_23),U_24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_22),U_23),c_Groups_Ouminus__class_Ouminus(U_22,U_24))
| ~ class_Rings_Oring(U_22) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__left]) ).
fof(f_15_2,plain,
! [U_27,U_26,U_25] :
( c_Groups_Ouminus__class_Ouminus(U_25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_25),U_26),U_27)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_25),c_Groups_Ouminus__class_Ouminus(U_25,U_26)),U_27)
| ~ class_Rings_Oring(U_25) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_25,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_25),U_26),U_27)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_25),c_Groups_Ouminus__class_Ouminus(U_25,U_26)),U_27)
| ~ class_Rings_Oring(U_25) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_n0]) ).
cnf(f_16_2,plain,
v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_oa]) ).
cnf(f_17_2,plain,
c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__0__right]) ).
fof(f_18_2,plain,
! [U_29,U_28] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_28),U_29),c_Groups_Ozero__class_Ozero(U_28)))
| ~ class_Rings_Ocomm__semiring__1(U_28) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_28),U_29),c_Groups_Ozero__class_Ozero(U_28)))
| ~ class_Rings_Ocomm__semiring__1(U_28) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_a____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_a]) ).
cnf(f_19_2,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_a____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_qa____),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_nnf,[status(thm)],[fact_pq0]) ).
fof(f_20_2,plain,
! [U_30] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_qa____),U_30) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),U_30) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_qa____),U_30) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),U_30) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__refl]) ).
fof(f_21_2,plain,
! [U_32,U_31] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_31),U_32),U_32))
| ~ class_Rings_Ocomm__semiring__1(U_31) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_31),U_32),U_32))
| ~ class_Rings_Ocomm__semiring__1(U_31) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__trans]) ).
fof(f_22_2,plain,
! [U_36,U_35,U_34,U_33] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_33),U_34),U_36))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_33),U_35),U_36))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_33),U_34),U_35))
| ~ class_Rings_Ocomm__semiring__1(U_33) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_33),U_34),U_36))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_33),U_35),U_36))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_33),U_34),U_35))
| ~ class_Rings_Ocomm__semiring__1(U_33) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [V_a,T_a] :
( V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__0__left]) ).
fof(f_23_2,plain,
! [U_38,U_37] :
( U_38 = c_Groups_Ozero__class_Ozero(U_37)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_37),c_Groups_Ozero__class_Ozero(U_37)),U_38))
| ~ class_Rings_Ocomm__semiring__1(U_37) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( U_38 = c_Groups_Ozero__class_Ozero(U_37)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_37),c_Groups_Ozero__class_Ozero(U_37)),U_38))
| ~ class_Rings_Ocomm__semiring__1(U_37) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__right]) ).
fof(f_24_2,plain,
! [U_42,U_41,U_40,U_39] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_39),U_41),U_42))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),U_41)),U_42))
| ~ class_Rings_Ocomm__semiring__1(U_39) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_39),U_41),U_42))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),U_41)),U_42))
| ~ class_Rings_Ocomm__semiring__1(U_39) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__left]) ).
fof(f_25_2,plain,
! [U_46,U_45,U_44,U_43] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_43),U_44),U_46))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_43),U_44),U_45)),U_46))
| ~ class_Rings_Ocomm__semiring__1(U_43) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_43),U_44),U_46))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_43),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_43),U_44),U_45)),U_46))
| ~ class_Rings_Ocomm__semiring__1(U_43) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [V_k,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a))
| V_a != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
| ~ class_Rings_Odvd(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvdI]) ).
fof(f_26_2,plain,
! [U_50,U_49,U_48,U_47] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_47),U_49),U_48))
| U_48 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_47),U_49),U_50)
| ~ class_Rings_Odvd(U_47) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_47),U_49),U_48))
| U_48 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_47),U_49),U_50)
| ~ class_Rings_Odvd(U_47) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono]) ).
fof(f_27_2,plain,
! [U_55,U_54,U_53,U_52,U_51] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_51),U_52),U_54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_51),U_53),U_55)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_51),U_54),U_55))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_51),U_52),U_53))
| ~ class_Rings_Ocomm__semiring__1(U_51) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_51),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_51),U_52),U_54)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_51),U_53),U_55)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_51),U_54),U_55))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_51),U_52),U_53))
| ~ class_Rings_Ocomm__semiring__1(U_51) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [V_b,V_c,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult]) ).
fof(f_28_2,plain,
! [U_59,U_58,U_57,U_56] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_56),U_57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_59),U_58)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_56),U_57),U_58))
| ~ class_Rings_Ocomm__semiring__1(U_56) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_56),U_57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_59),U_58)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_56),U_57),U_58))
| ~ class_Rings_Ocomm__semiring__1(U_56) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult2]) ).
fof(f_29_2,plain,
! [U_63,U_62,U_61,U_60] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_60),U_61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_62),U_63)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_60),U_61),U_62))
| ~ class_Rings_Ocomm__semiring__1(U_60) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_60),U_61),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_62),U_63)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_60),U_61),U_62))
| ~ class_Rings_Ocomm__semiring__1(U_60) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__triv__right]) ).
fof(f_30_2,plain,
! [U_66,U_65,U_64] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_64),U_65),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_64),U_66),U_65)))
| ~ class_Rings_Ocomm__semiring__1(U_64) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_64),U_65),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_64),U_66),U_65)))
| ~ class_Rings_Ocomm__semiring__1(U_64) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__triv__left]) ).
fof(f_31_2,plain,
! [U_69,U_68,U_67] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_67),U_68),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_67),U_68),U_69)))
| ~ class_Rings_Ocomm__semiring__1(U_67) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_67),U_68),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_67),U_68),U_69)))
| ~ class_Rings_Ocomm__semiring__1(U_67) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__dvd]) ).
fof(f_32_2,plain,
! [U_71,U_70] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_70),c_Groups_Oone__class_Oone(U_70)),U_71))
| ~ class_Rings_Ocomm__semiring__1(U_70) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_70),c_Groups_Oone__class_Oone(U_70)),U_71))
| ~ class_Rings_Ocomm__semiring__1(U_70) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)),V_y_2)) ) )
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff]) ).
fof(f_33_2,plain,
! [U_74,U_73,U_72] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),c_Groups_Ouminus__class_Ouminus(U_72,U_73)),U_74))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),U_73),U_74)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),U_73),U_74))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),c_Groups_Ouminus__class_Ouminus(U_72,U_73)),U_74)) ) )
| ~ class_Rings_Ocomm__ring__1(U_72) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),U_73),U_74))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),c_Groups_Ouminus__class_Ouminus(U_72,U_73)),U_74))
| ~ class_Rings_Ocomm__ring__1(U_72) ),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),c_Groups_Ouminus__class_Ouminus(U_72,U_73)),U_74))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_72),U_73),U_74))
| ~ class_Rings_Ocomm__ring__1(U_72) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))) ) )
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff]) ).
fof(f_34_2,plain,
! [U_77,U_76,U_75] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),c_Groups_Ouminus__class_Ouminus(U_75,U_77)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),U_77)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),U_77))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),c_Groups_Ouminus__class_Ouminus(U_75,U_77))) ) )
| ~ class_Rings_Ocomm__ring__1(U_75) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),U_77))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),c_Groups_Ouminus__class_Ouminus(U_75,U_77)))
| ~ class_Rings_Ocomm__ring__1(U_75) ),
inference(clausify,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),c_Groups_Ouminus__class_Ouminus(U_75,U_77)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_75),U_76),U_77))
| ~ class_Rings_Ocomm__ring__1(U_75) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [T_a] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J]) ).
fof(f_35_2,plain,
! [U_78] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_78),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_78))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_78))
| ~ class_Groups_Oab__group__add(U_78) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_78),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_78))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_78))
| ~ class_Groups_Oab__group__add(U_78) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
& V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left]) ).
fof(f_36_2,plain,
! [U_82,U_81,U_80,U_79] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_82)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),U_81),U_82))
& U_80 != c_Groups_Ozero__class_Ozero(U_79) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),U_81),U_82))
| U_80 = c_Groups_Ozero__class_Ozero(U_79)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_82))) ) )
| ~ class_Rings_Oidom(U_79) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),U_81),U_82))
| U_80 = c_Groups_Ozero__class_Ozero(U_79)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_82)))
| ~ class_Rings_Oidom(U_79) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( U_80 != c_Groups_Ozero__class_Ozero(U_79)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_82)))
| ~ class_Rings_Oidom(U_79) ),
inference(clausify,[status(thm)],[f_36_2]) ).
cnf(f_36_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),U_81),U_82))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_79),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_81)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),U_82)))
| ~ class_Rings_Oidom(U_79) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [V_b_2,V_c_2,V_aa_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
& V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right]) ).
fof(f_37_2,plain,
! [U_86,U_85,U_84,U_83] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_86),U_85)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),U_84),U_86))
& U_85 != c_Groups_Ozero__class_Ozero(U_83) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),U_84),U_86))
| U_85 = c_Groups_Ozero__class_Ozero(U_83)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_86),U_85))) ) )
| ~ class_Rings_Oidom(U_83) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),U_84),U_86))
| U_85 = c_Groups_Ozero__class_Ozero(U_83)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_86),U_85)))
| ~ class_Rings_Oidom(U_83) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( U_85 != c_Groups_Ozero__class_Ozero(U_83)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_86),U_85)))
| ~ class_Rings_Oidom(U_83) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_37_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),U_84),U_86))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_86),U_85)))
| ~ class_Rings_Oidom(U_83) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_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_38_2,plain,
! [U_91,U_90,U_89,U_88,U_87] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_88),U_89)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_90),U_91)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_88),U_90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_89),U_91))
| ~ class_Rings_Ocomm__semiring__1(U_87) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_88),U_89)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_90),U_91)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_88),U_90)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_87),U_89),U_91))
| ~ class_Rings_Ocomm__semiring__1(U_87) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_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_39_2,plain,
! [U_96,U_95,U_94,U_93,U_92] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_93),U_94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_95),U_96)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_95),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_93),U_94)),U_96))
| ~ class_Rings_Ocomm__semiring__1(U_92) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_93),U_94)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_95),U_96)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_95),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_92),U_93),U_94)),U_96))
| ~ class_Rings_Ocomm__semiring__1(U_92) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_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_40_2,plain,
! [U_101,U_100,U_99,U_98,U_97] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_98),U_99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_100),U_101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_100),U_101)))
| ~ class_Rings_Ocomm__semiring__1(U_97) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_98),U_99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_100),U_101)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_99),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_97),U_100),U_101)))
| ~ class_Rings_Ocomm__semiring__1(U_97) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_105,U_104,U_103,U_102] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),U_103),U_104)),U_105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),U_103),U_105)),U_104)
| ~ class_Rings_Ocomm__semiring__1(U_102) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),U_103),U_104)),U_105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_102),U_103),U_105)),U_104)
| ~ class_Rings_Ocomm__semiring__1(U_102) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_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_42_2,plain,
! [U_109,U_108,U_107,U_106] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),U_107),U_108)),U_109) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),U_107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),U_108),U_109))
| ~ class_Rings_Ocomm__semiring__1(U_106) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),U_107),U_108)),U_109) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),U_107),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_106),U_108),U_109))
| ~ class_Rings_Ocomm__semiring__1(U_106) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_113,U_112,U_111,U_110] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_112),U_113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_111),U_112)),U_113)
| ~ class_Rings_Ocomm__semiring__1(U_110) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_111),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_112),U_113)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_110),U_111),U_112)),U_113)
| ~ class_Rings_Ocomm__semiring__1(U_110) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_117,U_116,U_115,U_114] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_116),U_117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_115),U_117))
| ~ class_Rings_Ocomm__semiring__1(U_114) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_116),U_117)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_116),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_114),U_115),U_117))
| ~ class_Rings_Ocomm__semiring__1(U_114) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_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_45_2,plain,
! [U_120,U_119,U_118] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_118),U_119),U_120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_118),U_120),U_119)
| ~ class_Rings_Ocomm__semiring__1(U_118) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_118),U_119),U_120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_118),U_120),U_119)
| ~ class_Rings_Ocomm__semiring__1(U_118) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [V_qb_2,V_b_2,V_pb_2,V_aa_2,T_a] :
( ( ( c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) = c_Polynomial_OpCons(T_a,V_b_2,V_qb_2)
| V_pb_2 != V_qb_2
| V_aa_2 != V_b_2 )
& ( ( V_pb_2 = V_qb_2
& V_aa_2 = V_b_2 )
| c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2) != c_Polynomial_OpCons(T_a,V_b_2,V_qb_2) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff]) ).
fof(f_46_2,plain,
! [U_125,U_124,U_123,U_122,U_121] :
( ( ( c_Polynomial_OpCons(U_121,U_122,U_123) = c_Polynomial_OpCons(U_121,U_124,U_125)
| U_123 != U_125
| U_122 != U_124 )
& ( ( U_123 = U_125
& U_122 = U_124 )
| c_Polynomial_OpCons(U_121,U_122,U_123) != c_Polynomial_OpCons(U_121,U_124,U_125) ) )
| ~ class_Groups_Ozero(U_121) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( U_122 = U_124
| c_Polynomial_OpCons(U_121,U_122,U_123) != c_Polynomial_OpCons(U_121,U_124,U_125)
| ~ class_Groups_Ozero(U_121) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( U_123 = U_125
| c_Polynomial_OpCons(U_121,U_122,U_123) != c_Polynomial_OpCons(U_121,U_124,U_125)
| ~ class_Groups_Ozero(U_121) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_5,plain,
( c_Polynomial_OpCons(U_121,U_122,U_123) = c_Polynomial_OpCons(U_121,U_124,U_125)
| U_123 != U_125
| U_122 != U_124
| ~ class_Groups_Ozero(U_121) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_128,U_127,U_126] :
( U_128 = c_Groups_Ozero__class_Ozero(U_126)
| U_127 = c_Groups_Ozero__class_Ozero(U_126)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_126),U_127),U_128) != c_Groups_Ozero__class_Ozero(U_126)
| ~ class_Rings_Ono__zero__divisors(U_126) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( U_128 = c_Groups_Ozero__class_Ozero(U_126)
| U_127 = c_Groups_Ozero__class_Ozero(U_126)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_126),U_127),U_128) != c_Groups_Ozero__class_Ozero(U_126)
| ~ class_Rings_Ono__zero__divisors(U_126) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_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_48_2,plain,
! [U_131,U_130,U_129] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_130),U_131) != c_Groups_Ozero__class_Ozero(U_129)
| U_131 = c_Groups_Ozero__class_Ozero(U_129)
| U_130 = c_Groups_Ozero__class_Ozero(U_129)
| ~ class_Rings_Ono__zero__divisors(U_129) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_129),U_130),U_131) != c_Groups_Ozero__class_Ozero(U_129)
| U_131 = c_Groups_Ozero__class_Ozero(U_129)
| U_130 = c_Groups_Ozero__class_Ozero(U_129)
| ~ class_Rings_Ono__zero__divisors(U_129) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
& V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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_49_2,plain,
! [U_134,U_133,U_132] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_132),U_133),U_134) = c_Groups_Ozero__class_Ozero(U_132)
| ( U_134 != c_Groups_Ozero__class_Ozero(U_132)
& U_133 != c_Groups_Ozero__class_Ozero(U_132) ) )
& ( U_134 = c_Groups_Ozero__class_Ozero(U_132)
| U_133 = c_Groups_Ozero__class_Ozero(U_132)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_132),U_133),U_134) != c_Groups_Ozero__class_Ozero(U_132) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_132) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( U_134 = c_Groups_Ozero__class_Ozero(U_132)
| U_133 = c_Groups_Ozero__class_Ozero(U_132)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_132),U_133),U_134) != c_Groups_Ozero__class_Ozero(U_132)
| ~ class_Rings_Oring__no__zero__divisors(U_132) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( U_133 != c_Groups_Ozero__class_Ozero(U_132)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_132),U_133),U_134) = c_Groups_Ozero__class_Ozero(U_132)
| ~ class_Rings_Oring__no__zero__divisors(U_132) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_5,plain,
( U_134 != c_Groups_Ozero__class_Ozero(U_132)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_132),U_133),U_134) = c_Groups_Ozero__class_Ozero(U_132)
| ~ class_Rings_Oring__no__zero__divisors(U_132) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_136,U_135] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_135),U_136),c_Groups_Ozero__class_Ozero(U_135)) = c_Groups_Ozero__class_Ozero(U_135)
| ~ class_Rings_Ocomm__semiring__1(U_135) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_135),U_136),c_Groups_Ozero__class_Ozero(U_135)) = c_Groups_Ozero__class_Ozero(U_135)
| ~ class_Rings_Ocomm__semiring__1(U_135) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_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_51_2,plain,
! [U_138,U_137] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),c_Groups_Ozero__class_Ozero(U_137)) = c_Groups_Ozero__class_Ozero(U_137)
| ~ class_Rings_Omult__zero(U_137) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_137),U_138),c_Groups_Ozero__class_Ozero(U_137)) = c_Groups_Ozero__class_Ozero(U_137)
| ~ class_Rings_Omult__zero(U_137) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_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_52_2,plain,
! [U_140,U_139] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_139),c_Groups_Ozero__class_Ozero(U_139)),U_140) = c_Groups_Ozero__class_Ozero(U_139)
| ~ class_Rings_Ocomm__semiring__1(U_139) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_139),c_Groups_Ozero__class_Ozero(U_139)),U_140) = c_Groups_Ozero__class_Ozero(U_139)
| ~ class_Rings_Ocomm__semiring__1(U_139) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_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_53_2,plain,
! [U_142,U_141] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),c_Groups_Ozero__class_Ozero(U_141)),U_142) = c_Groups_Ozero__class_Ozero(U_141)
| ~ class_Rings_Omult__zero(U_141) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_141),c_Groups_Ozero__class_Ozero(U_141)),U_142) = c_Groups_Ozero__class_Ozero(U_141)
| ~ class_Rings_Omult__zero(U_141) ),
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_143] :
( c_Groups_Ozero__class_Ozero(U_143) != c_Groups_Oone__class_Oone(U_143)
| ~ class_Rings_Ozero__neq__one(U_143) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( c_Groups_Ozero__class_Ozero(U_143) != c_Groups_Oone__class_Oone(U_143)
| ~ class_Rings_Ozero__neq__one(U_143) ),
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_144] :
( c_Groups_Oone__class_Oone(U_144) != c_Groups_Ozero__class_Ozero(U_144)
| ~ class_Rings_Ozero__neq__one(U_144) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( c_Groups_Oone__class_Oone(U_144) != c_Groups_Ozero__class_Ozero(U_144)
| ~ class_Rings_Ozero__neq__one(U_144) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_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_56_2,plain,
! [U_146,U_145] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_146),c_Groups_Oone__class_Oone(U_145)) = U_146
| ~ class_Rings_Ocomm__semiring__1(U_145) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_145),U_146),c_Groups_Oone__class_Oone(U_145)) = U_146
| ~ class_Rings_Ocomm__semiring__1(U_145) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_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_57_2,plain,
! [U_148,U_147] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_147),c_Groups_Oone__class_Oone(U_147)),U_148) = U_148
| ~ class_Rings_Ocomm__semiring__1(U_147) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_147),c_Groups_Oone__class_Oone(U_147)),U_148) = U_148
| ~ class_Rings_Ocomm__semiring__1(U_147) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
| ( V_aa_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
& V_aa_2 != V_b_2 ) )
& ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_aa_2 = V_b_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_aa_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).
fof(f_58_2,plain,
! [U_151,U_150,U_149] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_151)
| ( U_150 != c_Groups_Ouminus__class_Ouminus(U_149,U_151)
& U_150 != U_151 ) )
& ( U_150 = c_Groups_Ouminus__class_Ouminus(U_149,U_151)
| U_150 = U_151
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_150) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_151) ) )
| ~ class_Rings_Oidom(U_149) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( U_150 = c_Groups_Ouminus__class_Ouminus(U_149,U_151)
| U_150 = U_151
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_150) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_151)
| ~ class_Rings_Oidom(U_149) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( U_150 != U_151
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_151)
| ~ class_Rings_Oidom(U_149) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_5,plain,
( U_150 != c_Groups_Ouminus__class_Ouminus(U_149,U_151)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_150),U_150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_149),U_151),U_151)
| ~ class_Rings_Oidom(U_149) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__minus]) ).
fof(f_59_2,plain,
! [U_154,U_153,U_152] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_152),c_Groups_Ouminus__class_Ouminus(U_152,U_153)),c_Groups_Ouminus__class_Ouminus(U_152,U_154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_152),U_153),U_154)
| ~ class_Rings_Oring(U_152) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_152),c_Groups_Ouminus__class_Ouminus(U_152,U_153)),c_Groups_Ouminus__class_Ouminus(U_152,U_154)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_152),U_153),U_154)
| ~ class_Rings_Oring(U_152) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__commute]) ).
fof(f_60_2,plain,
! [U_157,U_156,U_155] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_155),c_Groups_Ouminus__class_Ouminus(U_155,U_156)),U_157) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_155),U_156),c_Groups_Ouminus__class_Ouminus(U_155,U_157))
| ~ class_Rings_Oring(U_155) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_155),c_Groups_Ouminus__class_Ouminus(U_155,U_156)),U_157) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_155),U_156),c_Groups_Ouminus__class_Ouminus(U_155,U_157))
| ~ class_Rings_Oring(U_155) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)),
inference(fof_nnf,[status(thm)],[fact_ap_I1_J]) ).
cnf(f_61_2,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____))),v_pa____)),
inference(clausify,[status(thm)],[f_61_1]) ).
fof(f_62_1,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_qa____),v_na____)))
| v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(fof_nnf,[status(thm)],[fact_calculation]) ).
cnf(f_62_2,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_pa____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),v_qa____),v_na____)))
| v_qa____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
inference(clausify,[status(thm)],[f_62_1]) ).
fof(f_63_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus]) ).
fof(f_63_2,plain,
! [U_160,U_159,U_158] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_158),c_Groups_Ouminus__class_Ouminus(U_158,U_159)),U_160) = c_Groups_Ouminus__class_Ouminus(U_158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_158),U_159),U_160))
| ~ class_RealVector_Oreal__normed__algebra(U_158) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_158),c_Groups_Ouminus__class_Ouminus(U_158,U_159)),U_160) = c_Groups_Ouminus__class_Ouminus(U_158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_158),U_159),U_160))
| ~ class_RealVector_Oreal__normed__algebra(U_158) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left]) ).
fof(f_64_2,plain,
! [U_163,U_162,U_161] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_161),c_Groups_Ouminus__class_Ouminus(U_161,U_162)),U_163) = c_Groups_Ouminus__class_Ouminus(U_161,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_161),U_162),U_163))
| ~ class_RealVector_Oreal__normed__algebra(U_161) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_161),c_Groups_Ouminus__class_Ouminus(U_161,U_162)),U_163) = c_Groups_Ouminus__class_Ouminus(U_161,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_161),U_162),U_163))
| ~ class_RealVector_Oreal__normed__algebra(U_161) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,plain,
! [V_x,V_xa,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus]) ).
fof(f_65_2,plain,
! [U_166,U_165,U_164] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_165),c_Groups_Ouminus__class_Ouminus(U_164,U_166)) = c_Groups_Ouminus__class_Ouminus(U_164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_165),U_166))
| ~ class_RealVector_Oreal__normed__algebra(U_164) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_165),c_Groups_Ouminus__class_Ouminus(U_164,U_166)) = c_Groups_Ouminus__class_Ouminus(U_164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_164),U_165),U_166))
| ~ class_RealVector_Oreal__normed__algebra(U_164) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right]) ).
fof(f_66_2,plain,
! [U_169,U_168,U_167] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_167),U_168),c_Groups_Ouminus__class_Ouminus(U_167,U_169)) = c_Groups_Ouminus__class_Ouminus(U_167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_167),U_168),U_169))
| ~ class_RealVector_Oreal__normed__algebra(U_167) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_167),U_168),c_Groups_Ouminus__class_Ouminus(U_167,U_169)) = c_Groups_Ouminus__class_Ouminus(U_167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_167),U_168),U_169))
| ~ class_RealVector_Oreal__normed__algebra(U_167) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_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_67_2,plain,
! [U_171,U_170] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_170),U_171),c_Groups_Oone__class_Oone(U_170)) = U_171
| ~ class_Groups_Ocomm__monoid__mult(U_170) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_170),U_171),c_Groups_Oone__class_Oone(U_170)) = U_171
| ~ class_Groups_Ocomm__monoid__mult(U_170) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_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_68_2,plain,
! [U_173,U_172] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_172),U_173),c_Groups_Oone__class_Oone(U_172)) = U_173
| ~ class_Groups_Omonoid__mult(U_172) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_172),U_173),c_Groups_Oone__class_Oone(U_172)) = U_173
| ~ class_Groups_Omonoid__mult(U_172) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_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_69_2,plain,
! [U_175,U_174] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_174),c_Groups_Oone__class_Oone(U_174)),U_175) = U_175
| ~ class_Groups_Ocomm__monoid__mult(U_174) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_174),c_Groups_Oone__class_Oone(U_174)),U_175) = U_175
| ~ class_Groups_Ocomm__monoid__mult(U_174) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_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_70_2,plain,
! [U_177,U_176] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_176),c_Groups_Oone__class_Oone(U_176)),U_177) = U_177
| ~ class_Groups_Omonoid__mult(U_176) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_176),c_Groups_Oone__class_Oone(U_176)),U_177) = U_177
| ~ class_Groups_Omonoid__mult(U_176) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_aa_2
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) != V_aa_2 ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).
fof(f_71_2,plain,
! [U_179,U_178] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_178,U_179) = U_179
| U_179 != c_Groups_Ozero__class_Ozero(U_178) )
& ( U_179 = c_Groups_Ozero__class_Ozero(U_178)
| c_Groups_Ouminus__class_Ouminus(U_178,U_179) != U_179 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_178) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( U_179 = c_Groups_Ozero__class_Ozero(U_178)
| c_Groups_Ouminus__class_Ouminus(U_178,U_179) != U_179
| ~ class_Groups_Olinordered__ab__group__add(U_178) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_178,U_179) = U_179
| U_179 != c_Groups_Ozero__class_Ozero(U_178)
| ~ class_Groups_Olinordered__ab__group__add(U_178) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).
fof(f_72_2,plain,
! [U_181,U_180] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_180,U_181) = c_Groups_Ozero__class_Ozero(U_180)
| U_181 != c_Groups_Ozero__class_Ozero(U_180) )
& ( U_181 = c_Groups_Ozero__class_Ozero(U_180)
| c_Groups_Ouminus__class_Ouminus(U_180,U_181) != c_Groups_Ozero__class_Ozero(U_180) ) )
| ~ class_Groups_Ogroup__add(U_180) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( U_181 = c_Groups_Ozero__class_Ozero(U_180)
| c_Groups_Ouminus__class_Ouminus(U_180,U_181) != c_Groups_Ozero__class_Ozero(U_180)
| ~ class_Groups_Ogroup__add(U_180) ),
inference(clausify,[status(thm)],[f_72_2]) ).
cnf(f_72_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_180,U_181) = c_Groups_Ozero__class_Ozero(U_180)
| U_181 != c_Groups_Ozero__class_Ozero(U_180)
| ~ class_Groups_Ogroup__add(U_180) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_1,plain,
v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_assms_I3_J]) ).
cnf(f_73_2,plain,
v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_73_1]) ).
fof(f_74_1,plain,
! [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(fof_nnf,[status(thm)],[fact_assms_I1_J]) ).
fof(f_74_2,plain,
! [U_182] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),U_182) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_182) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q),U_182) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),U_182) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
inference(fof_nnf,[status(thm)],[fact_dpn]) ).
cnf(f_75_2,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_pa____) = v_na____,
inference(clausify,[status(thm)],[f_75_1]) ).
fof(f_76_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_76_2,plain,
! [U_184,U_183] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_183),U_184),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_184
| ~ class_Rings_Ocomm__semiring__1(U_183) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_183),U_184),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_184
| ~ class_Rings_Ocomm__semiring__1(U_183) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [V_qb_2,V_pb_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,V_qb_2)
| V_pb_2 != V_qb_2 )
& ( V_pb_2 = V_qb_2
| c_Polynomial_Opoly(T_a,V_pb_2) != c_Polynomial_Opoly(T_a,V_qb_2) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__eq__iff]) ).
fof(f_77_2,plain,
! [U_187,U_186,U_185] :
( ( ( c_Polynomial_Opoly(U_185,U_186) = c_Polynomial_Opoly(U_185,U_187)
| U_186 != U_187 )
& ( U_186 = U_187
| c_Polynomial_Opoly(U_185,U_186) != c_Polynomial_Opoly(U_185,U_187) ) )
| ~ class_Rings_Oidom(U_185)
| ~ class_Int_Oring__char__0(U_185) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( U_186 = U_187
| c_Polynomial_Opoly(U_185,U_186) != c_Polynomial_Opoly(U_185,U_187)
| ~ class_Rings_Oidom(U_185)
| ~ class_Int_Oring__char__0(U_185) ),
inference(clausify,[status(thm)],[f_77_2]) ).
cnf(f_77_4,plain,
( c_Polynomial_Opoly(U_185,U_186) = c_Polynomial_Opoly(U_185,U_187)
| U_186 != U_187
| ~ class_Rings_Oidom(U_185)
| ~ class_Int_Oring__char__0(U_185) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_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_78_2,plain,
! [U_191,U_190,U_189,U_188] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_188),hAPP(hAPP(c_Power_Opower__class_Opower(U_188),U_189),U_190)),U_191) = hAPP(hAPP(c_Power_Opower__class_Opower(U_188),U_189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_190),U_191))
| ~ class_Rings_Ocomm__semiring__1(U_188) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_188),hAPP(hAPP(c_Power_Opower__class_Opower(U_188),U_189),U_190)),U_191) = hAPP(hAPP(c_Power_Opower__class_Opower(U_188),U_189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_190),U_191))
| ~ class_Rings_Ocomm__semiring__1(U_188) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
! [V_x,V_n,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__power]) ).
fof(f_79_2,plain,
! [U_195,U_194,U_193,U_192] :
( hAPP(c_Polynomial_Opoly(U_192,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_192)),U_193),U_194)),U_195) = hAPP(hAPP(c_Power_Opower__class_Opower(U_192),hAPP(c_Polynomial_Opoly(U_192,U_193),U_195)),U_194)
| ~ class_Rings_Ocomm__semiring__1(U_192) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( hAPP(c_Polynomial_Opoly(U_192,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_192)),U_193),U_194)),U_195) = hAPP(hAPP(c_Power_Opower__class_Opower(U_192),hAPP(c_Polynomial_Opoly(U_192,U_193),U_195)),U_194)
| ~ class_Rings_Ocomm__semiring__1(U_192) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_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_80_2,plain,
! [U_199,U_198,U_197,U_196] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_196),U_197),U_198)),U_199) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_196),hAPP(hAPP(c_Power_Opower__class_Opower(U_196),U_197),U_199)),hAPP(hAPP(c_Power_Opower__class_Opower(U_196),U_198),U_199))
| ~ class_Rings_Ocomm__semiring__1(U_196) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_196),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_196),U_197),U_198)),U_199) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_196),hAPP(hAPP(c_Power_Opower__class_Opower(U_196),U_197),U_199)),hAPP(hAPP(c_Power_Opower__class_Opower(U_196),U_198),U_199))
| ~ class_Rings_Ocomm__semiring__1(U_196) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_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_81_2,plain,
! [U_201,U_200] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_200),U_201),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_200)
| ~ class_Rings_Ocomm__semiring__1(U_200) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_200),U_201),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_200)
| ~ class_Rings_Ocomm__semiring__1(U_200) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_1,plain,
! [V_pb_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pb_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Opoly(T_a,V_pb_2) != c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__zero]) ).
fof(f_82_2,plain,
! [U_203,U_202] :
( ( ( c_Polynomial_Opoly(U_202,U_203) = c_Polynomial_Opoly(U_202,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202)))
| U_203 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202)) )
& ( U_203 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202))
| c_Polynomial_Opoly(U_202,U_203) != c_Polynomial_Opoly(U_202,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202))) ) )
| ~ class_Rings_Oidom(U_202)
| ~ class_Int_Oring__char__0(U_202) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( U_203 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202))
| c_Polynomial_Opoly(U_202,U_203) != c_Polynomial_Opoly(U_202,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202)))
| ~ class_Rings_Oidom(U_202)
| ~ class_Int_Oring__char__0(U_202) ),
inference(clausify,[status(thm)],[f_82_2]) ).
cnf(f_82_4,plain,
( c_Polynomial_Opoly(U_202,U_203) = c_Polynomial_Opoly(U_202,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202)))
| U_203 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_202))
| ~ class_Rings_Oidom(U_202)
| ~ class_Int_Oring__char__0(U_202) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [V_aa_2,V_pb_2,T_a] :
( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
| ( c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
& ( c_Polynomial_Oorder(T_a,V_aa_2,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_aa_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__root]) ).
fof(f_83_2,plain,
! [U_206,U_205,U_204] :
( ( ( hAPP(c_Polynomial_Opoly(U_204,U_205),U_206) = c_Groups_Ozero__class_Ozero(U_204)
| ( c_Polynomial_Oorder(U_204,U_206,U_205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_205 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_204)) ) )
& ( c_Polynomial_Oorder(U_204,U_206,U_205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_205 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_204))
| hAPP(c_Polynomial_Opoly(U_204,U_205),U_206) != c_Groups_Ozero__class_Ozero(U_204) ) )
| ~ class_Rings_Oidom(U_204) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( c_Polynomial_Oorder(U_204,U_206,U_205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_205 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_204))
| hAPP(c_Polynomial_Opoly(U_204,U_205),U_206) != c_Groups_Ozero__class_Ozero(U_204)
| ~ class_Rings_Oidom(U_204) ),
inference(clausify,[status(thm)],[f_83_2]) ).
cnf(f_83_4,plain,
( U_205 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_204))
| hAPP(c_Polynomial_Opoly(U_204,U_205),U_206) = c_Groups_Ozero__class_Ozero(U_204)
| ~ class_Rings_Oidom(U_204) ),
inference(clausify,[status(thm)],[f_83_2]) ).
cnf(f_83_5,plain,
( c_Polynomial_Oorder(U_204,U_206,U_205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(U_204,U_205),U_206) = c_Groups_Ozero__class_Ozero(U_204)
| ~ class_Rings_Oidom(U_204) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__0]) ).
fof(f_84_2,plain,
! [U_208,U_207] :
( hAPP(c_Polynomial_Opoly(U_207,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_207))),U_208) = c_Groups_Ozero__class_Ozero(U_207)
| ~ class_Rings_Ocomm__semiring__0(U_207) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( hAPP(c_Polynomial_Opoly(U_207,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_207))),U_208) = c_Groups_Ozero__class_Ozero(U_207)
| ~ class_Rings_Ocomm__semiring__0(U_207) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__mult]) ).
fof(f_85_2,plain,
! [U_212,U_211,U_210,U_209] :
( hAPP(c_Polynomial_Opoly(U_209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_209)),U_210),U_211)),U_212) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),hAPP(c_Polynomial_Opoly(U_209,U_210),U_212)),hAPP(c_Polynomial_Opoly(U_209,U_211),U_212))
| ~ class_Rings_Ocomm__semiring__0(U_209) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( hAPP(c_Polynomial_Opoly(U_209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_209)),U_210),U_211)),U_212) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_209),hAPP(c_Polynomial_Opoly(U_209,U_210),U_212)),hAPP(c_Polynomial_Opoly(U_209,U_211),U_212))
| ~ class_Rings_Ocomm__semiring__0(U_209) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [V_x,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__minus]) ).
fof(f_86_2,plain,
! [U_215,U_214,U_213] :
( hAPP(c_Polynomial_Opoly(U_213,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_213),U_214)),U_215) = c_Groups_Ouminus__class_Ouminus(U_213,hAPP(c_Polynomial_Opoly(U_213,U_214),U_215))
| ~ class_Rings_Ocomm__ring(U_213) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( hAPP(c_Polynomial_Opoly(U_213,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_213),U_214)),U_215) = c_Groups_Ouminus__class_Ouminus(U_213,hAPP(c_Polynomial_Opoly(U_213,U_214),U_215))
| ~ class_Rings_Ocomm__ring(U_213) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__1]) ).
fof(f_87_2,plain,
! [U_217,U_216] :
( hAPP(c_Polynomial_Opoly(U_216,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_216))),U_217) = c_Groups_Oone__class_Oone(U_216)
| ~ class_Rings_Ocomm__semiring__1(U_216) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( hAPP(c_Polynomial_Opoly(U_216,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_216))),U_217) = c_Groups_Oone__class_Oone(U_216)
| ~ class_Rings_Ocomm__semiring__1(U_216) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_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_88_2,plain,
! [U_219,U_218] :
( ( ( c_Groups_Ozero__class_Ozero(U_218) = U_219
| U_219 != c_Groups_Ozero__class_Ozero(U_218) )
& ( U_219 = c_Groups_Ozero__class_Ozero(U_218)
| c_Groups_Ozero__class_Ozero(U_218) != U_219 ) )
| ~ class_Groups_Ozero(U_218) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( U_219 = c_Groups_Ozero__class_Ozero(U_218)
| c_Groups_Ozero__class_Ozero(U_218) != U_219
| ~ class_Groups_Ozero(U_218) ),
inference(clausify,[status(thm)],[f_88_2]) ).
cnf(f_88_4,plain,
( c_Groups_Ozero__class_Ozero(U_218) = U_219
| U_219 != c_Groups_Ozero__class_Ozero(U_218)
| ~ class_Groups_Ozero(U_218) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_223,U_222,U_221,U_220] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),U_221),U_222)),U_223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),U_221),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),U_222),U_223))
| ~ class_Groups_Oab__semigroup__mult(U_220) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),U_221),U_222)),U_223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),U_221),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_220),U_222),U_223))
| ~ class_Groups_Oab__semigroup__mult(U_220) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_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_90_2,plain,
! [U_225,U_224] :
( ( ( c_Groups_Oone__class_Oone(U_224) = U_225
| U_225 != c_Groups_Oone__class_Oone(U_224) )
& ( U_225 = c_Groups_Oone__class_Oone(U_224)
| c_Groups_Oone__class_Oone(U_224) != U_225 ) )
| ~ class_Groups_Oone(U_224) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( U_225 = c_Groups_Oone__class_Oone(U_224)
| c_Groups_Oone__class_Oone(U_224) != U_225
| ~ class_Groups_Oone(U_224) ),
inference(clausify,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( c_Groups_Oone__class_Oone(U_224) = U_225
| U_225 != c_Groups_Oone__class_Oone(U_224)
| ~ class_Groups_Oone(U_224) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
! [V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__minus]) ).
fof(f_91_2,plain,
! [U_227,U_226] :
( c_Groups_Ouminus__class_Ouminus(U_226,c_Groups_Ouminus__class_Ouminus(U_226,U_227)) = U_227
| ~ class_Groups_Ogroup__add(U_226) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_226,c_Groups_Ouminus__class_Ouminus(U_226,U_227)) = U_227
| ~ class_Groups_Ogroup__add(U_226) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_b_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) )
& ( V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
| V_aa_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).
fof(f_92_2,plain,
! [U_230,U_229,U_228] :
( ( ( U_229 = c_Groups_Ouminus__class_Ouminus(U_228,U_230)
| U_230 != c_Groups_Ouminus__class_Ouminus(U_228,U_229) )
& ( U_230 = c_Groups_Ouminus__class_Ouminus(U_228,U_229)
| U_229 != c_Groups_Ouminus__class_Ouminus(U_228,U_230) ) )
| ~ class_Groups_Ogroup__add(U_228) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( U_230 = c_Groups_Ouminus__class_Ouminus(U_228,U_229)
| U_229 != c_Groups_Ouminus__class_Ouminus(U_228,U_230)
| ~ class_Groups_Ogroup__add(U_228) ),
inference(clausify,[status(thm)],[f_92_2]) ).
cnf(f_92_4,plain,
( U_229 = c_Groups_Ouminus__class_Ouminus(U_228,U_230)
| U_230 != c_Groups_Ouminus__class_Ouminus(U_228,U_229)
| ~ class_Groups_Ogroup__add(U_228) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) != V_aa_2 )
& ( c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_aa_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) != V_b_2 ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).
fof(f_93_2,plain,
! [U_233,U_232,U_231] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_231,U_232) = U_233
| c_Groups_Ouminus__class_Ouminus(U_231,U_233) != U_232 )
& ( c_Groups_Ouminus__class_Ouminus(U_231,U_233) = U_232
| c_Groups_Ouminus__class_Ouminus(U_231,U_232) != U_233 ) )
| ~ class_Groups_Ogroup__add(U_231) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_231,U_233) = U_232
| c_Groups_Ouminus__class_Ouminus(U_231,U_232) != U_233
| ~ class_Groups_Ogroup__add(U_231) ),
inference(clausify,[status(thm)],[f_93_2]) ).
cnf(f_93_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_231,U_232) = U_233
| c_Groups_Ouminus__class_Ouminus(U_231,U_233) != U_232
| ~ class_Groups_Ogroup__add(U_231) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_aa_2 != V_b_2 )
& ( V_aa_2 = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).
fof(f_94_2,plain,
! [U_236,U_235,U_234] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_234,U_235) = c_Groups_Ouminus__class_Ouminus(U_234,U_236)
| U_235 != U_236 )
& ( U_235 = U_236
| c_Groups_Ouminus__class_Ouminus(U_234,U_235) != c_Groups_Ouminus__class_Ouminus(U_234,U_236) ) )
| ~ class_Groups_Ogroup__add(U_234) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( U_235 = U_236
| c_Groups_Ouminus__class_Ouminus(U_234,U_235) != c_Groups_Ouminus__class_Ouminus(U_234,U_236)
| ~ class_Groups_Ogroup__add(U_234) ),
inference(clausify,[status(thm)],[f_94_2]) ).
cnf(f_94_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_234,U_235) = c_Groups_Ouminus__class_Ouminus(U_234,U_236)
| U_235 != U_236
| ~ class_Groups_Ogroup__add(U_234) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [V_p,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__1]) ).
fof(f_95_2,plain,
! [U_239,U_238,U_237] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_237)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_237)),c_Polynomial_OpCons(U_237,c_Groups_Ouminus__class_Ouminus(U_237,U_238),c_Polynomial_OpCons(U_237,c_Groups_Oone__class_Oone(U_237),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))))),c_Polynomial_Oorder(U_237,U_238,U_239))),U_239))
| ~ class_Rings_Oidom(U_237) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_237)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_237)),c_Polynomial_OpCons(U_237,c_Groups_Ouminus__class_Ouminus(U_237,U_238),c_Polynomial_OpCons(U_237,c_Groups_Oone__class_Oone(U_237),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))))),c_Polynomial_Oorder(U_237,U_238,U_239))),U_239))
| ~ class_Rings_Oidom(U_237) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_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_96_2,plain,
! [U_241,U_240] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_240),c_Groups_Ozero__class_Ozero(U_240)),U_241) = c_Groups_Ozero__class_Ozero(U_240)
| ~ class_RealVector_Oreal__normed__algebra(U_240) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_240),c_Groups_Ozero__class_Ozero(U_240)),U_241) = c_Groups_Ozero__class_Ozero(U_240)
| ~ class_RealVector_Oreal__normed__algebra(U_240) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_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_97_2,plain,
! [U_243,U_242] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_242),c_Groups_Ozero__class_Ozero(U_242)),U_243) = c_Groups_Ozero__class_Ozero(U_242)
| ~ class_RealVector_Oreal__normed__algebra(U_242) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_242),c_Groups_Ozero__class_Ozero(U_242)),U_243) = c_Groups_Ozero__class_Ozero(U_242)
| ~ class_RealVector_Oreal__normed__algebra(U_242) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_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_98_2,plain,
! [U_245,U_244] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_244),U_245),c_Groups_Ozero__class_Ozero(U_244)) = c_Groups_Ozero__class_Ozero(U_244)
| ~ class_RealVector_Oreal__normed__algebra(U_244) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_244),U_245),c_Groups_Ozero__class_Ozero(U_244)) = c_Groups_Ozero__class_Ozero(U_244)
| ~ class_RealVector_Oreal__normed__algebra(U_244) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_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_99_2,plain,
! [U_247,U_246] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_246),U_247),c_Groups_Ozero__class_Ozero(U_246)) = c_Groups_Ozero__class_Ozero(U_246)
| ~ class_RealVector_Oreal__normed__algebra(U_246) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_246),U_247),c_Groups_Ozero__class_Ozero(U_246)) = c_Groups_Ozero__class_Ozero(U_246)
| ~ class_RealVector_Oreal__normed__algebra(U_246) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [V_c_2,V_pb_2,T_a] :
( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_c_2) = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2))
| hAPP(c_Polynomial_Opoly(T_a,V_pb_2),V_c_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__eq__0__iff__dvd]) ).
fof(f_100_2,plain,
! [U_250,U_249,U_248] :
( ( ( hAPP(c_Polynomial_Opoly(U_248,U_249),U_250) = c_Groups_Ozero__class_Ozero(U_248)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_248)),c_Polynomial_OpCons(U_248,c_Groups_Ouminus__class_Ouminus(U_248,U_250),c_Polynomial_OpCons(U_248,c_Groups_Oone__class_Oone(U_248),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_248))))),U_249)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_248)),c_Polynomial_OpCons(U_248,c_Groups_Ouminus__class_Ouminus(U_248,U_250),c_Polynomial_OpCons(U_248,c_Groups_Oone__class_Oone(U_248),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_248))))),U_249))
| hAPP(c_Polynomial_Opoly(U_248,U_249),U_250) != c_Groups_Ozero__class_Ozero(U_248) ) )
| ~ class_Rings_Oidom(U_248) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_248)),c_Polynomial_OpCons(U_248,c_Groups_Ouminus__class_Ouminus(U_248,U_250),c_Polynomial_OpCons(U_248,c_Groups_Oone__class_Oone(U_248),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_248))))),U_249))
| hAPP(c_Polynomial_Opoly(U_248,U_249),U_250) != c_Groups_Ozero__class_Ozero(U_248)
| ~ class_Rings_Oidom(U_248) ),
inference(clausify,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
( hAPP(c_Polynomial_Opoly(U_248,U_249),U_250) = c_Groups_Ozero__class_Ozero(U_248)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_248)),c_Polynomial_OpCons(U_248,c_Groups_Ouminus__class_Ouminus(U_248,U_250),c_Polynomial_OpCons(U_248,c_Groups_Oone__class_Oone(U_248),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_248))))),U_249))
| ~ class_Rings_Oidom(U_248) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [V_pb_2,V_c_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2))
| hAPP(c_Polynomial_Opoly(T_a,V_pb_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2)) != c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(c_Polynomial_Opoly(T_a,V_pb_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_pb_2)) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__iff__poly__eq__0]) ).
fof(f_101_2,plain,
! [U_253,U_252,U_251] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_251)),c_Polynomial_OpCons(U_251,U_252,c_Polynomial_OpCons(U_251,c_Groups_Oone__class_Oone(U_251),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_251))))),U_253))
| hAPP(c_Polynomial_Opoly(U_251,U_253),c_Groups_Ouminus__class_Ouminus(U_251,U_252)) != c_Groups_Ozero__class_Ozero(U_251) )
& ( hAPP(c_Polynomial_Opoly(U_251,U_253),c_Groups_Ouminus__class_Ouminus(U_251,U_252)) = c_Groups_Ozero__class_Ozero(U_251)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_251)),c_Polynomial_OpCons(U_251,U_252,c_Polynomial_OpCons(U_251,c_Groups_Oone__class_Oone(U_251),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_251))))),U_253)) ) )
| ~ class_Rings_Oidom(U_251) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( hAPP(c_Polynomial_Opoly(U_251,U_253),c_Groups_Ouminus__class_Ouminus(U_251,U_252)) = c_Groups_Ozero__class_Ozero(U_251)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_251)),c_Polynomial_OpCons(U_251,U_252,c_Polynomial_OpCons(U_251,c_Groups_Oone__class_Oone(U_251),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_251))))),U_253))
| ~ class_Rings_Oidom(U_251) ),
inference(clausify,[status(thm)],[f_101_2]) ).
cnf(f_101_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_251)),c_Polynomial_OpCons(U_251,U_252,c_Polynomial_OpCons(U_251,c_Groups_Oone__class_Oone(U_251),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_251))))),U_253))
| hAPP(c_Polynomial_Opoly(U_251,U_253),c_Groups_Ouminus__class_Ouminus(U_251,U_252)) != c_Groups_Ozero__class_Ozero(U_251)
| ~ class_Rings_Oidom(U_251) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__zero]) ).
fof(f_102_2,plain,
! [U_254] :
( c_Groups_Ouminus__class_Ouminus(U_254,c_Groups_Ozero__class_Ozero(U_254)) = c_Groups_Ozero__class_Ozero(U_254)
| ~ class_Groups_Ogroup__add(U_254) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_254,c_Groups_Ozero__class_Ozero(U_254)) = c_Groups_Ozero__class_Ozero(U_254)
| ~ class_Groups_Ogroup__add(U_254) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
| c_Groups_Ozero__class_Ozero(T_a) != V_aa_2 )
& ( c_Groups_Ozero__class_Ozero(T_a) = V_aa_2
| c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).
fof(f_103_2,plain,
! [U_256,U_255] :
( ( ( c_Groups_Ozero__class_Ozero(U_255) = c_Groups_Ouminus__class_Ouminus(U_255,U_256)
| c_Groups_Ozero__class_Ozero(U_255) != U_256 )
& ( c_Groups_Ozero__class_Ozero(U_255) = U_256
| c_Groups_Ozero__class_Ozero(U_255) != c_Groups_Ouminus__class_Ouminus(U_255,U_256) ) )
| ~ class_Groups_Ogroup__add(U_255) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( c_Groups_Ozero__class_Ozero(U_255) = U_256
| c_Groups_Ozero__class_Ozero(U_255) != c_Groups_Ouminus__class_Ouminus(U_255,U_256)
| ~ class_Groups_Ogroup__add(U_255) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_4,plain,
( c_Groups_Ozero__class_Ozero(U_255) = c_Groups_Ouminus__class_Ouminus(U_255,U_256)
| c_Groups_Ozero__class_Ozero(U_255) != U_256
| ~ class_Groups_Ogroup__add(U_255) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [V_aa_2,T_a] :
( ( ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).
fof(f_104_2,plain,
! [U_258,U_257] :
( ( ( U_258 = c_Groups_Ouminus__class_Ouminus(U_257,U_258)
| U_258 != c_Groups_Ozero__class_Ozero(U_257) )
& ( U_258 = c_Groups_Ozero__class_Ozero(U_257)
| U_258 != c_Groups_Ouminus__class_Ouminus(U_257,U_258) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_257) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( U_258 = c_Groups_Ozero__class_Ozero(U_257)
| U_258 != c_Groups_Ouminus__class_Ouminus(U_257,U_258)
| ~ class_Groups_Olinordered__ab__group__add(U_257) ),
inference(clausify,[status(thm)],[f_104_2]) ).
cnf(f_104_4,plain,
( U_258 = c_Groups_Ouminus__class_Ouminus(U_257,U_258)
| U_258 != c_Groups_Ozero__class_Ozero(U_257)
| ~ class_Groups_Olinordered__ab__group__add(U_257) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____)),
inference(fof_nnf,[status(thm)],[fact_ap_I2_J]) ).
cnf(f_105_2,plain,
~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex,v_a____,v_pa____)))),v_pa____)),
inference(clausify,[status(thm)],[f_105_1]) ).
fof(f_106_1,plain,
! [V_a] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,V_a,v_pa____),v_na____),
inference(fof_nnf,[status(thm)],[fact_oop]) ).
fof(f_106_2,plain,
! [U_259] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,U_259,v_pa____),v_na____),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(tc_Complex_Ocomplex,U_259,v_pa____),v_na____),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__minus]) ).
fof(f_107_2,plain,
! [U_262,U_261,U_260] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_260),c_Groups_Ouminus__class_Ouminus(U_260,U_261)),U_262) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_260),hAPP(hAPP(c_Power_Opower__class_Opower(U_260),c_Groups_Ouminus__class_Ouminus(U_260,c_Groups_Oone__class_Oone(U_260))),U_262)),hAPP(hAPP(c_Power_Opower__class_Opower(U_260),U_261),U_262))
| ~ class_Rings_Oring__1(U_260) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_260),c_Groups_Ouminus__class_Ouminus(U_260,U_261)),U_262) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_260),hAPP(hAPP(c_Power_Opower__class_Opower(U_260),c_Groups_Ouminus__class_Ouminus(U_260,c_Groups_Oone__class_Oone(U_260))),U_262)),hAPP(hAPP(c_Power_Opower__class_Opower(U_260),U_261),U_262))
| ~ class_Rings_Oring__1(U_260) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_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_108_2,plain,
! [U_264,U_263] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_263),c_Groups_Ozero__class_Ozero(U_263)),U_264) = c_Groups_Ozero__class_Ozero(U_263)
| U_264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_263),c_Groups_Ozero__class_Ozero(U_263)),U_264) = c_Groups_Oone__class_Oone(U_263)
| U_264 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_263)
| ~ class_Power_Opower(U_263) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_263),c_Groups_Ozero__class_Ozero(U_263)),U_264) = c_Groups_Oone__class_Oone(U_263)
| U_264 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_263)
| ~ class_Power_Opower(U_263) ),
inference(clausify,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_263),c_Groups_Ozero__class_Ozero(U_263)),U_264) = c_Groups_Ozero__class_Ozero(U_263)
| U_264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_263)
| ~ class_Power_Opower(U_263) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_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_109_2,plain,
! [U_266,U_265] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_265),U_266),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_265)
| ~ class_Power_Opower(U_265) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_265),U_266),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_265)
| ~ class_Power_Opower(U_265) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [V_nb_2,V_aa_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_nb_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_aa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_nb_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_110_2,plain,
! [U_269,U_268,U_267] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_267),U_268),U_269) = c_Groups_Ozero__class_Ozero(U_267)
| U_269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_268 != c_Groups_Ozero__class_Ozero(U_267) )
& ( ( U_269 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_268 = c_Groups_Ozero__class_Ozero(U_267) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_267),U_268),U_269) != c_Groups_Ozero__class_Ozero(U_267) ) )
| ~ class_Rings_Ozero__neq__one(U_267)
| ~ class_Rings_Ono__zero__divisors(U_267)
| ~ class_Rings_Omult__zero(U_267)
| ~ class_Power_Opower(U_267) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( U_268 = c_Groups_Ozero__class_Ozero(U_267)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_267),U_268),U_269) != c_Groups_Ozero__class_Ozero(U_267)
| ~ class_Rings_Ozero__neq__one(U_267)
| ~ class_Rings_Ono__zero__divisors(U_267)
| ~ class_Rings_Omult__zero(U_267)
| ~ class_Power_Opower(U_267) ),
inference(clausify,[status(thm)],[f_110_2]) ).
cnf(f_110_4,plain,
( U_269 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_267),U_268),U_269) != c_Groups_Ozero__class_Ozero(U_267)
| ~ class_Rings_Ozero__neq__one(U_267)
| ~ class_Rings_Ono__zero__divisors(U_267)
| ~ class_Rings_Omult__zero(U_267)
| ~ class_Power_Opower(U_267) ),
inference(clausify,[status(thm)],[f_110_2]) ).
cnf(f_110_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_267),U_268),U_269) = c_Groups_Ozero__class_Ozero(U_267)
| U_269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_268 != c_Groups_Ozero__class_Ozero(U_267)
| ~ class_Rings_Ozero__neq__one(U_267)
| ~ class_Rings_Ono__zero__divisors(U_267)
| ~ class_Rings_Omult__zero(U_267)
| ~ class_Power_Opower(U_267) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
! [V_a,V_p,T_a] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p))
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__2]) ).
fof(f_111_2,plain,
! [U_272,U_271,U_270] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_270)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_270)),c_Polynomial_OpCons(U_270,c_Groups_Ouminus__class_Ouminus(U_270,U_272),c_Polynomial_OpCons(U_270,c_Groups_Oone__class_Oone(U_270),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_270))))),c_Nat_OSuc(c_Polynomial_Oorder(U_270,U_272,U_271)))),U_271))
| U_271 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_270))
| ~ class_Rings_Oidom(U_270) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_270)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_270)),c_Polynomial_OpCons(U_270,c_Groups_Ouminus__class_Ouminus(U_270,U_272),c_Polynomial_OpCons(U_270,c_Groups_Oone__class_Oone(U_270),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_270))))),c_Nat_OSuc(c_Polynomial_Oorder(U_270,U_272,U_271)))),U_271))
| U_271 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_270))
| ~ class_Rings_Oidom(U_270) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [V_a,V_p,T_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p)))),V_p))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)) )
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order]) ).
fof(f_112_2,plain,
! [U_275,U_274,U_273] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_273)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_273)),c_Polynomial_OpCons(U_273,c_Groups_Ouminus__class_Ouminus(U_273,U_275),c_Polynomial_OpCons(U_273,c_Groups_Oone__class_Oone(U_273),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_273))))),c_Nat_OSuc(c_Polynomial_Oorder(U_273,U_275,U_274)))),U_274))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_273)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_273)),c_Polynomial_OpCons(U_273,c_Groups_Ouminus__class_Ouminus(U_273,U_275),c_Polynomial_OpCons(U_273,c_Groups_Oone__class_Oone(U_273),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_273))))),c_Polynomial_Oorder(U_273,U_275,U_274))),U_274)) )
| U_274 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_273))
| ~ class_Rings_Oidom(U_273) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_273)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_273)),c_Polynomial_OpCons(U_273,c_Groups_Ouminus__class_Ouminus(U_273,U_275),c_Polynomial_OpCons(U_273,c_Groups_Oone__class_Oone(U_273),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_273))))),c_Polynomial_Oorder(U_273,U_275,U_274))),U_274))
| U_274 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_273))
| ~ class_Rings_Oidom(U_273) ),
inference(clausify,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_273)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_273)),c_Polynomial_OpCons(U_273,c_Groups_Ouminus__class_Ouminus(U_273,U_275),c_Polynomial_OpCons(U_273,c_Groups_Oone__class_Oone(U_273),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_273))))),c_Nat_OSuc(c_Polynomial_Oorder(U_273,U_275,U_274)))),U_274))
| U_274 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_273))
| ~ class_Rings_Oidom(U_273) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [V_n,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power__same]) ).
fof(f_113_2,plain,
! [U_279,U_278,U_277,U_276] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_276),hAPP(hAPP(c_Power_Opower__class_Opower(U_276),U_277),U_279)),hAPP(hAPP(c_Power_Opower__class_Opower(U_276),U_278),U_279)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_276),U_277),U_278))
| ~ class_Rings_Ocomm__semiring__1(U_276) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_276),hAPP(hAPP(c_Power_Opower__class_Opower(U_276),U_277),U_279)),hAPP(hAPP(c_Power_Opower__class_Opower(U_276),U_278),U_279)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_276),U_277),U_278))
| ~ class_Rings_Ocomm__semiring__1(U_276) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_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_114_2,plain,
! [U_281,U_280] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_280),c_Groups_Oone__class_Oone(U_280)),U_281) = c_Groups_Oone__class_Oone(U_280)
| ~ class_Groups_Omonoid__mult(U_280) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_280),c_Groups_Oone__class_Oone(U_280)),U_281) = c_Groups_Oone__class_Oone(U_280)
| ~ class_Groups_Omonoid__mult(U_280) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = v_n,
inference(fof_nnf,[status(thm)],[fact_assms_I2_J]) ).
cnf(f_115_2,plain,
c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) = v_n,
inference(clausify,[status(thm)],[f_115_1]) ).
fof(f_116_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_116_2,plain,
! [U_282] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_282) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_282) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_284,U_283] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_283),U_284) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_283 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_284 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_283 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_283),U_284) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_288,U_286] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_286),U_288) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_286 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_288 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_287,U_285] :
( U_285 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_287 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_285),U_287) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
cnf(f_117_4,plain,
( U_285 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_287 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_285),U_287) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_5,plain,
( U_288 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_286),U_288) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_6,plain,
( U_286 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_286),U_288) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__one__le__power]) ).
fof(f_118_2,plain,
! [U_290,U_289] :
( 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_289),U_290))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_289) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_289),U_290))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_289) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_1,plain,
! [V_p,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__pCons__le]) ).
fof(f_119_2,plain,
! [U_293,U_292,U_291] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_291,c_Polynomial_OpCons(U_291,U_292,U_293)),c_Nat_OSuc(c_Polynomial_Odegree(U_291,U_293)))
| ~ class_Groups_Ozero(U_291) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
cnf(f_119_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_291,c_Polynomial_OpCons(U_291,U_292,U_293)),c_Nat_OSuc(c_Polynomial_Odegree(U_291,U_293)))
| ~ class_Groups_Ozero(U_291) ),
inference(clausify,[status(thm)],[f_119_2]) ).
fof(f_120_1,plain,
! [V_n,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),V_n))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__power__le]) ).
fof(f_120_2,plain,
! [U_296,U_295,U_294] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_294,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_294)),U_295),U_296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(U_294,U_295)),U_296))
| ~ class_Rings_Ocomm__semiring__1(U_294) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
cnf(f_120_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_294,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_294)),U_295),U_296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(U_294,U_295)),U_296))
| ~ class_Rings_Ocomm__semiring__1(U_294) ),
inference(clausify,[status(thm)],[f_120_2]) ).
fof(f_121_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__base]) ).
fof(f_121_2,plain,
! [U_300,U_299,U_298,U_297] :
( U_298 = U_300
| ~ c_Orderings_Oord__class_Oless__eq(U_297,c_Groups_Ozero__class_Ozero(U_297),U_300)
| ~ c_Orderings_Oord__class_Oless__eq(U_297,c_Groups_Ozero__class_Ozero(U_297),U_298)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_297),U_298),c_Nat_OSuc(U_299)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_297),U_300),c_Nat_OSuc(U_299))
| ~ class_Rings_Olinordered__semidom(U_297) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( U_298 = U_300
| ~ c_Orderings_Oord__class_Oless__eq(U_297,c_Groups_Ozero__class_Ozero(U_297),U_300)
| ~ c_Orderings_Oord__class_Oless__eq(U_297,c_Groups_Ozero__class_Ozero(U_297),U_298)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_297),U_298),c_Nat_OSuc(U_299)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_297),U_300),c_Nat_OSuc(U_299))
| ~ class_Rings_Olinordered__semidom(U_297) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base]) ).
fof(f_122_2,plain,
! [U_304,U_303,U_302,U_301] :
( c_Orderings_Oord__class_Oless__eq(U_301,U_302,U_304)
| ~ c_Orderings_Oord__class_Oless__eq(U_301,c_Groups_Ozero__class_Ozero(U_301),U_304)
| ~ c_Orderings_Oord__class_Oless__eq(U_301,hAPP(hAPP(c_Power_Opower__class_Opower(U_301),U_302),c_Nat_OSuc(U_303)),hAPP(hAPP(c_Power_Opower__class_Opower(U_301),U_304),c_Nat_OSuc(U_303)))
| ~ class_Rings_Olinordered__semidom(U_301) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_301,U_302,U_304)
| ~ c_Orderings_Oord__class_Oless__eq(U_301,c_Groups_Ozero__class_Ozero(U_301),U_304)
| ~ c_Orderings_Oord__class_Oless__eq(U_301,hAPP(hAPP(c_Power_Opower__class_Opower(U_301),U_302),c_Nat_OSuc(U_303)),hAPP(hAPP(c_Power_Opower__class_Opower(U_301),U_304),c_Nat_OSuc(U_303)))
| ~ class_Rings_Olinordered__semidom(U_301) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).
fof(f_123_2,plain,
! [U_308,U_307,U_306,U_305] :
( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(hAPP(c_Power_Opower__class_Opower(U_305),U_308),U_306),hAPP(hAPP(c_Power_Opower__class_Opower(U_305),U_308),U_307))
| ~ c_Orderings_Oord__class_Oless__eq(U_305,c_Groups_Oone__class_Oone(U_305),U_308)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_306,U_307)
| ~ class_Rings_Olinordered__semidom(U_305) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_305,hAPP(hAPP(c_Power_Opower__class_Opower(U_305),U_308),U_306),hAPP(hAPP(c_Power_Opower__class_Opower(U_305),U_308),U_307))
| ~ c_Orderings_Oord__class_Oless__eq(U_305,c_Groups_Oone__class_Oone(U_305),U_308)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_306,U_307)
| ~ class_Rings_Olinordered__semidom(U_305) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [V_a,V_p,T_a] :
( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__pCons__eq]) ).
fof(f_124_2,plain,
! [U_311,U_310,U_309] :
( c_Polynomial_Odegree(U_309,c_Polynomial_OpCons(U_309,U_311,U_310)) = c_Nat_OSuc(c_Polynomial_Odegree(U_309,U_310))
| U_310 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_309))
| ~ class_Groups_Ozero(U_309) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( c_Polynomial_Odegree(U_309,c_Polynomial_OpCons(U_309,U_311,U_310)) = c_Nat_OSuc(c_Polynomial_Odegree(U_309,U_310))
| U_310 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_309))
| ~ class_Groups_Ozero(U_309) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [V_q,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))
| V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__imp__degree__le]) ).
fof(f_125_2,plain,
! [U_314,U_313,U_312] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_312,U_313),c_Polynomial_Odegree(U_312,U_314))
| U_314 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_312))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_312)),U_313),U_314))
| ~ class_Rings_Oidom(U_312) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_312,U_313),c_Polynomial_Odegree(U_312,U_314))
| U_314 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_312))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_312)),U_313),U_314))
| ~ class_Rings_Oidom(U_312) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).
fof(f_126_2,plain,
! [U_318,U_317,U_316,U_315] :
( c_Orderings_Oord__class_Oless__eq(U_315,hAPP(hAPP(c_Power_Opower__class_Opower(U_315),U_318),U_317),hAPP(hAPP(c_Power_Opower__class_Opower(U_315),U_318),U_316))
| ~ c_Orderings_Oord__class_Oless__eq(U_315,U_318,c_Groups_Oone__class_Oone(U_315))
| ~ c_Orderings_Oord__class_Oless__eq(U_315,c_Groups_Ozero__class_Ozero(U_315),U_318)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_316,U_317)
| ~ class_Rings_Olinordered__semidom(U_315) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_315,hAPP(hAPP(c_Power_Opower__class_Opower(U_315),U_318),U_317),hAPP(hAPP(c_Power_Opower__class_Opower(U_315),U_318),U_316))
| ~ c_Orderings_Oord__class_Oless__eq(U_315,U_318,c_Groups_Oone__class_Oone(U_315))
| ~ c_Orderings_Oord__class_Oless__eq(U_315,c_Groups_Ozero__class_Ozero(U_315),U_318)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_316,U_317)
| ~ class_Rings_Olinordered__semidom(U_315) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [V_a,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(T_a,V_a,V_p),c_Polynomial_Odegree(T_a,V_p))
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__degree]) ).
fof(f_127_2,plain,
! [U_321,U_320,U_319] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(U_319,U_321,U_320),c_Polynomial_Odegree(U_319,U_320))
| U_320 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_319))
| ~ class_Rings_Oidom(U_319) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Oorder(U_319,U_321,U_320),c_Polynomial_Odegree(U_319,U_320))
| U_320 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_319))
| ~ class_Rings_Oidom(U_319) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).
fof(f_128_2,plain,
! [U_324,U_323,U_322] :
( c_Orderings_Oord__class_Oless__eq(U_322,c_Groups_Ouminus__class_Ouminus(U_322,U_324),c_Groups_Ouminus__class_Ouminus(U_322,U_323))
| ~ c_Orderings_Oord__class_Oless__eq(U_322,U_323,U_324)
| ~ class_Groups_Oordered__ab__group__add(U_322) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_322,c_Groups_Ouminus__class_Ouminus(U_322,U_324),c_Groups_Ouminus__class_Ouminus(U_322,U_323))
| ~ c_Orderings_Oord__class_Oless__eq(U_322,U_323,U_324)
| ~ class_Groups_Oordered__ab__group__add(U_322) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [V_aa_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).
fof(f_129_2,plain,
! [U_327,U_326,U_325] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ouminus__class_Ouminus(U_325,U_326),c_Groups_Ouminus__class_Ouminus(U_325,U_327))
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_327,U_326) )
& ( c_Orderings_Oord__class_Oless__eq(U_325,U_327,U_326)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ouminus__class_Ouminus(U_325,U_326),c_Groups_Ouminus__class_Ouminus(U_325,U_327)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_325) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_325,U_327,U_326)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ouminus__class_Ouminus(U_325,U_326),c_Groups_Ouminus__class_Ouminus(U_325,U_327))
| ~ class_Groups_Oordered__ab__group__add(U_325) ),
inference(clausify,[status(thm)],[f_129_2]) ).
cnf(f_129_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ouminus__class_Ouminus(U_325,U_326),c_Groups_Ouminus__class_Ouminus(U_325,U_327))
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_327,U_326)
| ~ class_Groups_Oordered__ab__group__add(U_325) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).
fof(f_130_2,plain,
! [U_330,U_329,U_328] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_329),U_330)
| ~ c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_330),U_329) )
& ( c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_330),U_329)
| ~ c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_329),U_330) ) )
| ~ class_Groups_Oordered__ab__group__add(U_328) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_330),U_329)
| ~ c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_329),U_330)
| ~ class_Groups_Oordered__ab__group__add(U_328) ),
inference(clausify,[status(thm)],[f_130_2]) ).
cnf(f_130_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_329),U_330)
| ~ c_Orderings_Oord__class_Oless__eq(U_328,c_Groups_Ouminus__class_Ouminus(U_328,U_330),U_329)
| ~ class_Groups_Oordered__ab__group__add(U_328) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).
fof(f_131_2,plain,
! [U_333,U_332,U_331] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_331,U_332,c_Groups_Ouminus__class_Ouminus(U_331,U_333))
| ~ c_Orderings_Oord__class_Oless__eq(U_331,U_333,c_Groups_Ouminus__class_Ouminus(U_331,U_332)) )
& ( c_Orderings_Oord__class_Oless__eq(U_331,U_333,c_Groups_Ouminus__class_Ouminus(U_331,U_332))
| ~ c_Orderings_Oord__class_Oless__eq(U_331,U_332,c_Groups_Ouminus__class_Ouminus(U_331,U_333)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_331) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_331,U_333,c_Groups_Ouminus__class_Ouminus(U_331,U_332))
| ~ c_Orderings_Oord__class_Oless__eq(U_331,U_332,c_Groups_Ouminus__class_Ouminus(U_331,U_333))
| ~ class_Groups_Oordered__ab__group__add(U_331) ),
inference(clausify,[status(thm)],[f_131_2]) ).
cnf(f_131_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_331,U_332,c_Groups_Ouminus__class_Ouminus(U_331,U_333))
| ~ c_Orderings_Oord__class_Oless__eq(U_331,U_333,c_Groups_Ouminus__class_Ouminus(U_331,U_332))
| ~ class_Groups_Oordered__ab__group__add(U_331) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [V_p,T_a] :
( c_Polynomial_Odegree(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Polynomial_Odegree(T_a,V_p)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__minus]) ).
fof(f_132_2,plain,
! [U_335,U_334] :
( c_Polynomial_Odegree(U_334,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_334),U_335)) = c_Polynomial_Odegree(U_334,U_335)
| ~ class_Groups_Oab__group__add(U_334) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( c_Polynomial_Odegree(U_334,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_334),U_335)) = c_Polynomial_Odegree(U_334,U_335)
| ~ class_Groups_Oab__group__add(U_334) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_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_133_2,plain,
! [U_337,U_336] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_336),c_Groups_Ozero__class_Ozero(U_336)),c_Nat_OSuc(U_337)) = c_Groups_Ozero__class_Ozero(U_336)
| ~ class_Rings_Osemiring__0(U_336)
| ~ class_Power_Opower(U_336) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_336),c_Groups_Ozero__class_Ozero(U_336)),c_Nat_OSuc(U_337)) = c_Groups_Ozero__class_Ozero(U_336)
| ~ class_Rings_Osemiring__0(U_336)
| ~ class_Power_Opower(U_336) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_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_134_2,plain,
! [U_340,U_339,U_338] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_338),U_339),c_Nat_OSuc(U_340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_338),hAPP(hAPP(c_Power_Opower__class_Opower(U_338),U_339),U_340)),U_339)
| ~ class_Groups_Omonoid__mult(U_338) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_338),U_339),c_Nat_OSuc(U_340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_338),hAPP(hAPP(c_Power_Opower__class_Opower(U_338),U_339),U_340)),U_339)
| ~ class_Groups_Omonoid__mult(U_338) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_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_135_2,plain,
! [U_343,U_342,U_341] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_341),U_342),c_Nat_OSuc(U_343)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_341),U_342),hAPP(hAPP(c_Power_Opower__class_Opower(U_341),U_342),U_343))
| ~ class_Power_Opower(U_341) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_341),U_342),c_Nat_OSuc(U_343)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_341),U_342),hAPP(hAPP(c_Power_Opower__class_Opower(U_341),U_342),U_343))
| ~ class_Power_Opower(U_341) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mono]) ).
fof(f_136_2,plain,
! [U_347,U_346,U_345,U_344] :
( c_Orderings_Oord__class_Oless__eq(U_344,hAPP(hAPP(c_Power_Opower__class_Opower(U_344),U_345),U_347),hAPP(hAPP(c_Power_Opower__class_Opower(U_344),U_346),U_347))
| ~ c_Orderings_Oord__class_Oless__eq(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345)
| ~ c_Orderings_Oord__class_Oless__eq(U_344,U_345,U_346)
| ~ class_Rings_Olinordered__semidom(U_344) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_344,hAPP(hAPP(c_Power_Opower__class_Opower(U_344),U_345),U_347),hAPP(hAPP(c_Power_Opower__class_Opower(U_344),U_346),U_347))
| ~ c_Orderings_Oord__class_Oless__eq(U_344,c_Groups_Ozero__class_Ozero(U_344),U_345)
| ~ c_Orderings_Oord__class_Oless__eq(U_344,U_345,U_346)
| ~ class_Rings_Olinordered__semidom(U_344) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power]) ).
fof(f_137_2,plain,
! [U_350,U_349,U_348] :
( c_Orderings_Oord__class_Oless__eq(U_348,c_Groups_Ozero__class_Ozero(U_348),hAPP(hAPP(c_Power_Opower__class_Opower(U_348),U_349),U_350))
| ~ c_Orderings_Oord__class_Oless__eq(U_348,c_Groups_Ozero__class_Ozero(U_348),U_349)
| ~ class_Rings_Olinordered__semidom(U_348) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_348,c_Groups_Ozero__class_Ozero(U_348),hAPP(hAPP(c_Power_Opower__class_Opower(U_348),U_349),U_350))
| ~ c_Orderings_Oord__class_Oless__eq(U_348,c_Groups_Ozero__class_Ozero(U_348),U_349)
| ~ class_Rings_Olinordered__semidom(U_348) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__le__power]) ).
fof(f_138_2,plain,
! [U_353,U_352,U_351] :
( c_Orderings_Oord__class_Oless__eq(U_351,c_Groups_Oone__class_Oone(U_351),hAPP(hAPP(c_Power_Opower__class_Opower(U_351),U_352),U_353))
| ~ c_Orderings_Oord__class_Oless__eq(U_351,c_Groups_Oone__class_Oone(U_351),U_352)
| ~ class_Rings_Olinordered__semidom(U_351) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_351,c_Groups_Oone__class_Oone(U_351),hAPP(hAPP(c_Power_Opower__class_Opower(U_351),U_352),U_353))
| ~ c_Orderings_Oord__class_Oless__eq(U_351,c_Groups_Oone__class_Oone(U_351),U_352)
| ~ class_Rings_Olinordered__semidom(U_351) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_1,plain,
! [V_m,V_b,V_n,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__dvd]) ).
fof(f_139_2,plain,
! [U_358,U_357,U_356,U_355,U_354] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_354),hAPP(hAPP(c_Power_Opower__class_Opower(U_354),U_355),U_358)),U_357))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_358,U_356)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_354),hAPP(hAPP(c_Power_Opower__class_Opower(U_354),U_355),U_356)),U_357))
| ~ class_Rings_Ocomm__semiring__1(U_354) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_354),hAPP(hAPP(c_Power_Opower__class_Opower(U_354),U_355),U_358)),U_357))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_358,U_356)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_354),hAPP(hAPP(c_Power_Opower__class_Opower(U_354),U_355),U_356)),U_357))
| ~ class_Rings_Ocomm__semiring__1(U_354) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [V_m,V_n,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power__le]) ).
fof(f_140_2,plain,
! [U_363,U_362,U_361,U_360,U_359] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_359),hAPP(hAPP(c_Power_Opower__class_Opower(U_359),U_360),U_362)),hAPP(hAPP(c_Power_Opower__class_Opower(U_359),U_361),U_363)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_362,U_363)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_359),U_360),U_361))
| ~ class_Rings_Ocomm__semiring__1(U_359) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_359),hAPP(hAPP(c_Power_Opower__class_Opower(U_359),U_360),U_362)),hAPP(hAPP(c_Power_Opower__class_Opower(U_359),U_361),U_363)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_362,U_363)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_359),U_360),U_361))
| ~ class_Rings_Ocomm__semiring__1(U_359) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_1,plain,
! [V_a,V_n,V_m,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd]) ).
fof(f_141_2,plain,
! [U_367,U_366,U_365,U_364] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_364),hAPP(hAPP(c_Power_Opower__class_Opower(U_364),U_367),U_365)),hAPP(hAPP(c_Power_Opower__class_Opower(U_364),U_367),U_366)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_365,U_366)
| ~ class_Rings_Ocomm__semiring__1(U_364) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_364),hAPP(hAPP(c_Power_Opower__class_Opower(U_364),U_367),U_365)),hAPP(hAPP(c_Power_Opower__class_Opower(U_364),U_367),U_366)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_365,U_366)
| ~ class_Rings_Ocomm__semiring__1(U_364) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [V_a,V_p,T_a] :
( ( ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__pCons__eq__if]) ).
fof(f_142_2,plain,
! [U_370,U_369,U_368] :
( ( ( c_Polynomial_Odegree(U_368,c_Polynomial_OpCons(U_368,U_370,U_369)) = c_Nat_OSuc(c_Polynomial_Odegree(U_368,U_369))
| U_369 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_368)) )
& ( c_Polynomial_Odegree(U_368,c_Polynomial_OpCons(U_368,U_370,U_369)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_369 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_368)) ) )
| ~ class_Groups_Ozero(U_368) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( c_Polynomial_Odegree(U_368,c_Polynomial_OpCons(U_368,U_370,U_369)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_369 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_368))
| ~ class_Groups_Ozero(U_368) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( c_Polynomial_Odegree(U_368,c_Polynomial_OpCons(U_368,U_370,U_369)) = c_Nat_OSuc(c_Polynomial_Odegree(U_368,U_369))
| U_369 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_368))
| ~ class_Groups_Ozero(U_368) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [T_a] :
( c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__0]) ).
fof(f_143_2,plain,
! [U_371] :
( c_Polynomial_Odegree(U_371,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_371))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(U_371) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( c_Polynomial_Odegree(U_371,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_371))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(U_371) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le]) ).
fof(f_144_2,plain,
! [U_374,U_373,U_372] :
( c_Orderings_Oord__class_Oless__eq(U_372,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_372),U_373),U_374),c_Groups_Ozero__class_Ozero(U_372))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_374)
| ~ c_Orderings_Oord__class_Oless__eq(U_372,U_373,c_Groups_Ozero__class_Ozero(U_372)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_372,U_374,c_Groups_Ozero__class_Ozero(U_372))
| ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_373) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_372) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_372,U_374,c_Groups_Ozero__class_Ozero(U_372))
| ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_373)
| c_Orderings_Oord__class_Oless__eq(U_372,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_372),U_373),U_374),c_Groups_Ozero__class_Ozero(U_372))
| ~ class_Rings_Oordered__cancel__semiring(U_372) ),
inference(clausify,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_374)
| ~ c_Orderings_Oord__class_Oless__eq(U_372,U_373,c_Groups_Ozero__class_Ozero(U_372))
| c_Orderings_Oord__class_Oless__eq(U_372,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_372),U_373),U_374),c_Groups_Ozero__class_Ozero(U_372))
| ~ class_Rings_Oordered__cancel__semiring(U_372) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le]) ).
fof(f_145_2,plain,
! [U_377,U_376,U_375] :
( c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_375),U_376),U_377))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_375,U_377,c_Groups_Ozero__class_Ozero(U_375))
| ~ c_Orderings_Oord__class_Oless__eq(U_375,U_376,c_Groups_Ozero__class_Ozero(U_375)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_377)
| ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_376) ) )
| ~ class_Rings_Oordered__ring(U_375) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_377)
| ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_376)
| c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_375),U_376),U_377))
| ~ class_Rings_Oordered__ring(U_375) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_375,U_377,c_Groups_Ozero__class_Ozero(U_375))
| ~ c_Orderings_Oord__class_Oless__eq(U_375,U_376,c_Groups_Ozero__class_Ozero(U_375))
| c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_375),U_376),U_377))
| ~ class_Rings_Oordered__ring(U_375) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono]) ).
fof(f_146_2,plain,
! [U_382,U_381,U_380,U_379,U_378] :
( c_Orderings_Oord__class_Oless__eq(U_378,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_378),U_379),U_381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_378),U_380),U_382))
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_381)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_380)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,U_381,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,U_379,U_380)
| ~ class_Rings_Oordered__semiring(U_378) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_378,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_378),U_379),U_381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_378),U_380),U_382))
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_381)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_380)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,U_381,U_382)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,U_379,U_380)
| ~ class_Rings_Oordered__semiring(U_378) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__mono_H]) ).
fof(f_147_2,plain,
! [U_387,U_386,U_385,U_384,U_383] :
( c_Orderings_Oord__class_Oless__eq(U_383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_383),U_384),U_386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_383),U_385),U_387))
| ~ c_Orderings_Oord__class_Oless__eq(U_383,c_Groups_Ozero__class_Ozero(U_383),U_386)
| ~ c_Orderings_Oord__class_Oless__eq(U_383,c_Groups_Ozero__class_Ozero(U_383),U_384)
| ~ c_Orderings_Oord__class_Oless__eq(U_383,U_386,U_387)
| ~ c_Orderings_Oord__class_Oless__eq(U_383,U_384,U_385)
| ~ class_Rings_Oordered__semiring(U_383) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_383),U_384),U_386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_383),U_385),U_387))
| ~ c_Orderings_Oord__class_Oless__eq(U_383,c_Groups_Ozero__class_Ozero(U_383),U_386)
| ~ c_Orderings_Oord__class_Oless__eq(U_383,c_Groups_Ozero__class_Ozero(U_383),U_384)
| ~ c_Orderings_Oord__class_Oless__eq(U_383,U_386,U_387)
| ~ c_Orderings_Oord__class_Oless__eq(U_383,U_384,U_385)
| ~ class_Rings_Oordered__semiring(U_383) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg]) ).
fof(f_148_2,plain,
! [U_391,U_390,U_389,U_388] :
( c_Orderings_Oord__class_Oless__eq(U_388,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_388),U_391),U_390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_388),U_391),U_389))
| ~ c_Orderings_Oord__class_Oless__eq(U_388,U_391,c_Groups_Ozero__class_Ozero(U_388))
| ~ c_Orderings_Oord__class_Oless__eq(U_388,U_389,U_390)
| ~ class_Rings_Oordered__ring(U_388) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_388,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_388),U_391),U_390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_388),U_391),U_389))
| ~ c_Orderings_Oord__class_Oless__eq(U_388,U_391,c_Groups_Ozero__class_Ozero(U_388))
| ~ c_Orderings_Oord__class_Oless__eq(U_388,U_389,U_390)
| ~ class_Rings_Oordered__ring(U_388) ),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg]) ).
fof(f_149_2,plain,
! [U_395,U_394,U_393,U_392] :
( c_Orderings_Oord__class_Oless__eq(U_392,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_392),U_394),U_395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_392),U_393),U_395))
| ~ c_Orderings_Oord__class_Oless__eq(U_392,U_395,c_Groups_Ozero__class_Ozero(U_392))
| ~ c_Orderings_Oord__class_Oless__eq(U_392,U_393,U_394)
| ~ class_Rings_Oordered__ring(U_392) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_392,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_392),U_394),U_395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_392),U_393),U_395))
| ~ c_Orderings_Oord__class_Oless__eq(U_392,U_395,c_Groups_Ozero__class_Ozero(U_392))
| ~ c_Orderings_Oord__class_Oless__eq(U_392,U_393,U_394)
| ~ class_Rings_Oordered__ring(U_392) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__comm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono]) ).
fof(f_150_2,plain,
! [U_399,U_398,U_397,U_396] :
( c_Orderings_Oord__class_Oless__eq(U_396,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_396),U_399),U_397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_396),U_399),U_398))
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_399)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,U_397,U_398)
| ~ class_Rings_Oordered__comm__semiring(U_396) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_396,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_396),U_399),U_397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_396),U_399),U_398))
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_399)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,U_397,U_398)
| ~ class_Rings_Oordered__comm__semiring(U_396) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__mono]) ).
fof(f_151_2,plain,
! [U_403,U_402,U_401,U_400] :
( c_Orderings_Oord__class_Oless__eq(U_400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_400),U_403),U_401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_400),U_403),U_402))
| ~ c_Orderings_Oord__class_Oless__eq(U_400,c_Groups_Ozero__class_Ozero(U_400),U_403)
| ~ c_Orderings_Oord__class_Oless__eq(U_400,U_401,U_402)
| ~ class_Rings_Oordered__semiring(U_400) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_400,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_400),U_403),U_401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_400),U_403),U_402))
| ~ c_Orderings_Oord__class_Oless__eq(U_400,c_Groups_Ozero__class_Ozero(U_400),U_403)
| ~ c_Orderings_Oord__class_Oless__eq(U_400,U_401,U_402)
| ~ class_Rings_Oordered__semiring(U_400) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Oordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__mono]) ).
fof(f_152_2,plain,
! [U_407,U_406,U_405,U_404] :
( c_Orderings_Oord__class_Oless__eq(U_404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_404),U_405),U_407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_404),U_406),U_407))
| ~ c_Orderings_Oord__class_Oless__eq(U_404,c_Groups_Ozero__class_Ozero(U_404),U_407)
| ~ c_Orderings_Oord__class_Oless__eq(U_404,U_405,U_406)
| ~ class_Rings_Oordered__semiring(U_404) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_404),U_405),U_407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_404),U_406),U_407))
| ~ c_Orderings_Oord__class_Oless__eq(U_404,c_Groups_Ozero__class_Ozero(U_404),U_407)
| ~ c_Orderings_Oord__class_Oless__eq(U_404,U_405,U_406)
| ~ class_Rings_Oordered__semiring(U_404) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos]) ).
fof(f_153_2,plain,
! [U_410,U_409,U_408] :
( c_Orderings_Oord__class_Oless__eq(U_408,c_Groups_Ozero__class_Ozero(U_408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_408),U_409),U_410))
| ~ c_Orderings_Oord__class_Oless__eq(U_408,U_410,c_Groups_Ozero__class_Ozero(U_408))
| ~ c_Orderings_Oord__class_Oless__eq(U_408,U_409,c_Groups_Ozero__class_Ozero(U_408))
| ~ class_Rings_Oordered__ring(U_408) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_408,c_Groups_Ozero__class_Ozero(U_408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_408),U_409),U_410))
| ~ c_Orderings_Oord__class_Oless__eq(U_408,U_410,c_Groups_Ozero__class_Ozero(U_408))
| ~ c_Orderings_Oord__class_Oless__eq(U_408,U_409,c_Groups_Ozero__class_Ozero(U_408))
| ~ class_Rings_Oordered__ring(U_408) ),
inference(clausify,[status(thm)],[f_153_2]) ).
fof(f_154_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg]) ).
fof(f_154_2,plain,
! [U_413,U_412,U_411] :
( c_Orderings_Oord__class_Oless__eq(U_411,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_411),U_412),U_413),c_Groups_Ozero__class_Ozero(U_411))
| ~ c_Orderings_Oord__class_Oless__eq(U_411,c_Groups_Ozero__class_Ozero(U_411),U_413)
| ~ c_Orderings_Oord__class_Oless__eq(U_411,U_412,c_Groups_Ozero__class_Ozero(U_411))
| ~ class_Rings_Oordered__cancel__semiring(U_411) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_411,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_411),U_412),U_413),c_Groups_Ozero__class_Ozero(U_411))
| ~ c_Orderings_Oord__class_Oless__eq(U_411,c_Groups_Ozero__class_Ozero(U_411),U_413)
| ~ c_Orderings_Oord__class_Oless__eq(U_411,U_412,c_Groups_Ozero__class_Ozero(U_411))
| ~ class_Rings_Oordered__cancel__semiring(U_411) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2]) ).
fof(f_155_2,plain,
! [U_416,U_415,U_414] :
( c_Orderings_Oord__class_Oless__eq(U_414,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_414),U_416),U_415),c_Groups_Ozero__class_Ozero(U_414))
| ~ c_Orderings_Oord__class_Oless__eq(U_414,U_416,c_Groups_Ozero__class_Ozero(U_414))
| ~ c_Orderings_Oord__class_Oless__eq(U_414,c_Groups_Ozero__class_Ozero(U_414),U_415)
| ~ class_Rings_Oordered__cancel__semiring(U_414) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_414,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_414),U_416),U_415),c_Groups_Ozero__class_Ozero(U_414))
| ~ c_Orderings_Oord__class_Oless__eq(U_414,U_416,c_Groups_Ozero__class_Ozero(U_414))
| ~ c_Orderings_Oord__class_Oless__eq(U_414,c_Groups_Ozero__class_Ozero(U_414),U_415)
| ~ class_Rings_Oordered__cancel__semiring(U_414) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos]) ).
fof(f_156_2,plain,
! [U_419,U_418,U_417] :
( c_Orderings_Oord__class_Oless__eq(U_417,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_417),U_418),U_419),c_Groups_Ozero__class_Ozero(U_417))
| ~ c_Orderings_Oord__class_Oless__eq(U_417,U_419,c_Groups_Ozero__class_Ozero(U_417))
| ~ c_Orderings_Oord__class_Oless__eq(U_417,c_Groups_Ozero__class_Ozero(U_417),U_418)
| ~ class_Rings_Oordered__cancel__semiring(U_417) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_417,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_417),U_418),U_419),c_Groups_Ozero__class_Ozero(U_417))
| ~ c_Orderings_Oord__class_Oless__eq(U_417,U_419,c_Groups_Ozero__class_Ozero(U_417))
| ~ c_Orderings_Oord__class_Oless__eq(U_417,c_Groups_Ozero__class_Ozero(U_417),U_418)
| ~ class_Rings_Oordered__cancel__semiring(U_417) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Oordered__cancel__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg]) ).
fof(f_157_2,plain,
! [U_422,U_421,U_420] :
( c_Orderings_Oord__class_Oless__eq(U_420,c_Groups_Ozero__class_Ozero(U_420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_420),U_421),U_422))
| ~ c_Orderings_Oord__class_Oless__eq(U_420,c_Groups_Ozero__class_Ozero(U_420),U_422)
| ~ c_Orderings_Oord__class_Oless__eq(U_420,c_Groups_Ozero__class_Ozero(U_420),U_421)
| ~ class_Rings_Oordered__cancel__semiring(U_420) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_420,c_Groups_Ozero__class_Ozero(U_420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_420),U_421),U_422))
| ~ c_Orderings_Oord__class_Oless__eq(U_420,c_Groups_Ozero__class_Ozero(U_420),U_422)
| ~ c_Orderings_Oord__class_Oless__eq(U_420,c_Groups_Ozero__class_Ozero(U_420),U_421)
| ~ class_Rings_Oordered__cancel__semiring(U_420) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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_158_2,plain,
! [U_425,U_424,U_423] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_425)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,U_424,c_Groups_Ozero__class_Ozero(U_423)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_423,U_425,c_Groups_Ozero__class_Ozero(U_423))
| ~ c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_424) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_425)
& c_Orderings_Oord__class_Oless__eq(U_423,U_424,c_Groups_Ozero__class_Ozero(U_423)) )
| ( c_Orderings_Oord__class_Oless__eq(U_423,U_425,c_Groups_Ozero__class_Ozero(U_423))
& c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_424) )
| ~ c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_423) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_423,U_424,c_Groups_Ozero__class_Ozero(U_423))
| c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_424)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423))
| ~ class_Rings_Olinordered__ring__strict(U_423) ),
inference(clausify,[status(thm)],[f_158_2]) ).
cnf(f_158_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_425)
| c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_424)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423))
| ~ class_Rings_Olinordered__ring__strict(U_423) ),
inference(clausify,[status(thm)],[f_158_2]) ).
cnf(f_158_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_423,U_424,c_Groups_Ozero__class_Ozero(U_423))
| c_Orderings_Oord__class_Oless__eq(U_423,U_425,c_Groups_Ozero__class_Ozero(U_423))
| ~ c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423))
| ~ class_Rings_Olinordered__ring__strict(U_423) ),
inference(clausify,[status(thm)],[f_158_2]) ).
cnf(f_158_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_425)
| c_Orderings_Oord__class_Oless__eq(U_423,U_425,c_Groups_Ozero__class_Ozero(U_423))
| ~ c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423))
| ~ class_Rings_Olinordered__ring__strict(U_423) ),
inference(clausify,[status(thm)],[f_158_2]) ).
cnf(f_158_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_423,U_425,c_Groups_Ozero__class_Ozero(U_423))
| ~ c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_424)
| c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423))
| ~ class_Rings_Olinordered__ring__strict(U_423) ),
inference(clausify,[status(thm)],[f_158_2]) ).
cnf(f_158_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_425)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,U_424,c_Groups_Ozero__class_Ozero(U_423))
| c_Orderings_Oord__class_Oless__eq(U_423,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_423),U_424),U_425),c_Groups_Ozero__class_Ozero(U_423))
| ~ class_Rings_Olinordered__ring__strict(U_423) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_b_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).
fof(f_159_2,plain,
! [U_428,U_427,U_426] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_426,U_428,c_Groups_Ozero__class_Ozero(U_426))
| ~ c_Orderings_Oord__class_Oless__eq(U_426,U_427,c_Groups_Ozero__class_Ozero(U_426)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_428)
| ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_427) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_426,U_428,c_Groups_Ozero__class_Ozero(U_426))
& c_Orderings_Oord__class_Oless__eq(U_426,U_427,c_Groups_Ozero__class_Ozero(U_426)) )
| ( c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_428)
& c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_427) )
| ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_426) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_426,U_427,c_Groups_Ozero__class_Ozero(U_426))
| c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_427)
| ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428))
| ~ class_Rings_Olinordered__ring__strict(U_426) ),
inference(clausify,[status(thm)],[f_159_2]) ).
cnf(f_159_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_426,U_428,c_Groups_Ozero__class_Ozero(U_426))
| c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_427)
| ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428))
| ~ class_Rings_Olinordered__ring__strict(U_426) ),
inference(clausify,[status(thm)],[f_159_2]) ).
cnf(f_159_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_426,U_427,c_Groups_Ozero__class_Ozero(U_426))
| c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_428)
| ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428))
| ~ class_Rings_Olinordered__ring__strict(U_426) ),
inference(clausify,[status(thm)],[f_159_2]) ).
cnf(f_159_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_426,U_428,c_Groups_Ozero__class_Ozero(U_426))
| c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_428)
| ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428))
| ~ class_Rings_Olinordered__ring__strict(U_426) ),
inference(clausify,[status(thm)],[f_159_2]) ).
cnf(f_159_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_428)
| ~ c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),U_427)
| c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428))
| ~ class_Rings_Olinordered__ring__strict(U_426) ),
inference(clausify,[status(thm)],[f_159_2]) ).
cnf(f_159_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_426,U_428,c_Groups_Ozero__class_Ozero(U_426))
| ~ c_Orderings_Oord__class_Oless__eq(U_426,U_427,c_Groups_Ozero__class_Ozero(U_426))
| c_Orderings_Oord__class_Oless__eq(U_426,c_Groups_Ozero__class_Ozero(U_426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_426),U_427),U_428))
| ~ class_Rings_Olinordered__ring__strict(U_426) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__square]) ).
fof(f_160_2,plain,
! [U_430,U_429] :
( c_Orderings_Oord__class_Oless__eq(U_429,c_Groups_Ozero__class_Ozero(U_429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_429),U_430),U_430))
| ~ class_Rings_Olinordered__ring(U_429) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_429,c_Groups_Ozero__class_Ozero(U_429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_429),U_430),U_430))
| ~ class_Rings_Olinordered__ring(U_429) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__one]) ).
fof(f_161_2,plain,
! [U_431] :
( c_Orderings_Oord__class_Oless__eq(U_431,c_Groups_Ozero__class_Ozero(U_431),c_Groups_Oone__class_Oone(U_431))
| ~ class_Rings_Olinordered__semidom(U_431) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_431,c_Groups_Ozero__class_Ozero(U_431),c_Groups_Oone__class_Oone(U_431))
| ~ class_Rings_Olinordered__semidom(U_431) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [T_a] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__le__zero]) ).
fof(f_162_2,plain,
! [U_432] :
( ~ c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oone__class_Oone(U_432),c_Groups_Ozero__class_Ozero(U_432))
| ~ class_Rings_Olinordered__semidom(U_432) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oone__class_Oone(U_432),c_Groups_Ozero__class_Ozero(U_432))
| ~ class_Rings_Olinordered__semidom(U_432) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_435,U_434,U_433] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_433),U_434),c_Nat_OSuc(U_435)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_433),U_434),hAPP(hAPP(c_Power_Opower__class_Opower(U_433),U_434),U_435))
| ~ class_Rings_Ocomm__semiring__1(U_433) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_433),U_434),c_Nat_OSuc(U_435)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_433),U_434),hAPP(hAPP(c_Power_Opower__class_Opower(U_433),U_434),U_435))
| ~ class_Rings_Ocomm__semiring__1(U_433) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_438,U_437,U_436] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_436),U_437),hAPP(hAPP(c_Power_Opower__class_Opower(U_436),U_437),U_438)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_436),U_437),c_Nat_OSuc(U_438))
| ~ class_Rings_Ocomm__semiring__1(U_436) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_436),U_437),hAPP(hAPP(c_Power_Opower__class_Opower(U_436),U_437),U_438)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_436),U_437),c_Nat_OSuc(U_438))
| ~ class_Rings_Ocomm__semiring__1(U_436) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_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_165_2,plain,
! [U_441,U_440,U_439] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Power_Opower__class_Opower(U_439),U_440),U_441)),U_440) = hAPP(hAPP(c_Power_Opower__class_Opower(U_439),U_440),c_Nat_OSuc(U_441))
| ~ class_Rings_Ocomm__semiring__1(U_439) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Power_Opower__class_Opower(U_439),U_440),U_441)),U_440) = hAPP(hAPP(c_Power_Opower__class_Opower(U_439),U_440),c_Nat_OSuc(U_441))
| ~ class_Rings_Ocomm__semiring__1(U_439) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).
fof(f_166_2,plain,
! [U_443,U_442] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ouminus__class_Ouminus(U_442,U_443),U_443)
| ~ c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ozero__class_Ozero(U_442),U_443) )
& ( c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ozero__class_Ozero(U_442),U_443)
| ~ c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ouminus__class_Ouminus(U_442,U_443),U_443) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_442) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ozero__class_Ozero(U_442),U_443)
| ~ c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ouminus__class_Ouminus(U_442,U_443),U_443)
| ~ class_Groups_Olinordered__ab__group__add(U_442) ),
inference(clausify,[status(thm)],[f_166_2]) ).
cnf(f_166_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ouminus__class_Ouminus(U_442,U_443),U_443)
| ~ c_Orderings_Oord__class_Oless__eq(U_442,c_Groups_Ozero__class_Ozero(U_442),U_443)
| ~ class_Groups_Olinordered__ab__group__add(U_442) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).
fof(f_167_2,plain,
! [U_445,U_444] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ouminus__class_Ouminus(U_444,U_445),c_Groups_Ozero__class_Ozero(U_444))
| ~ c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ozero__class_Ozero(U_444),U_445) )
& ( c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ozero__class_Ozero(U_444),U_445)
| ~ c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ouminus__class_Ouminus(U_444,U_445),c_Groups_Ozero__class_Ozero(U_444)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_444) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ozero__class_Ozero(U_444),U_445)
| ~ c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ouminus__class_Ouminus(U_444,U_445),c_Groups_Ozero__class_Ozero(U_444))
| ~ class_Groups_Oordered__ab__group__add(U_444) ),
inference(clausify,[status(thm)],[f_167_2]) ).
cnf(f_167_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ouminus__class_Ouminus(U_444,U_445),c_Groups_Ozero__class_Ozero(U_444))
| ~ c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Ozero__class_Ozero(U_444),U_445)
| ~ class_Groups_Oordered__ab__group__add(U_444) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).
fof(f_168_2,plain,
! [U_447,U_446] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ouminus__class_Ouminus(U_446,U_447))
| ~ c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ozero__class_Ozero(U_446)) )
& ( c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ozero__class_Ozero(U_446))
| ~ c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ouminus__class_Ouminus(U_446,U_447)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_446) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ozero__class_Ozero(U_446))
| ~ c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ouminus__class_Ouminus(U_446,U_447))
| ~ class_Groups_Olinordered__ab__group__add(U_446) ),
inference(clausify,[status(thm)],[f_168_2]) ).
cnf(f_168_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ouminus__class_Ouminus(U_446,U_447))
| ~ c_Orderings_Oord__class_Oless__eq(U_446,U_447,c_Groups_Ozero__class_Ozero(U_446))
| ~ class_Groups_Olinordered__ab__group__add(U_446) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).
fof(f_169_2,plain,
! [U_449,U_448] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_448,c_Groups_Ozero__class_Ozero(U_448),c_Groups_Ouminus__class_Ouminus(U_448,U_449))
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_449,c_Groups_Ozero__class_Ozero(U_448)) )
& ( c_Orderings_Oord__class_Oless__eq(U_448,U_449,c_Groups_Ozero__class_Ozero(U_448))
| ~ c_Orderings_Oord__class_Oless__eq(U_448,c_Groups_Ozero__class_Ozero(U_448),c_Groups_Ouminus__class_Ouminus(U_448,U_449)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_448) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_448,U_449,c_Groups_Ozero__class_Ozero(U_448))
| ~ c_Orderings_Oord__class_Oless__eq(U_448,c_Groups_Ozero__class_Ozero(U_448),c_Groups_Ouminus__class_Ouminus(U_448,U_449))
| ~ class_Groups_Oordered__ab__group__add(U_448) ),
inference(clausify,[status(thm)],[f_169_2]) ).
cnf(f_169_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_448,c_Groups_Ozero__class_Ozero(U_448),c_Groups_Ouminus__class_Ouminus(U_448,U_449))
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_449,c_Groups_Ozero__class_Ozero(U_448))
| ~ class_Groups_Oordered__ab__group__add(U_448) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_1,plain,
! [T_a] :
( c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__1]) ).
fof(f_170_2,plain,
! [U_450] :
( c_Polynomial_Odegree(U_450,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_450))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__1(U_450) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( c_Polynomial_Odegree(U_450,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_450))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__1(U_450) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [V_a,T_a] :
( c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__pCons__0]) ).
fof(f_171_2,plain,
! [U_452,U_451] :
( c_Polynomial_Odegree(U_451,c_Polynomial_OpCons(U_451,U_452,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_451)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(U_451) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( c_Polynomial_Odegree(U_451,c_Polynomial_OpCons(U_451,U_452,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_451)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(U_451) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le]) ).
fof(f_172_2,plain,
! [U_455,U_454,U_453] :
( c_Orderings_Oord__class_Oless__eq(U_453,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_453),U_455),U_454),U_454)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,U_455,c_Groups_Oone__class_Oone(U_453))
| ~ c_Orderings_Oord__class_Oless__eq(U_453,c_Groups_Ozero__class_Ozero(U_453),U_455)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,c_Groups_Ozero__class_Ozero(U_453),U_454)
| ~ class_Rings_Olinordered__idom(U_453) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_453,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_453),U_455),U_454),U_454)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,U_455,c_Groups_Oone__class_Oone(U_453))
| ~ c_Orderings_Oord__class_Oless__eq(U_453,c_Groups_Ozero__class_Ozero(U_453),U_455)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,c_Groups_Ozero__class_Ozero(U_453),U_454)
| ~ class_Rings_Olinordered__idom(U_453) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le]) ).
fof(f_173_2,plain,
! [U_458,U_457,U_456] :
( c_Orderings_Oord__class_Oless__eq(U_456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_456),U_457),U_458),U_457)
| ~ c_Orderings_Oord__class_Oless__eq(U_456,U_458,c_Groups_Oone__class_Oone(U_456))
| ~ c_Orderings_Oord__class_Oless__eq(U_456,c_Groups_Ozero__class_Ozero(U_456),U_458)
| ~ c_Orderings_Oord__class_Oless__eq(U_456,c_Groups_Ozero__class_Ozero(U_456),U_457)
| ~ class_Rings_Olinordered__idom(U_456) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_456),U_457),U_458),U_457)
| ~ c_Orderings_Oord__class_Oless__eq(U_456,U_458,c_Groups_Oone__class_Oone(U_456))
| ~ c_Orderings_Oord__class_Oless__eq(U_456,c_Groups_Ozero__class_Ozero(U_456),U_458)
| ~ c_Orderings_Oord__class_Oless__eq(U_456,c_Groups_Ozero__class_Ozero(U_456),U_457)
| ~ class_Rings_Olinordered__idom(U_456) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_462,U_461,U_460,U_459] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_459),U_460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_461),U_462)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_459),hAPP(hAPP(c_Power_Opower__class_Opower(U_459),U_460),U_461)),U_462)
| ~ class_Groups_Omonoid__mult(U_459) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_459),U_460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_461),U_462)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_459),hAPP(hAPP(c_Power_Opower__class_Opower(U_459),U_460),U_461)),U_462)
| ~ class_Groups_Omonoid__mult(U_459) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_464,U_463] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_463),U_464),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_464
| ~ class_Groups_Omonoid__mult(U_463) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_463),U_464),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_464
| ~ class_Groups_Omonoid__mult(U_463) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [V_n,V_a,T_a] :
( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)) = V_n
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__linear__power]) ).
fof(f_176_2,plain,
! [U_467,U_466,U_465] :
( c_Polynomial_Odegree(U_465,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_465)),c_Polynomial_OpCons(U_465,U_466,c_Polynomial_OpCons(U_465,c_Groups_Oone__class_Oone(U_465),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_465))))),U_467)) = U_467
| ~ class_Rings_Ocomm__semiring__1(U_465) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( c_Polynomial_Odegree(U_465,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_465)),c_Polynomial_OpCons(U_465,U_466,c_Polynomial_OpCons(U_465,c_Groups_Oone__class_Oone(U_465),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_465))))),U_467)) = U_467
| ~ class_Rings_Ocomm__semiring__1(U_465) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_470,U_469,U_468] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_468),U_469),U_470) != c_Groups_Ozero__class_Ozero(U_468)
| U_469 = c_Groups_Ozero__class_Ozero(U_468)
| ~ class_Rings_Oring__1__no__zero__divisors(U_468) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_468),U_469),U_470) != c_Groups_Ozero__class_Ozero(U_468)
| U_469 = c_Groups_Ozero__class_Ozero(U_468)
| ~ class_Rings_Oring__1__no__zero__divisors(U_468) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_474,U_473,U_472,U_471] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_471),U_472),U_473)),U_474) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_471),hAPP(hAPP(c_Power_Opower__class_Opower(U_471),U_472),U_474)),hAPP(hAPP(c_Power_Opower__class_Opower(U_471),U_473),U_474))
| ~ class_Groups_Ocomm__monoid__mult(U_471) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_471),U_472),U_473)),U_474) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_471),hAPP(hAPP(c_Power_Opower__class_Opower(U_471),U_472),U_474)),hAPP(hAPP(c_Power_Opower__class_Opower(U_471),U_473),U_474))
| ~ class_Groups_Ocomm__monoid__mult(U_471) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_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_179_2,plain,
! [U_477,U_476,U_475] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),hAPP(hAPP(c_Power_Opower__class_Opower(U_475),U_476),U_477)),U_476) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),U_476),hAPP(hAPP(c_Power_Opower__class_Opower(U_475),U_476),U_477))
| ~ class_Groups_Omonoid__mult(U_475) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),hAPP(hAPP(c_Power_Opower__class_Opower(U_475),U_476),U_477)),U_476) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_475),U_476),hAPP(hAPP(c_Power_Opower__class_Opower(U_475),U_476),U_477))
| ~ class_Groups_Omonoid__mult(U_475) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
inference(fof_nnf,[status(thm)],[fact_le0]) ).
fof(f_180_2,plain,
! [U_478] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_478),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_478),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_1,plain,
! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)),
inference(fof_nnf,[status(thm)],[fact_dvd__1__left]) ).
fof(f_181_2,plain,
! [U_479] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_479)),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_479)),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_1,plain,
! [V_n,V_r,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self]) ).
fof(f_182_2,plain,
! [U_482,U_481,U_480] :
( c_Orderings_Oord__class_Oless__eq(U_480,hAPP(hAPP(c_Power_Opower__class_Opower(U_480),U_481),c_Nat_OSuc(U_482)),U_481)
| ~ c_Orderings_Oord__class_Oless__eq(U_480,U_481,c_Groups_Oone__class_Oone(U_480))
| ~ c_Orderings_Oord__class_Oless__eq(U_480,c_Groups_Ozero__class_Ozero(U_480),U_481)
| ~ class_Rings_Olinordered__semidom(U_480) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_480,hAPP(hAPP(c_Power_Opower__class_Opower(U_480),U_481),c_Nat_OSuc(U_482)),U_481)
| ~ c_Orderings_Oord__class_Oless__eq(U_480,U_481,c_Groups_Oone__class_Oone(U_480))
| ~ c_Orderings_Oord__class_Oless__eq(U_480,c_Groups_Ozero__class_Ozero(U_480),U_481)
| ~ class_Rings_Olinordered__semidom(U_480) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_1,plain,
! [B_m] :
( ! [B_p,B_q] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),B_q),B_m)))
| B_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Odegree(tc_Complex_Ocomplex,B_p) != B_m
| ? [B_x] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_p),B_x) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,v_na____) ),
inference(fof_nnf,[status(thm)],[fact_IH]) ).
fof(f_183_2,plain,
! [U_486] :
( ! [U_485,U_484] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_485),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_484),U_486)))
| U_486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Odegree(tc_Complex_Ocomplex,U_485) != U_486
| ? [U_483] :
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_484),U_483) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_485),U_483) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_486,v_na____) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_486] :
( ! [U_485,U_484] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_485),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_484),U_486)))
| U_486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Odegree(tc_Complex_Ocomplex,U_485) != U_486
| ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_484),sK2(U_486,U_485,U_484)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_485),sK2(U_486,U_485,U_484)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_486,v_na____) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_483,sK2(U_486,U_485,U_484))],[f_183_2]) ).
cnf(f_183_4,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_485),sK2(U_486,U_485,U_484)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_485),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_484),U_486)))
| U_486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Odegree(tc_Complex_Ocomplex,U_485) != U_486
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_486,v_na____) ),
inference(clausify,[status(thm)],[f_183_3]) ).
cnf(f_183_5,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_484),sK2(U_486,U_485,U_484)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_485),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),U_484),U_486)))
| U_486 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Odegree(tc_Complex_Ocomplex,U_485) != U_486
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_486,v_na____) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_nb_2)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).
fof(f_184_2,plain,
! [U_488,U_487] :
( ( 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_487),U_488))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_488)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_487) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_488)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_487) )
| ~ 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_487),U_488)) ) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
( ! [U_492,U_490] :
( 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_490),U_492))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_492)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_490) )
& ! [U_491,U_489] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_491)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_489) )
| ~ 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_489),U_491)) ) ),
inference(miniscope,[status(thm)],[f_184_2]) ).
cnf(f_184_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_489)
| ~ 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_489),U_491)) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_491)
| ~ 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_489),U_491)) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_490),U_492))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_492)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_490) ),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
& V_x_2 != V_y_2 ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__disj]) ).
fof(f_185_2,plain,
! [U_495,U_494,U_493] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_494),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_495),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( U_494 != c_Groups_Ouminus__class_Ouminus(U_493,U_495)
& U_494 != U_495 ) )
& ( U_494 = c_Groups_Ouminus__class_Ouminus(U_493,U_495)
| U_494 = U_495
| hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_494),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_495),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(U_493) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( U_494 = c_Groups_Ouminus__class_Ouminus(U_493,U_495)
| U_494 = U_495
| hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_494),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_495),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(U_493) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_4,plain,
( U_494 != U_495
| hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_494),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_495),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(U_493) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_5,plain,
( U_494 != c_Groups_Ouminus__class_Ouminus(U_493,U_495)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_494),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_493),U_495),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ class_Rings_Oidom(U_493) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_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_186_2,plain,
! [U_497,U_496] :
( U_496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_497 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_496 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_496),U_497) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( U_496 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_497 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_496 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_496),U_497) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).
fof(f_187_2,plain,
! [U_500,U_499,U_498] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_498)),U_499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_498)),U_500))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_499,U_500) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_499,U_500)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_498)),U_499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_498)),U_500)) ) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
( ! [U_506,U_504] :
( ! [U_502] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_502)),U_504),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_502)),U_506))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_504,U_506) )
& ! [U_505,U_503] :
( ! [U_501] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_501)),U_503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_501)),U_505))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_503,U_505) ) ),
inference(miniscope,[status(thm)],[f_187_2]) ).
cnf(f_187_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_501)),U_503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_501)),U_505))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_503,U_505) ),
inference(clausify,[status(thm)],[f_187_3]) ).
cnf(f_187_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_502)),U_504),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_502)),U_506))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_504,U_506) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_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_188_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_188_1]) ).
fof(f_189_1,plain,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(f_189_2,plain,
! [U_507] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_507),U_507)),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_507),U_507)),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_less__zeroE]) ).
fof(f_190_2,plain,
! [U_508] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_508,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_190_1]) ).
cnf(f_190_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_508,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_190_2]) ).
fof(f_191_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).
fof(f_191_2,plain,
! [U_510,U_509] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_509),c_Nat_OSuc(U_510))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_509,U_510) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_509),c_Nat_OSuc(U_510))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_509,U_510) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_lessI]) ).
fof(f_192_2,plain,
! [U_511] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_511,c_Nat_OSuc(U_511)),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_511,c_Nat_OSuc(U_511)),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_zero__less__Suc]) ).
fof(f_193_2,plain,
! [U_512] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_512)),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_512)),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_1,plain,
! [V_y_2,V_x_2] :
( ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| V_x_2 != V_y_2 ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff]) ).
fof(f_194_2,plain,
! [U_514,U_513] :
( ( U_513 = U_514
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_514),U_513))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_513),U_514)) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_514),U_513))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_513),U_514)) )
| U_513 != U_514 ) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ! [U_518,U_516] :
( U_516 = U_518
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_518),U_516))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_516),U_518)) )
& ! [U_517,U_515] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_517),U_515))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_515),U_517)) )
| U_515 != U_517 ) ),
inference(miniscope,[status(thm)],[f_194_2]) ).
cnf(f_194_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_515),U_517))
| U_515 != U_517 ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_517),U_515))
| U_515 != U_517 ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_6,plain,
( U_516 = U_518
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_518),U_516))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_516),U_518)) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) )
& ( V_x_2 = V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less]) ).
fof(f_195_2,plain,
! [U_520,U_519] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_519),U_520))
| ( U_519 != U_520
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_520),U_519))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_519),U_520)) ) ) )
& ( U_519 = U_520
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_520),U_519))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_519),U_520)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_519),U_520)) ) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
( ! [U_524,U_522] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_522),U_524))
| ( U_522 != U_524
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_524),U_522))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_522),U_524)) ) ) )
& ! [U_523,U_521] :
( U_521 = U_523
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_523),U_521))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_521),U_523)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_521),U_523)) ) ),
inference(miniscope,[status(thm)],[f_195_2]) ).
cnf(f_195_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_521),U_523))
| U_521 = U_523
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_521),U_523)) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_523),U_521))
| U_521 = U_523
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_521),U_523)) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_6,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_524),U_522))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_522),U_524))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_522),U_524)) ),
inference(clausify,[status(thm)],[f_195_3]) ).
cnf(f_195_7,plain,
( U_522 != U_524
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_522),U_524)) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [V_y_2,V_x_2] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le]) ).
fof(f_196_2,plain,
! [U_526,U_525] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_526),U_525))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_525),U_526)) )
| U_525 = U_526
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_525),U_526)) )
& ( ( U_525 != U_526
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_525),U_526)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_526),U_525))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_525),U_526)) ) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( ! [U_530,U_528] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_530),U_528))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_528),U_530)) )
| U_528 = U_530
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_528),U_530)) )
& ! [U_529,U_527] :
( ( U_527 != U_529
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_527),U_529)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_529),U_527))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_527),U_529)) ) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
cnf(f_196_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_527),U_529))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_529),U_527))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_527),U_529)) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_5,plain,
( U_527 != U_529
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_529),U_527))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_527),U_529)) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_6,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_528),U_530))
| U_528 = U_530
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_528),U_530)) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_530),U_528))
| U_528 = U_530
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_528),U_530)) ),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_1,plain,
! [V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
| V_a = V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(f_197_2,plain,
! [U_532,U_531] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_532),U_531))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_531),U_532)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_531),U_532))
| U_531 = U_532 ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_531),U_532))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_531),U_532))
| U_531 = U_532 ),
inference(clausify,[status(thm)],[f_197_2]) ).
cnf(f_197_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_532),U_531))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_531),U_532))
| U_531 = U_532 ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| V_x != V_y ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl]) ).
fof(f_198_2,plain,
! [U_534,U_533] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_533),U_534))
| U_533 != U_534 ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_533),U_534))
| U_533 != U_534 ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_1,plain,
! [V_x_2,V_y_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv]) ).
fof(f_199_2,plain,
! [U_536,U_535] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_536),U_535))
| U_536 != U_535 )
& ( U_536 = U_535
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_536),U_535)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_535),U_536)) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( U_536 = U_535
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_536),U_535))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_535),U_536)) ),
inference(clausify,[status(thm)],[f_199_2]) ).
cnf(f_199_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_536),U_535))
| U_536 != U_535
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_535),U_536)) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_1,plain,
! [V_y,V_x] :
( V_x = V_y
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(f_200_2,plain,
! [U_538,U_537] :
( U_537 = U_538
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_538),U_537))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_537),U_538)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_537),U_538)) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_537),U_538))
| U_537 = U_538
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_537),U_538)) ),
inference(clausify,[status(thm)],[f_200_2]) ).
cnf(f_200_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_538),U_537))
| U_537 = U_538
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_537),U_538)) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_1,plain,
! [V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(f_201_2,plain,
! [U_540,U_539] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_540),U_539))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_539),U_540)) )
| U_539 = U_540
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_539),U_540)) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_539),U_540))
| U_539 = U_540
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_539),U_540)) ),
inference(clausify,[status(thm)],[f_201_2]) ).
cnf(f_201_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_540),U_539))
| U_539 = U_540
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_539),U_540)) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_1,plain,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
| V_a != V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__le__trans]) ).
fof(f_202_2,plain,
! [U_543,U_542,U_541] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_541),U_543))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_542),U_543))
| U_541 != U_542 ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_541),U_543))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_542),U_543))
| U_541 != U_542 ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_1,plain,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
| V_b != V_c
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__le__eq__trans]) ).
fof(f_203_2,plain,
! [U_546,U_545,U_544] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_544),U_546))
| U_545 != U_546
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_544),U_545)) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_544),U_546))
| U_545 != U_546
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_544),U_545)) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__antisym]) ).
fof(f_204_2,plain,
! [U_548,U_547] :
( U_547 = U_548
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_548),U_547))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_547),U_548)) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( U_547 = U_548
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_548),U_547))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_547),U_548)) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_1,plain,
! [V_y,V_x] :
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym]) ).
fof(f_205_2,plain,
! [U_550,U_549] :
( U_549 = U_550
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_550),U_549))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_549),U_550)) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( U_549 = U_550
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_550),U_549))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_549),U_550)) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_1,plain,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans]) ).
fof(f_206_2,plain,
! [U_553,U_552,U_551] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_551),U_553))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_552),U_553))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_551),U_552)) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_551),U_553))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_552),U_553))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_551),U_552)) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_1,plain,
! [V_c,V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
| V_a != V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__less__trans]) ).
fof(f_207_2,plain,
! [U_556,U_555,U_554] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_556),U_554))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_554),U_556)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_556),U_555))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_555),U_556))
| U_554 != U_555 ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_554),U_556))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_556),U_555))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_555),U_556))
| U_554 != U_555 ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_556),U_554))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_556),U_555))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_555),U_556))
| U_554 != U_555 ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_1,plain,
! [V_z,V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(f_208_2,plain,
! [U_559,U_558,U_557] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_559),U_557))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_557),U_559)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_559),U_558))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_558),U_559))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_557),U_558)) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_557),U_559))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_559),U_558))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_558),U_559))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_557),U_558)) ),
inference(clausify,[status(thm)],[f_208_2]) ).
cnf(f_208_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_559),U_557))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_559),U_558))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_558),U_559))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_557),U_558)) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [V_y,V_x] :
( V_x != V_y
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__neq]) ).
fof(f_209_2,plain,
! [U_561,U_560] :
( U_560 != U_561
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_561),U_560))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_560),U_561)) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( U_560 != U_561
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_561),U_560))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_560),U_561)) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__not__sym]) ).
fof(f_210_2,plain,
! [U_563,U_562] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_562),U_563))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_563),U_562))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_563),U_562))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_562),U_563)) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_562),U_563))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_563),U_562))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_563),U_562))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_562),U_563)) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__le]) ).
fof(f_211_2,plain,
! [U_565,U_564] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_564),U_565))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_565),U_564))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_564),U_565)) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_564),U_565))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_565),U_564))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_564),U_565)) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__less]) ).
fof(f_212_2,plain,
! [U_567,U_566] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_566),U_567))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_567),U_566))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_567),U_566))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_566),U_567)) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_566),U_567))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_567),U_566))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_567),U_566))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_566),U_567)) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_1,plain,
! [V_y,V_x] :
( V_x != V_y
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq]) ).
fof(f_213_2,plain,
! [U_569,U_568] :
( U_568 != U_569
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_569),U_568))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_568),U_569)) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( U_568 != U_569
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_569),U_568))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_568),U_569)) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_1,plain,
! [V_y,V_x] :
( V_y != V_x
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq2]) ).
fof(f_214_2,plain,
! [U_571,U_570] :
( U_571 != U_570
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_571),U_570))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_570),U_571)) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( U_571 != U_570
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_571),U_570))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_570),U_571)) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_1,plain,
! [V_c,V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
| V_b != V_c
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__less__eq__trans]) ).
fof(f_215_2,plain,
! [U_574,U_573,U_572] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_574),U_572))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_572),U_574)) )
| U_573 != U_574
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_573),U_572))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_572),U_573)) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_572),U_574))
| U_573 != U_574
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_573),U_572))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_572),U_573)) ),
inference(clausify,[status(thm)],[f_215_2]) ).
cnf(f_215_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_574),U_572))
| U_573 != U_574
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_573),U_572))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_572),U_573)) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_1,plain,
! [V_z,V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(f_216_2,plain,
! [U_577,U_576,U_575] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_577),U_575))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_575),U_577)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_576),U_577))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_576),U_575))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_575),U_576)) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_575),U_577))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_576),U_577))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_576),U_575))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_575),U_576)) ),
inference(clausify,[status(thm)],[f_216_2]) ).
cnf(f_216_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_577),U_575))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_576),U_577))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_576),U_575))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_575),U_576)) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym_H]) ).
fof(f_217_2,plain,
! [U_579,U_578] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_578),U_579))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_579),U_578))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_579),U_578))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_578),U_579)) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_578),U_579))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_579),U_578))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_579),U_578))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_578),U_579)) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_1,plain,
! [V_z,V_y,V_x] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(f_218_2,plain,
! [U_582,U_581,U_580] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_582),U_580))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_580),U_582)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_582),U_581))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_581),U_582))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_581),U_580))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_580),U_581)) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_580),U_582))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_582),U_581))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_581),U_582))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_581),U_580))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_580),U_581)) ),
inference(clausify,[status(thm)],[f_218_2]) ).
cnf(f_218_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_582),U_580))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_582),U_581))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_581),U_582))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_581),U_580))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_580),U_581)) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym]) ).
fof(f_219_2,plain,
! [U_584,U_583] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_583),U_584))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_584),U_583))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_584),U_583))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_583),U_584)) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_583),U_584))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_584),U_583))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_584),U_583))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_583),U_584)) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| V_x = V_y
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(f_220_2,plain,
! [U_587,U_586,U_585] :
( c_Orderings_Oord__class_Oless(U_585,U_587,U_586)
| c_Orderings_Oord__class_Oless(U_585,U_586,U_587)
| U_586 = U_587
| ~ class_Rings_Olinordered__idom(U_585) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( c_Orderings_Oord__class_Oless(U_585,U_587,U_586)
| c_Orderings_Oord__class_Oless(U_585,U_586,U_587)
| U_586 = U_587
| ~ class_Rings_Olinordered__idom(U_585) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_1,plain,
! [V_P_2,V_nb_2,V_m_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2))
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2) )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2))
& V_m_2 = V_nb_2 )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_nb_2),V_m_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_221_2,plain,
! [U_590,U_589,U_588] :
( hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| ( ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_589,U_588) )
| ( ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
& U_588 = U_589 )
| ( ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_588,U_589) ) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_589,U_588)
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| U_588 = U_589
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_588,U_589) ),
inference(clausify,[status(thm)],[f_221_2]) ).
cnf(f_221_4,plain,
( ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| U_588 = U_589
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_588,U_589) ),
inference(clausify,[status(thm)],[f_221_2]) ).
cnf(f_221_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_589,U_588)
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_588,U_589) ),
inference(clausify,[status(thm)],[f_221_2]) ).
cnf(f_221_6,plain,
( ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_588,U_589) ),
inference(clausify,[status(thm)],[f_221_2]) ).
cnf(f_221_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_589,U_588)
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| U_588 = U_589
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588)) ),
inference(clausify,[status(thm)],[f_221_2]) ).
cnf(f_221_8,plain,
( ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| U_588 = U_589
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588)) ),
inference(clausify,[status(thm)],[f_221_2]) ).
cnf(f_221_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_589,U_588)
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588)) ),
inference(clausify,[status(thm)],[f_221_2]) ).
cnf(f_221_10,plain,
( ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588))
| ~ hBOOL(hAPP(hAPP(U_590,U_589),U_588)) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_1,plain,
! [V_t,V_s] :
( V_s != V_t
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).
fof(f_222_2,plain,
! [U_592,U_591] :
( U_591 != U_592
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_591,U_592) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( U_591 != U_592
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_591,U_592) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_1,plain,
! [V_m,V_n] :
( V_m != V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).
fof(f_223_2,plain,
! [U_594,U_593] :
( U_594 != U_593
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_593,U_594) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( U_594 != U_593
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_593,U_594) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).
fof(f_224_2,plain,
! [U_595] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_595,U_595),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_595,U_595),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
| V_x = V_y ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(f_225_2,plain,
! [U_597,U_596] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_597,U_596)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_596,U_597)
| U_596 = U_597 ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_597,U_596)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_596,U_597)
| U_596 = U_597 ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_1,plain,
! [V_nb_2,V_m_2] :
( ( V_m_2 != V_nb_2
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| V_m_2 = V_nb_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).
fof(f_226_2,plain,
! [U_599,U_598] :
( ( U_598 != U_599
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_599,U_598)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_598,U_599) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_599,U_598)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_598,U_599)
| U_598 = U_599 ) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
( ! [U_603,U_601] :
( U_601 != U_603
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_603,U_601)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_601,U_603) ) )
& ! [U_602,U_600] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602,U_600)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_600,U_602)
| U_600 = U_602 ) ),
inference(miniscope,[status(thm)],[f_226_2]) ).
cnf(f_226_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_602,U_600)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_600,U_602)
| U_600 = U_602 ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_601,U_603)
| U_601 != U_603 ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_603,U_601)
| U_601 != U_603 ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).
fof(f_227_2,plain,
! [U_604] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_604,U_604),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_604,U_604),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_not__less0]) ).
fof(f_228_2,plain,
! [U_605] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_605,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_605,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_1,plain,
! [V_nb_2] :
( ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
| V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).
fof(f_229_2,plain,
! [U_606] :
( ( U_606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_606) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_606)
| U_606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
( ! [U_608] :
( U_608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_608) )
& ! [U_607] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_607)
| U_607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_229_2]) ).
cnf(f_229_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_607)
| U_607 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_229_3]) ).
cnf(f_229_5,plain,
( U_608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_608) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_less__nat__zero__code]) ).
fof(f_230_2,plain,
! [U_609] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_609,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_609,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_1,plain,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ),
inference(fof_nnf,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(f_231_2,plain,
! [U_611,U_610] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_611),U_610))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_610,U_611)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_610) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_611),U_610))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_610,U_611)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_610) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_1,plain,
! [V_n,V_m] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).
fof(f_232_2,plain,
! [U_613,U_612] :
( U_613 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_612,U_613) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_613] :
( ! [U_612] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_612,U_613)
| U_613 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_232_2]) ).
cnf(f_232_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_612,U_613)
| U_613 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_gr0I]) ).
fof(f_233_2,plain,
! [U_614] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_614)
| U_614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_614)
| U_614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD]) ).
fof(f_234_2,plain,
! [U_616,U_615] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_615,U_616)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_615),c_Nat_OSuc(U_616)) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_615,U_616)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_615),c_Nat_OSuc(U_616)) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessD]) ).
fof(f_235_2,plain,
! [U_618,U_617] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_617,U_618)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_617),U_618) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_617,U_618)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_617),U_618) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_1,plain,
! [V_n,V_m] :
( V_m = V_n
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_less__SucE]) ).
fof(f_236_2,plain,
! [U_620,U_619] :
( U_619 = U_620
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_619,U_620)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_619,c_Nat_OSuc(U_620)) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( U_619 = U_620
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_619,U_620)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_619,c_Nat_OSuc(U_620)) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).
fof(f_237_2,plain,
! [U_623,U_622,U_621] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_621),U_623)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_622,U_623)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_621,U_622) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_621),U_623)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_622,U_623)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_621,U_622) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
| c_Nat_OSuc(V_m) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).
fof(f_238_2,plain,
! [U_625,U_624] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_624),U_625)
| c_Nat_OSuc(U_624) = U_625
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_624,U_625) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_624),U_625)
| c_Nat_OSuc(U_624) = U_625
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_624,U_625) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).
fof(f_239_2,plain,
! [U_627,U_626] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_626,c_Nat_OSuc(U_627))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_626,U_627) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_626,c_Nat_OSuc(U_627))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_626,U_627) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [V_m,V_n] :
( V_m = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).
fof(f_240_2,plain,
! [U_629,U_628] :
( U_629 = U_628
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_628,c_Nat_OSuc(U_629))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_628,U_629) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( U_629 = U_628
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_628,c_Nat_OSuc(U_629))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_628,U_629) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_1,plain,
! [V_m_2,V_nb_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
| V_nb_2 != V_m_2 )
& ( V_nb_2 = V_m_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(f_241_2,plain,
! [U_631,U_630] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_630,c_Nat_OSuc(U_631))
| U_630 != U_631 )
& ( U_630 = U_631
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_630,c_Nat_OSuc(U_631)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_630,U_631) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( U_630 = U_631
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_630,c_Nat_OSuc(U_631))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_630,U_631) ),
inference(clausify,[status(thm)],[f_241_2]) ).
cnf(f_241_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_630,c_Nat_OSuc(U_631))
| U_630 != U_631
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_630,U_631) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).
fof(f_242_2,plain,
! [U_633,U_632] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_632),c_Nat_OSuc(U_633))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_632,U_633) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_632,U_633)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_632),c_Nat_OSuc(U_633)) ) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
( ! [U_637,U_635] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_635),c_Nat_OSuc(U_637))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_635,U_637) )
& ! [U_636,U_634] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_634,U_636)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_634),c_Nat_OSuc(U_636)) ) ),
inference(miniscope,[status(thm)],[f_242_2]) ).
cnf(f_242_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_634,U_636)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_634),c_Nat_OSuc(U_636)) ),
inference(clausify,[status(thm)],[f_242_3]) ).
cnf(f_242_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_635),c_Nat_OSuc(U_637))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_635,U_637) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
| ( V_m_2 != V_nb_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) )
& ( V_m_2 = V_nb_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).
fof(f_243_2,plain,
! [U_639,U_638] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_638,c_Nat_OSuc(U_639))
| ( U_638 != U_639
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_638,U_639) ) )
& ( U_638 = U_639
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_638,U_639)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_638,c_Nat_OSuc(U_639)) ) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
( ! [U_643,U_641] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_641,c_Nat_OSuc(U_643))
| ( U_641 != U_643
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_641,U_643) ) )
& ! [U_642,U_640] :
( U_640 = U_642
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_640,U_642)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_640,c_Nat_OSuc(U_642)) ) ),
inference(miniscope,[status(thm)],[f_243_2]) ).
cnf(f_243_4,plain,
( U_640 = U_642
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_640,U_642)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_640,c_Nat_OSuc(U_642)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_641,U_643)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_641,c_Nat_OSuc(U_643)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_6,plain,
( U_641 != U_643
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_641,c_Nat_OSuc(U_643)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_1,plain,
! [V_nb_2,V_m_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).
fof(f_244_2,plain,
! [U_645,U_644] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_644,U_645)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_645,c_Nat_OSuc(U_644)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_645,c_Nat_OSuc(U_644))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_644,U_645) ) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( ! [U_649,U_647] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_647,U_649)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_649,c_Nat_OSuc(U_647)) )
& ! [U_648,U_646] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_648,c_Nat_OSuc(U_646))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_646,U_648) ) ),
inference(miniscope,[status(thm)],[f_244_2]) ).
cnf(f_244_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_648,c_Nat_OSuc(U_646))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_646,U_648) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_647,U_649)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_649,c_Nat_OSuc(U_647)) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ( V_m != V_n
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le]) ).
fof(f_245_2,plain,
! [U_651,U_650] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_650,U_651)
| ( U_650 != U_651
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_650,U_651) ) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_650,U_651)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_650,U_651) ),
inference(clausify,[status(thm)],[f_245_2]) ).
cnf(f_245_4,plain,
( U_650 != U_651
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_650,U_651) ),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| V_m = V_n
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less]) ).
fof(f_246_2,plain,
! [U_653,U_652] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_652,U_653)
| U_652 = U_653
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_652,U_653) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_652,U_653)
| U_652 = U_653
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_652,U_653) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).
fof(f_247_2,plain,
! [U_655,U_654] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_654,U_655)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_654,U_655) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_654,U_655)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_654,U_655) ),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ( V_m_2 != V_nb_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) )
& ( V_m_2 = V_nb_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).
fof(f_248_2,plain,
! [U_657,U_656] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_656,U_657)
| ( U_656 != U_657
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_656,U_657) ) )
& ( U_656 = U_657
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_656,U_657)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_656,U_657) ) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
( ! [U_661,U_659] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_659,U_661)
| ( U_659 != U_661
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_659,U_661) ) )
& ! [U_660,U_658] :
( U_658 = U_660
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_658,U_660)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_658,U_660) ) ),
inference(miniscope,[status(thm)],[f_248_2]) ).
cnf(f_248_4,plain,
( U_658 = U_660
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_658,U_660)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_658,U_660) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_659,U_661)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_659,U_661) ),
inference(clausify,[status(thm)],[f_248_3]) ).
cnf(f_248_6,plain,
( U_659 != U_661
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_659,U_661) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| V_m_2 = V_nb_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( ( V_m_2 != V_nb_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).
fof(f_249_2,plain,
! [U_663,U_662] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_662,U_663)
| U_662 = U_663
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_662,U_663) )
& ( ( U_662 != U_663
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_662,U_663) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_662,U_663) ) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
( ! [U_667,U_665] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_665,U_667)
| U_665 = U_667
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_665,U_667) )
& ! [U_666,U_664] :
( ( U_664 != U_666
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_664,U_666) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_664,U_666) ) ),
inference(miniscope,[status(thm)],[f_249_2]) ).
cnf(f_249_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_664,U_666)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_664,U_666) ),
inference(clausify,[status(thm)],[f_249_3]) ).
cnf(f_249_5,plain,
( U_664 != U_666
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_664,U_666) ),
inference(clausify,[status(thm)],[f_249_3]) ).
cnf(f_249_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_665,U_667)
| U_665 = U_667
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_665,U_667) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_250_2,plain,
! [U_671,U_670,U_669,U_668] :
( ( ( c_Orderings_Oord__class_Oless(U_668,hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_670),hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_671))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_670,U_671) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_670,U_671)
| ~ c_Orderings_Oord__class_Oless(U_668,hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_670),hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_671)) ) )
| ~ c_Orderings_Oord__class_Oless(U_668,c_Groups_Oone__class_Oone(U_668),U_669)
| ~ class_Rings_Olinordered__semidom(U_668) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_670,U_671)
| ~ c_Orderings_Oord__class_Oless(U_668,hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_670),hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_671))
| ~ c_Orderings_Oord__class_Oless(U_668,c_Groups_Oone__class_Oone(U_668),U_669)
| ~ class_Rings_Olinordered__semidom(U_668) ),
inference(clausify,[status(thm)],[f_250_2]) ).
cnf(f_250_4,plain,
( c_Orderings_Oord__class_Oless(U_668,hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_670),hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),U_671))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_670,U_671)
| ~ c_Orderings_Oord__class_Oless(U_668,c_Groups_Oone__class_Oone(U_668),U_669)
| ~ class_Rings_Olinordered__semidom(U_668) ),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp]) ).
fof(f_251_2,plain,
! [U_675,U_674,U_673,U_672] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_674,U_675)
| ~ c_Orderings_Oord__class_Oless(U_672,hAPP(hAPP(c_Power_Opower__class_Opower(U_672),U_673),U_674),hAPP(hAPP(c_Power_Opower__class_Opower(U_672),U_673),U_675))
| ~ c_Orderings_Oord__class_Oless(U_672,c_Groups_Oone__class_Oone(U_672),U_673)
| ~ class_Rings_Olinordered__semidom(U_672) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_674,U_675)
| ~ c_Orderings_Oord__class_Oless(U_672,hAPP(hAPP(c_Power_Opower__class_Opower(U_672),U_673),U_674),hAPP(hAPP(c_Power_Opower__class_Opower(U_672),U_673),U_675))
| ~ c_Orderings_Oord__class_Oless(U_672,c_Groups_Oone__class_Oone(U_672),U_673)
| ~ class_Rings_Olinordered__semidom(U_672) ),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).
fof(f_252_2,plain,
! [U_679,U_678,U_677,U_676] :
( c_Orderings_Oord__class_Oless(U_676,hAPP(hAPP(c_Power_Opower__class_Opower(U_676),U_679),U_677),hAPP(hAPP(c_Power_Opower__class_Opower(U_676),U_679),U_678))
| ~ c_Orderings_Oord__class_Oless(U_676,c_Groups_Oone__class_Oone(U_676),U_679)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_677,U_678)
| ~ class_Rings_Olinordered__semidom(U_676) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
( c_Orderings_Oord__class_Oless(U_676,hAPP(hAPP(c_Power_Opower__class_Opower(U_676),U_679),U_677),hAPP(hAPP(c_Power_Opower__class_Opower(U_676),U_679),U_678))
| ~ c_Orderings_Oord__class_Oless(U_676,c_Groups_Oone__class_Oone(U_676),U_679)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_677,U_678)
| ~ class_Rings_Olinordered__semidom(U_676) ),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).
fof(f_253_2,plain,
! [U_682,U_681,U_680] :
( ( ( c_Orderings_Oord__class_Oless(U_680,U_681,c_Groups_Ouminus__class_Ouminus(U_680,U_682))
| ~ c_Orderings_Oord__class_Oless(U_680,U_682,c_Groups_Ouminus__class_Ouminus(U_680,U_681)) )
& ( c_Orderings_Oord__class_Oless(U_680,U_682,c_Groups_Ouminus__class_Ouminus(U_680,U_681))
| ~ c_Orderings_Oord__class_Oless(U_680,U_681,c_Groups_Ouminus__class_Ouminus(U_680,U_682)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_680) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( c_Orderings_Oord__class_Oless(U_680,U_682,c_Groups_Ouminus__class_Ouminus(U_680,U_681))
| ~ c_Orderings_Oord__class_Oless(U_680,U_681,c_Groups_Ouminus__class_Ouminus(U_680,U_682))
| ~ class_Groups_Oordered__ab__group__add(U_680) ),
inference(clausify,[status(thm)],[f_253_2]) ).
cnf(f_253_4,plain,
( c_Orderings_Oord__class_Oless(U_680,U_681,c_Groups_Ouminus__class_Ouminus(U_680,U_682))
| ~ c_Orderings_Oord__class_Oless(U_680,U_682,c_Groups_Ouminus__class_Ouminus(U_680,U_681))
| ~ class_Groups_Oordered__ab__group__add(U_680) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).
fof(f_254_2,plain,
! [U_685,U_684,U_683] :
( ( ( c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_684),U_685)
| ~ c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_685),U_684) )
& ( c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_685),U_684)
| ~ c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_684),U_685) ) )
| ~ class_Groups_Oordered__ab__group__add(U_683) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
( c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_685),U_684)
| ~ c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_684),U_685)
| ~ class_Groups_Oordered__ab__group__add(U_683) ),
inference(clausify,[status(thm)],[f_254_2]) ).
cnf(f_254_4,plain,
( c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_684),U_685)
| ~ c_Orderings_Oord__class_Oless(U_683,c_Groups_Ouminus__class_Ouminus(U_683,U_685),U_684)
| ~ class_Groups_Oordered__ab__group__add(U_683) ),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_1,plain,
! [V_aa_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).
fof(f_255_2,plain,
! [U_688,U_687,U_686] :
( ( ( c_Orderings_Oord__class_Oless(U_686,c_Groups_Ouminus__class_Ouminus(U_686,U_687),c_Groups_Ouminus__class_Ouminus(U_686,U_688))
| ~ c_Orderings_Oord__class_Oless(U_686,U_688,U_687) )
& ( c_Orderings_Oord__class_Oless(U_686,U_688,U_687)
| ~ c_Orderings_Oord__class_Oless(U_686,c_Groups_Ouminus__class_Ouminus(U_686,U_687),c_Groups_Ouminus__class_Ouminus(U_686,U_688)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_686) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( c_Orderings_Oord__class_Oless(U_686,U_688,U_687)
| ~ c_Orderings_Oord__class_Oless(U_686,c_Groups_Ouminus__class_Ouminus(U_686,U_687),c_Groups_Ouminus__class_Ouminus(U_686,U_688))
| ~ class_Groups_Oordered__ab__group__add(U_686) ),
inference(clausify,[status(thm)],[f_255_2]) ).
cnf(f_255_4,plain,
( c_Orderings_Oord__class_Oless(U_686,c_Groups_Ouminus__class_Ouminus(U_686,U_687),c_Groups_Ouminus__class_Ouminus(U_686,U_688))
| ~ c_Orderings_Oord__class_Oless(U_686,U_688,U_687)
| ~ class_Groups_Oordered__ab__group__add(U_686) ),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_1,plain,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).
fof(f_256_2,plain,
! [U_691,U_690,U_689] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_690,U_691)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_689),U_690),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_689),U_691))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_689) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_690,U_691)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_689),U_690),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_689),U_691))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_689) ),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_1,plain,
! [V_nb_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_nb_2))
| ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) )
& ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_257_2,plain,
! [U_693,U_692] :
( ( 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_692),U_693))
| ( U_693 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_692) ) )
& ( U_693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_692)
| ~ 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_692),U_693)) ) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
( ! [U_697,U_695] :
( 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_695),U_697))
| ( U_697 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_695) ) )
& ! [U_696,U_694] :
( U_696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_694)
| ~ 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_694),U_696)) ) ),
inference(miniscope,[status(thm)],[f_257_2]) ).
cnf(f_257_4,plain,
( U_696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_694)
| ~ 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_694),U_696)) ),
inference(clausify,[status(thm)],[f_257_3]) ).
cnf(f_257_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_695)
| 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_695),U_697)) ),
inference(clausify,[status(thm)],[f_257_3]) ).
cnf(f_257_6,plain,
( U_697 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_695),U_697)) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
| ( ! [B_j] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_nb_2)
| V_m_2 != c_Nat_OSuc(B_j) )
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_nb_2)
& V_m_2 = c_Nat_OSuc(B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).
fof(f_258_2,plain,
! [U_701,U_700] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_700,c_Nat_OSuc(U_701))
| ( ! [U_699] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_699,U_701)
| U_700 != c_Nat_OSuc(U_699) )
& U_700 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_698] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_698,U_701)
& U_700 = c_Nat_OSuc(U_698) )
| U_700 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_700,c_Nat_OSuc(U_701)) ) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_705,U_703] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_703,c_Nat_OSuc(U_705))
| ( ! [U_699] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_699,U_705)
| U_703 != c_Nat_OSuc(U_699) )
& U_703 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_704,U_702] :
( ? [U_698] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_698,U_704)
& U_702 = c_Nat_OSuc(U_698) )
| U_702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_702,c_Nat_OSuc(U_704)) ) ),
inference(miniscope,[status(thm)],[f_258_2]) ).
fof(f_258_4,plain,
( ! [U_705,U_703] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_703,c_Nat_OSuc(U_705))
| ( ! [U_699] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_699,U_705)
| U_703 != c_Nat_OSuc(U_699) )
& U_703 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_704,U_702] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK3(U_704,U_702),U_704)
& U_702 = c_Nat_OSuc(sK3(U_704,U_702)) )
| U_702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_702,c_Nat_OSuc(U_704)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_698,sK3(U_704,U_702))],[f_258_3]) ).
cnf(f_258_5,plain,
( U_702 = c_Nat_OSuc(sK3(U_704,U_702))
| U_702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_702,c_Nat_OSuc(U_704)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK3(U_704,U_702),U_704)
| U_702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_702,c_Nat_OSuc(U_704)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_7,plain,
( U_703 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_703,c_Nat_OSuc(U_705)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
cnf(f_258_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_699,U_705)
| U_703 != c_Nat_OSuc(U_699)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_703,c_Nat_OSuc(U_705)) ),
inference(clausify,[status(thm)],[f_258_4]) ).
fof(f_259_1,plain,
! [V_nb_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).
fof(f_259_2,plain,
! [U_706] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_706,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_706 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_706 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_706,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
( ! [U_708] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_708,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_707] :
( U_707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_707,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_259_2]) ).
cnf(f_259_4,plain,
( U_707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_707,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_708,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_708 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_nb_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
| ! [B_m] : V_nb_2 != c_Nat_OSuc(B_m) )
& ( ? [B_m] : V_nb_2 = c_Nat_OSuc(B_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).
fof(f_260_2,plain,
! [U_711] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_711)
| ! [U_710] : U_711 != c_Nat_OSuc(U_710) )
& ( ? [U_709] : U_711 = c_Nat_OSuc(U_709)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_711) ) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_713] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_713)
| ! [U_710] : U_713 != c_Nat_OSuc(U_710) )
& ! [U_712] :
( ? [U_709] : U_712 = c_Nat_OSuc(U_709)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_712) ) ),
inference(miniscope,[status(thm)],[f_260_2]) ).
fof(f_260_4,plain,
( ! [U_713] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_713)
| ! [U_710] : U_713 != c_Nat_OSuc(U_710) )
& ! [U_712] :
( U_712 = c_Nat_OSuc(sK4(U_712))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_712) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_709,sK4(U_712))],[f_260_3]) ).
cnf(f_260_5,plain,
( U_712 = c_Nat_OSuc(sK4(U_712))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_712) ),
inference(clausify,[status(thm)],[f_260_4]) ).
cnf(f_260_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_713)
| U_713 != c_Nat_OSuc(U_710) ),
inference(clausify,[status(thm)],[f_260_4]) ).
fof(f_261_1,plain,
! [V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__imp__le]) ).
fof(f_261_2,plain,
! [U_715,U_714] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_714,U_715)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_715)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_714),U_715)) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_714,U_715)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_715)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_714),U_715)) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD]) ).
fof(f_262_2,plain,
! [U_717,U_716] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_716,U_717)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_716),U_717) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_716,U_717)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_716),U_717) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_1,plain,
! [V_nb_2,V_m_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2))
| V_nb_2 != V_m_2 )
& ( V_nb_2 = V_m_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,c_Nat_OSuc(V_m_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ),
inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).
fof(f_263_2,plain,
! [U_719,U_718] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_719,c_Nat_OSuc(U_718))
| U_719 != U_718 )
& ( U_719 = U_718
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_719,c_Nat_OSuc(U_718)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_718,U_719) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( U_719 = U_718
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_719,c_Nat_OSuc(U_718))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_718,U_719) ),
inference(clausify,[status(thm)],[f_263_2]) ).
cnf(f_263_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_719,c_Nat_OSuc(U_718))
| U_719 != U_718
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_718,U_719) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).
fof(f_264_2,plain,
! [U_721,U_720] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_720),U_721)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_720,U_721) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_720),U_721)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_720,U_721) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc]) ).
fof(f_265_2,plain,
! [U_723,U_722] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_722,c_Nat_OSuc(U_723))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_722,U_723) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_722,c_Nat_OSuc(U_723))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_722,U_723) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).
fof(f_266_2,plain,
! [U_725,U_724] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_724),U_725)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_724,U_725) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_724,U_725)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_724),U_725) ) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
( ! [U_729,U_727] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_727),U_729)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_727,U_729) )
& ! [U_728,U_726] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_726,U_728)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_726),U_728) ) ),
inference(miniscope,[status(thm)],[f_266_2]) ).
cnf(f_266_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_726,U_728)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_726),U_728) ),
inference(clausify,[status(thm)],[f_266_3]) ).
cnf(f_266_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_727),U_729)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_727,U_729) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).
fof(f_267_2,plain,
! [U_731,U_730] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_730,c_Nat_OSuc(U_731))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_730,U_731) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_730,U_731)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_730,c_Nat_OSuc(U_731)) ) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
( ! [U_735,U_733] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_733,c_Nat_OSuc(U_735))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_733,U_735) )
& ! [U_734,U_732] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_732,U_734)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_732,c_Nat_OSuc(U_734)) ) ),
inference(miniscope,[status(thm)],[f_267_2]) ).
cnf(f_267_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_732,U_734)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_732,c_Nat_OSuc(U_734)) ),
inference(clausify,[status(thm)],[f_267_3]) ).
cnf(f_267_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_733,c_Nat_OSuc(U_735))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_733,U_735) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [V_m_2,V_nb_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_nb_2,V_m_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).
fof(f_268_2,plain,
! [U_737,U_736] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_736,U_737)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_736),U_737) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_736),U_737)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_736,U_737) ) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
( ! [U_741,U_739] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_739,U_741)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_739),U_741) )
& ! [U_740,U_738] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_738),U_740)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_738,U_740) ) ),
inference(miniscope,[status(thm)],[f_268_2]) ).
cnf(f_268_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_738),U_740)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_738,U_740) ),
inference(clausify,[status(thm)],[f_268_3]) ).
cnf(f_268_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_739,U_741)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_739),U_741) ),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).
fof(f_269_2,plain,
! [U_743,U_742] :
( ( 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_742),U_743))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_743)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_742) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_743)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_742) )
| ~ 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_742),U_743)) ) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_747,U_745] :
( 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_745),U_747))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_747)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_745) )
& ! [U_746,U_744] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_746)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_744) )
| ~ 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_744),U_746)) ) ),
inference(miniscope,[status(thm)],[f_269_2]) ).
cnf(f_269_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_744)
| ~ 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_744),U_746)) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_746)
| ~ 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_744),U_746)) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_745),U_747))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_747)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_745) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).
fof(f_270_2,plain,
! [U_750,U_749,U_748] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_748),U_749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_748),U_750))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_749,U_750)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_748) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_749,U_750)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_748) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_748),U_749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_748),U_750)) ) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
( ! [U_756,U_754,U_752] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_752),U_754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_752),U_756))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_754,U_756)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_752) )
& ! [U_755,U_753,U_751] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_753,U_755)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_751) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_751),U_753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_751),U_755)) ) ),
inference(miniscope,[status(thm)],[f_270_2]) ).
cnf(f_270_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_751)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_751),U_753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_751),U_755)) ),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_270_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_753,U_755)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_751),U_753),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_751),U_755)) ),
inference(clausify,[status(thm)],[f_270_3]) ).
cnf(f_270_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_752),U_754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_752),U_756))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_754,U_756)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_752) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_1,plain,
! [V_nb_2,V_k_2,V_m_2] :
( ( 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_nb_2),V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).
fof(f_271_2,plain,
! [U_759,U_758,U_757] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_759),U_758))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_757,U_759)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_758) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_757,U_759)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_758) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_757),U_758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_759),U_758)) ) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
( ! [U_765,U_763,U_761] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_761),U_763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_765),U_763))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_761,U_765)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_763) )
& ! [U_764,U_762,U_760] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_760,U_764)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_762) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_760),U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_764),U_762)) ) ),
inference(miniscope,[status(thm)],[f_271_2]) ).
cnf(f_271_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_762)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_760),U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_764),U_762)) ),
inference(clausify,[status(thm)],[f_271_3]) ).
cnf(f_271_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_760,U_764)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_760),U_762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_764),U_762)) ),
inference(clausify,[status(thm)],[f_271_3]) ).
cnf(f_271_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_761),U_763),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_765),U_763))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_761,U_765)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_763) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).
fof(f_272_2,plain,
! [U_768,U_767,U_766] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_766),U_768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_767),U_768))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_768)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_766,U_767) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_766),U_768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_767),U_768))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_768)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_766,U_767) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).
fof(f_273_2,plain,
! [U_771,U_770,U_769] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_771),U_769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_771),U_770))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_771)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_769,U_770) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_771),U_769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_771),U_770))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_771)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_769,U_770) ),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel]) ).
fof(f_274_2,plain,
! [U_774,U_773,U_772] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_773),U_774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_772)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_772),U_773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_772),U_774))) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_773),U_774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_772)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_772),U_773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_772),U_774))) ),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1]) ).
fof(f_275_2,plain,
! [U_777,U_776,U_775] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_775)),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_775)),U_777))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_776,U_777) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_776,U_777)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_775)),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_775)),U_777)) ) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_783,U_781] :
( ! [U_779] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_779)),U_781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_779)),U_783))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_781,U_783) )
& ! [U_782,U_780] :
( ! [U_778] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_778)),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_778)),U_782))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_780,U_782) ) ),
inference(miniscope,[status(thm)],[f_275_2]) ).
cnf(f_275_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_778)),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_778)),U_782))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_780,U_782) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_779)),U_781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_779)),U_783))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_781,U_783) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).
fof(f_276_2,plain,
! [U_787,U_786,U_785,U_784] :
( c_Orderings_Oord__class_Oless(U_784,hAPP(hAPP(c_Power_Opower__class_Opower(U_784),U_787),U_786),hAPP(hAPP(c_Power_Opower__class_Opower(U_784),U_787),U_785))
| ~ c_Orderings_Oord__class_Oless(U_784,U_787,c_Groups_Oone__class_Oone(U_784))
| ~ c_Orderings_Oord__class_Oless(U_784,c_Groups_Ozero__class_Ozero(U_784),U_787)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_785,U_786)
| ~ class_Rings_Olinordered__semidom(U_784) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( c_Orderings_Oord__class_Oless(U_784,hAPP(hAPP(c_Power_Opower__class_Opower(U_784),U_787),U_786),hAPP(hAPP(c_Power_Opower__class_Opower(U_784),U_787),U_785))
| ~ c_Orderings_Oord__class_Oless(U_784,U_787,c_Groups_Oone__class_Oone(U_784))
| ~ c_Orderings_Oord__class_Oless(U_784,c_Groups_Ozero__class_Ozero(U_784),U_787)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_785,U_786)
| ~ class_Rings_Olinordered__semidom(U_784) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).
fof(f_277_2,plain,
! [U_790,U_789,U_788] :
( c_Orderings_Oord__class_Oless(U_788,c_Groups_Oone__class_Oone(U_788),hAPP(hAPP(c_Power_Opower__class_Opower(U_788),U_789),U_790))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_790)
| ~ c_Orderings_Oord__class_Oless(U_788,c_Groups_Oone__class_Oone(U_788),U_789)
| ~ class_Rings_Olinordered__semidom(U_788) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( c_Orderings_Oord__class_Oless(U_788,c_Groups_Oone__class_Oone(U_788),hAPP(hAPP(c_Power_Opower__class_Opower(U_788),U_789),U_790))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_790)
| ~ c_Orderings_Oord__class_Oless(U_788,c_Groups_Oone__class_Oone(U_788),U_789)
| ~ class_Rings_Olinordered__semidom(U_788) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).
fof(f_278_2,plain,
! [U_794,U_793,U_792,U_791] :
( c_Orderings_Oord__class_Oless(U_791,hAPP(hAPP(c_Power_Opower__class_Opower(U_791),U_792),U_794),hAPP(hAPP(c_Power_Opower__class_Opower(U_791),U_793),U_794))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_794)
| ~ c_Orderings_Oord__class_Oless__eq(U_791,c_Groups_Ozero__class_Ozero(U_791),U_792)
| ~ c_Orderings_Oord__class_Oless(U_791,U_792,U_793)
| ~ class_Rings_Olinordered__semidom(U_791) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( c_Orderings_Oord__class_Oless(U_791,hAPP(hAPP(c_Power_Opower__class_Opower(U_791),U_792),U_794),hAPP(hAPP(c_Power_Opower__class_Opower(U_791),U_793),U_794))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_794)
| ~ c_Orderings_Oord__class_Oless__eq(U_791,c_Groups_Ozero__class_Ozero(U_791),U_792)
| ~ c_Orderings_Oord__class_Oless(U_791,U_792,U_793)
| ~ class_Rings_Olinordered__semidom(U_791) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__square__less__zero]) ).
fof(f_279_2,plain,
! [U_796,U_795] :
( ~ c_Orderings_Oord__class_Oless(U_795,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_795),U_796),U_796),c_Groups_Ozero__class_Ozero(U_795))
| ~ class_Rings_Olinordered__ring(U_795) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_795,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_795),U_796),U_796),c_Groups_Ozero__class_Ozero(U_795))
| ~ class_Rings_Olinordered__ring(U_795) ),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_1,plain,
! [V_b_2,V_c_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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_280_2,plain,
! [U_800,U_799,U_798,U_797] :
( ( ( c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799))
| ( ( ~ c_Orderings_Oord__class_Oless(U_797,U_800,U_798)
| ~ c_Orderings_Oord__class_Oless(U_797,U_799,c_Groups_Ozero__class_Ozero(U_797)) )
& ( ~ c_Orderings_Oord__class_Oless(U_797,U_798,U_800)
| ~ c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_799) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_797,U_800,U_798)
& c_Orderings_Oord__class_Oless(U_797,U_799,c_Groups_Ozero__class_Ozero(U_797)) )
| ( c_Orderings_Oord__class_Oless(U_797,U_798,U_800)
& c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_799) )
| ~ c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_797) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( c_Orderings_Oord__class_Oless(U_797,U_799,c_Groups_Ozero__class_Ozero(U_797))
| c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_799)
| ~ c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799))
| ~ class_Rings_Olinordered__ring__strict(U_797) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_4,plain,
( c_Orderings_Oord__class_Oless(U_797,U_800,U_798)
| c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_799)
| ~ c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799))
| ~ class_Rings_Olinordered__ring__strict(U_797) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_5,plain,
( c_Orderings_Oord__class_Oless(U_797,U_799,c_Groups_Ozero__class_Ozero(U_797))
| c_Orderings_Oord__class_Oless(U_797,U_798,U_800)
| ~ c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799))
| ~ class_Rings_Olinordered__ring__strict(U_797) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_6,plain,
( c_Orderings_Oord__class_Oless(U_797,U_800,U_798)
| c_Orderings_Oord__class_Oless(U_797,U_798,U_800)
| ~ c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799))
| ~ class_Rings_Olinordered__ring__strict(U_797) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_797,U_798,U_800)
| ~ c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_799)
| c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799))
| ~ class_Rings_Olinordered__ring__strict(U_797) ),
inference(clausify,[status(thm)],[f_280_2]) ).
cnf(f_280_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_797,U_800,U_798)
| ~ c_Orderings_Oord__class_Oless(U_797,U_799,c_Groups_Ozero__class_Ozero(U_797))
| c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_800),U_799))
| ~ class_Rings_Olinordered__ring__strict(U_797) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)
& c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_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_281_2,plain,
! [U_804,U_803,U_802,U_801] :
( ( ( c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804))
| ( ( ~ c_Orderings_Oord__class_Oless(U_801,U_804,U_803)
| ~ c_Orderings_Oord__class_Oless(U_801,U_802,c_Groups_Ozero__class_Ozero(U_801)) )
& ( ~ c_Orderings_Oord__class_Oless(U_801,U_803,U_804)
| ~ c_Orderings_Oord__class_Oless(U_801,c_Groups_Ozero__class_Ozero(U_801),U_802) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_801,U_804,U_803)
& c_Orderings_Oord__class_Oless(U_801,U_802,c_Groups_Ozero__class_Ozero(U_801)) )
| ( c_Orderings_Oord__class_Oless(U_801,U_803,U_804)
& c_Orderings_Oord__class_Oless(U_801,c_Groups_Ozero__class_Ozero(U_801),U_802) )
| ~ c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_801) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( c_Orderings_Oord__class_Oless(U_801,U_802,c_Groups_Ozero__class_Ozero(U_801))
| c_Orderings_Oord__class_Oless(U_801,c_Groups_Ozero__class_Ozero(U_801),U_802)
| ~ c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804))
| ~ class_Rings_Olinordered__ring__strict(U_801) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_4,plain,
( c_Orderings_Oord__class_Oless(U_801,U_804,U_803)
| c_Orderings_Oord__class_Oless(U_801,c_Groups_Ozero__class_Ozero(U_801),U_802)
| ~ c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804))
| ~ class_Rings_Olinordered__ring__strict(U_801) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_5,plain,
( c_Orderings_Oord__class_Oless(U_801,U_802,c_Groups_Ozero__class_Ozero(U_801))
| c_Orderings_Oord__class_Oless(U_801,U_803,U_804)
| ~ c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804))
| ~ class_Rings_Olinordered__ring__strict(U_801) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_6,plain,
( c_Orderings_Oord__class_Oless(U_801,U_804,U_803)
| c_Orderings_Oord__class_Oless(U_801,U_803,U_804)
| ~ c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804))
| ~ class_Rings_Olinordered__ring__strict(U_801) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_801,U_803,U_804)
| ~ c_Orderings_Oord__class_Oless(U_801,c_Groups_Ozero__class_Ozero(U_801),U_802)
| c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804))
| ~ class_Rings_Olinordered__ring__strict(U_801) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_801,U_804,U_803)
| ~ c_Orderings_Oord__class_Oless(U_801,U_802,c_Groups_Ozero__class_Ozero(U_801))
| c_Orderings_Oord__class_Oless(U_801,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_804))
| ~ class_Rings_Olinordered__ring__strict(U_801) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
| ~ 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_282_2,plain,
! [U_808,U_807,U_806,U_805] :
( ( ( c_Orderings_Oord__class_Oless(U_805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_808))
| ~ c_Orderings_Oord__class_Oless(U_805,U_807,U_808) )
& ( c_Orderings_Oord__class_Oless(U_805,U_807,U_808)
| ~ c_Orderings_Oord__class_Oless(U_805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_808)) ) )
| ~ c_Orderings_Oord__class_Oless(U_805,c_Groups_Ozero__class_Ozero(U_805),U_806)
| ~ class_Rings_Olinordered__ring__strict(U_805) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( c_Orderings_Oord__class_Oless(U_805,U_807,U_808)
| ~ c_Orderings_Oord__class_Oless(U_805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_808))
| ~ c_Orderings_Oord__class_Oless(U_805,c_Groups_Ozero__class_Ozero(U_805),U_806)
| ~ class_Rings_Olinordered__ring__strict(U_805) ),
inference(clausify,[status(thm)],[f_282_2]) ).
cnf(f_282_4,plain,
( c_Orderings_Oord__class_Oless(U_805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_808))
| ~ c_Orderings_Oord__class_Oless(U_805,U_807,U_808)
| ~ c_Orderings_Oord__class_Oless(U_805,c_Groups_Ozero__class_Ozero(U_805),U_806)
| ~ class_Rings_Olinordered__ring__strict(U_805) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__pos]) ).
fof(f_283_2,plain,
! [U_811,U_810,U_809] :
( c_Orderings_Oord__class_Oless(U_809,c_Groups_Ozero__class_Ozero(U_809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_810),U_811))
| ~ c_Orderings_Oord__class_Oless(U_809,c_Groups_Ozero__class_Ozero(U_809),U_811)
| ~ c_Orderings_Oord__class_Oless(U_809,c_Groups_Ozero__class_Ozero(U_809),U_810)
| ~ class_Rings_Olinordered__semiring__strict(U_809) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( c_Orderings_Oord__class_Oless(U_809,c_Groups_Ozero__class_Ozero(U_809),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_810),U_811))
| ~ c_Orderings_Oord__class_Oless(U_809,c_Groups_Ozero__class_Ozero(U_809),U_811)
| ~ c_Orderings_Oord__class_Oless(U_809,c_Groups_Ozero__class_Ozero(U_809),U_810)
| ~ class_Rings_Olinordered__semiring__strict(U_809) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg]) ).
fof(f_284_2,plain,
! [U_814,U_813,U_812] :
( c_Orderings_Oord__class_Oless(U_812,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_812),U_813),U_814),c_Groups_Ozero__class_Ozero(U_812))
| ~ c_Orderings_Oord__class_Oless(U_812,U_814,c_Groups_Ozero__class_Ozero(U_812))
| ~ c_Orderings_Oord__class_Oless(U_812,c_Groups_Ozero__class_Ozero(U_812),U_813)
| ~ class_Rings_Olinordered__semiring__strict(U_812) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( c_Orderings_Oord__class_Oless(U_812,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_812),U_813),U_814),c_Groups_Ozero__class_Ozero(U_812))
| ~ c_Orderings_Oord__class_Oless(U_812,U_814,c_Groups_Ozero__class_Ozero(U_812))
| ~ c_Orderings_Oord__class_Oless(U_812,c_Groups_Ozero__class_Ozero(U_812),U_813)
| ~ class_Rings_Olinordered__semiring__strict(U_812) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2]) ).
fof(f_285_2,plain,
! [U_817,U_816,U_815] :
( c_Orderings_Oord__class_Oless(U_815,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),U_817),U_816),c_Groups_Ozero__class_Ozero(U_815))
| ~ c_Orderings_Oord__class_Oless(U_815,U_817,c_Groups_Ozero__class_Ozero(U_815))
| ~ c_Orderings_Oord__class_Oless(U_815,c_Groups_Ozero__class_Ozero(U_815),U_816)
| ~ class_Rings_Olinordered__semiring__strict(U_815) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
cnf(f_285_3,plain,
( c_Orderings_Oord__class_Oless(U_815,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_815),U_817),U_816),c_Groups_Ozero__class_Ozero(U_815))
| ~ c_Orderings_Oord__class_Oless(U_815,U_817,c_Groups_Ozero__class_Ozero(U_815))
| ~ c_Orderings_Oord__class_Oless(U_815,c_Groups_Ozero__class_Ozero(U_815),U_816)
| ~ class_Rings_Olinordered__semiring__strict(U_815) ),
inference(clausify,[status(thm)],[f_285_2]) ).
fof(f_286_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos]) ).
fof(f_286_2,plain,
! [U_820,U_819,U_818] :
( c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),U_820)
| ~ c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),U_819)
| ~ c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_819),U_820))
| ~ class_Rings_Olinordered__semiring__strict(U_818) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),U_820)
| ~ c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),U_819)
| ~ c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_819),U_820))
| ~ class_Rings_Olinordered__semiring__strict(U_818) ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_1,plain,
! [V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2]) ).
fof(f_287_2,plain,
! [U_823,U_822,U_821] :
( c_Orderings_Oord__class_Oless(U_821,c_Groups_Ozero__class_Ozero(U_821),U_822)
| ~ c_Orderings_Oord__class_Oless(U_821,c_Groups_Ozero__class_Ozero(U_821),U_823)
| ~ c_Orderings_Oord__class_Oless(U_821,c_Groups_Ozero__class_Ozero(U_821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_823))
| ~ class_Rings_Olinordered__semiring__strict(U_821) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( c_Orderings_Oord__class_Oless(U_821,c_Groups_Ozero__class_Ozero(U_821),U_822)
| ~ c_Orderings_Oord__class_Oless(U_821,c_Groups_Ozero__class_Ozero(U_821),U_823)
| ~ c_Orderings_Oord__class_Oless(U_821,c_Groups_Ozero__class_Ozero(U_821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_823))
| ~ class_Rings_Olinordered__semiring__strict(U_821) ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
| ~ 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_288_2,plain,
! [U_827,U_826,U_825,U_824] :
( ( ( c_Orderings_Oord__class_Oless(U_824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_827))
| ~ c_Orderings_Oord__class_Oless(U_824,U_827,U_826) )
& ( c_Orderings_Oord__class_Oless(U_824,U_827,U_826)
| ~ c_Orderings_Oord__class_Oless(U_824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_827)) ) )
| ~ c_Orderings_Oord__class_Oless(U_824,U_825,c_Groups_Ozero__class_Ozero(U_824))
| ~ class_Rings_Olinordered__ring__strict(U_824) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( c_Orderings_Oord__class_Oless(U_824,U_827,U_826)
| ~ c_Orderings_Oord__class_Oless(U_824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_827))
| ~ c_Orderings_Oord__class_Oless(U_824,U_825,c_Groups_Ozero__class_Ozero(U_824))
| ~ class_Rings_Olinordered__ring__strict(U_824) ),
inference(clausify,[status(thm)],[f_288_2]) ).
cnf(f_288_4,plain,
( c_Orderings_Oord__class_Oless(U_824,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_826),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_827))
| ~ c_Orderings_Oord__class_Oless(U_824,U_827,U_826)
| ~ c_Orderings_Oord__class_Oless(U_824,U_825,c_Groups_Ozero__class_Ozero(U_824))
| ~ class_Rings_Olinordered__ring__strict(U_824) ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__pos]) ).
fof(f_289_2,plain,
! [U_830,U_829,U_828] :
( c_Orderings_Oord__class_Oless(U_828,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_828),U_829),U_830),c_Groups_Ozero__class_Ozero(U_828))
| ~ c_Orderings_Oord__class_Oless(U_828,c_Groups_Ozero__class_Ozero(U_828),U_830)
| ~ c_Orderings_Oord__class_Oless(U_828,U_829,c_Groups_Ozero__class_Ozero(U_828))
| ~ class_Rings_Olinordered__semiring__strict(U_828) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( c_Orderings_Oord__class_Oless(U_828,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_828),U_829),U_830),c_Groups_Ozero__class_Ozero(U_828))
| ~ c_Orderings_Oord__class_Oless(U_828,c_Groups_Ozero__class_Ozero(U_828),U_830)
| ~ c_Orderings_Oord__class_Oless(U_828,U_829,c_Groups_Ozero__class_Ozero(U_828))
| ~ class_Rings_Olinordered__semiring__strict(U_828) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__neg__neg]) ).
fof(f_290_2,plain,
! [U_833,U_832,U_831] :
( c_Orderings_Oord__class_Oless(U_831,c_Groups_Ozero__class_Ozero(U_831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_831),U_832),U_833))
| ~ c_Orderings_Oord__class_Oless(U_831,U_833,c_Groups_Ozero__class_Ozero(U_831))
| ~ c_Orderings_Oord__class_Oless(U_831,U_832,c_Groups_Ozero__class_Ozero(U_831))
| ~ class_Rings_Olinordered__ring__strict(U_831) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( c_Orderings_Oord__class_Oless(U_831,c_Groups_Ozero__class_Ozero(U_831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_831),U_832),U_833))
| ~ c_Orderings_Oord__class_Oless(U_831,U_833,c_Groups_Ozero__class_Ozero(U_831))
| ~ c_Orderings_Oord__class_Oless(U_831,U_832,c_Groups_Ozero__class_Ozero(U_831))
| ~ class_Rings_Olinordered__ring__strict(U_831) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono]) ).
fof(f_291_2,plain,
! [U_837,U_836,U_835,U_834] :
( c_Orderings_Oord__class_Oless(U_834,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_834),U_835),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_834),U_836),U_837))
| ~ c_Orderings_Oord__class_Oless(U_834,c_Groups_Ozero__class_Ozero(U_834),U_837)
| ~ c_Orderings_Oord__class_Oless(U_834,U_835,U_836)
| ~ class_Rings_Olinordered__semiring__strict(U_834) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( c_Orderings_Oord__class_Oless(U_834,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_834),U_835),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_834),U_836),U_837))
| ~ c_Orderings_Oord__class_Oless(U_834,c_Groups_Ozero__class_Ozero(U_834),U_837)
| ~ c_Orderings_Oord__class_Oless(U_834,U_835,U_836)
| ~ class_Rings_Olinordered__semiring__strict(U_834) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono]) ).
fof(f_292_2,plain,
! [U_841,U_840,U_839,U_838] :
( c_Orderings_Oord__class_Oless(U_838,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_838),U_841),U_839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_838),U_841),U_840))
| ~ c_Orderings_Oord__class_Oless(U_838,c_Groups_Ozero__class_Ozero(U_838),U_841)
| ~ c_Orderings_Oord__class_Oless(U_838,U_839,U_840)
| ~ class_Rings_Olinordered__semiring__strict(U_838) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
( c_Orderings_Oord__class_Oless(U_838,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_838),U_841),U_839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_838),U_841),U_840))
| ~ c_Orderings_Oord__class_Oless(U_838,c_Groups_Ozero__class_Ozero(U_838),U_841)
| ~ c_Orderings_Oord__class_Oless(U_838,U_839,U_840)
| ~ class_Rings_Olinordered__semiring__strict(U_838) ),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__comm__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono]) ).
fof(f_293_2,plain,
! [U_845,U_844,U_843,U_842] :
( c_Orderings_Oord__class_Oless(U_842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_842),U_845),U_843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_842),U_845),U_844))
| ~ c_Orderings_Oord__class_Oless(U_842,c_Groups_Ozero__class_Ozero(U_842),U_845)
| ~ c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_842) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
( c_Orderings_Oord__class_Oless(U_842,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_842),U_845),U_843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_842),U_845),U_844))
| ~ c_Orderings_Oord__class_Oless(U_842,c_Groups_Ozero__class_Ozero(U_842),U_845)
| ~ c_Orderings_Oord__class_Oless(U_842,U_843,U_844)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_842) ),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg]) ).
fof(f_294_2,plain,
! [U_849,U_848,U_847,U_846] :
( c_Orderings_Oord__class_Oless(U_846,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_846),U_848),U_849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_846),U_847),U_849))
| ~ c_Orderings_Oord__class_Oless(U_846,U_849,c_Groups_Ozero__class_Ozero(U_846))
| ~ c_Orderings_Oord__class_Oless(U_846,U_847,U_848)
| ~ class_Rings_Olinordered__ring__strict(U_846) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( c_Orderings_Oord__class_Oless(U_846,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_846),U_848),U_849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_846),U_847),U_849))
| ~ c_Orderings_Oord__class_Oless(U_846,U_849,c_Groups_Ozero__class_Ozero(U_846))
| ~ c_Orderings_Oord__class_Oless(U_846,U_847,U_848)
| ~ class_Rings_Olinordered__ring__strict(U_846) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg]) ).
fof(f_295_2,plain,
! [U_853,U_852,U_851,U_850] :
( c_Orderings_Oord__class_Oless(U_850,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_853),U_852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_853),U_851))
| ~ c_Orderings_Oord__class_Oless(U_850,U_853,c_Groups_Ozero__class_Ozero(U_850))
| ~ c_Orderings_Oord__class_Oless(U_850,U_851,U_852)
| ~ class_Rings_Olinordered__ring__strict(U_850) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
( c_Orderings_Oord__class_Oless(U_850,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_853),U_852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_853),U_851))
| ~ c_Orderings_Oord__class_Oless(U_850,U_853,c_Groups_Ozero__class_Ozero(U_850))
| ~ c_Orderings_Oord__class_Oless(U_850,U_851,U_852)
| ~ class_Rings_Olinordered__ring__strict(U_850) ),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_1,plain,
! [T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__one__less__zero]) ).
fof(f_296_2,plain,
! [U_854] :
( ~ c_Orderings_Oord__class_Oless(U_854,c_Groups_Oone__class_Oone(U_854),c_Groups_Ozero__class_Ozero(U_854))
| ~ class_Rings_Olinordered__semidom(U_854) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_854,c_Groups_Oone__class_Oone(U_854),c_Groups_Ozero__class_Ozero(U_854))
| ~ class_Rings_Olinordered__semidom(U_854) ),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__one]) ).
fof(f_297_2,plain,
! [U_855] :
( c_Orderings_Oord__class_Oless(U_855,c_Groups_Ozero__class_Ozero(U_855),c_Groups_Oone__class_Oone(U_855))
| ~ class_Rings_Olinordered__semidom(U_855) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
( c_Orderings_Oord__class_Oless(U_855,c_Groups_Ozero__class_Ozero(U_855),c_Groups_Oone__class_Oone(U_855))
| ~ class_Rings_Olinordered__semidom(U_855) ),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).
fof(f_298_2,plain,
! [U_857,U_856] :
( ( ( c_Orderings_Oord__class_Oless(U_856,c_Groups_Ozero__class_Ozero(U_856),c_Groups_Ouminus__class_Ouminus(U_856,U_857))
| ~ c_Orderings_Oord__class_Oless(U_856,U_857,c_Groups_Ozero__class_Ozero(U_856)) )
& ( c_Orderings_Oord__class_Oless(U_856,U_857,c_Groups_Ozero__class_Ozero(U_856))
| ~ c_Orderings_Oord__class_Oless(U_856,c_Groups_Ozero__class_Ozero(U_856),c_Groups_Ouminus__class_Ouminus(U_856,U_857)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_856) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( c_Orderings_Oord__class_Oless(U_856,U_857,c_Groups_Ozero__class_Ozero(U_856))
| ~ c_Orderings_Oord__class_Oless(U_856,c_Groups_Ozero__class_Ozero(U_856),c_Groups_Ouminus__class_Ouminus(U_856,U_857))
| ~ class_Groups_Oordered__ab__group__add(U_856) ),
inference(clausify,[status(thm)],[f_298_2]) ).
cnf(f_298_4,plain,
( c_Orderings_Oord__class_Oless(U_856,c_Groups_Ozero__class_Ozero(U_856),c_Groups_Ouminus__class_Ouminus(U_856,U_857))
| ~ c_Orderings_Oord__class_Oless(U_856,U_857,c_Groups_Ozero__class_Ozero(U_856))
| ~ class_Groups_Oordered__ab__group__add(U_856) ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).
fof(f_299_2,plain,
! [U_859,U_858] :
( ( ( c_Orderings_Oord__class_Oless(U_858,c_Groups_Ouminus__class_Ouminus(U_858,U_859),c_Groups_Ozero__class_Ozero(U_858))
| ~ c_Orderings_Oord__class_Oless(U_858,c_Groups_Ozero__class_Ozero(U_858),U_859) )
& ( c_Orderings_Oord__class_Oless(U_858,c_Groups_Ozero__class_Ozero(U_858),U_859)
| ~ c_Orderings_Oord__class_Oless(U_858,c_Groups_Ouminus__class_Ouminus(U_858,U_859),c_Groups_Ozero__class_Ozero(U_858)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_858) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( c_Orderings_Oord__class_Oless(U_858,c_Groups_Ozero__class_Ozero(U_858),U_859)
| ~ c_Orderings_Oord__class_Oless(U_858,c_Groups_Ouminus__class_Ouminus(U_858,U_859),c_Groups_Ozero__class_Ozero(U_858))
| ~ class_Groups_Oordered__ab__group__add(U_858) ),
inference(clausify,[status(thm)],[f_299_2]) ).
cnf(f_299_4,plain,
( c_Orderings_Oord__class_Oless(U_858,c_Groups_Ouminus__class_Ouminus(U_858,U_859),c_Groups_Ozero__class_Ozero(U_858))
| ~ c_Orderings_Oord__class_Oless(U_858,c_Groups_Ozero__class_Ozero(U_858),U_859)
| ~ class_Groups_Oordered__ab__group__add(U_858) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).
fof(f_300_2,plain,
! [U_861,U_860] :
( ( ( c_Orderings_Oord__class_Oless(U_860,c_Groups_Ouminus__class_Ouminus(U_860,U_861),U_861)
| ~ c_Orderings_Oord__class_Oless(U_860,c_Groups_Ozero__class_Ozero(U_860),U_861) )
& ( c_Orderings_Oord__class_Oless(U_860,c_Groups_Ozero__class_Ozero(U_860),U_861)
| ~ c_Orderings_Oord__class_Oless(U_860,c_Groups_Ouminus__class_Ouminus(U_860,U_861),U_861) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_860) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
( c_Orderings_Oord__class_Oless(U_860,c_Groups_Ozero__class_Ozero(U_860),U_861)
| ~ c_Orderings_Oord__class_Oless(U_860,c_Groups_Ouminus__class_Ouminus(U_860,U_861),U_861)
| ~ class_Groups_Olinordered__ab__group__add(U_860) ),
inference(clausify,[status(thm)],[f_300_2]) ).
cnf(f_300_4,plain,
( c_Orderings_Oord__class_Oless(U_860,c_Groups_Ouminus__class_Ouminus(U_860,U_861),U_861)
| ~ c_Orderings_Oord__class_Oless(U_860,c_Groups_Ozero__class_Ozero(U_860),U_861)
| ~ class_Groups_Olinordered__ab__group__add(U_860) ),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).
fof(f_301_2,plain,
! [U_863,U_862] :
( ( ( c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ouminus__class_Ouminus(U_862,U_863))
| ~ c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ozero__class_Ozero(U_862)) )
& ( c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ozero__class_Ozero(U_862))
| ~ c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ouminus__class_Ouminus(U_862,U_863)) ) )
| ~ class_Rings_Olinordered__idom(U_862) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
( c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ozero__class_Ozero(U_862))
| ~ c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ouminus__class_Ouminus(U_862,U_863))
| ~ class_Rings_Olinordered__idom(U_862) ),
inference(clausify,[status(thm)],[f_301_2]) ).
cnf(f_301_4,plain,
( c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ouminus__class_Ouminus(U_862,U_863))
| ~ c_Orderings_Oord__class_Oless(U_862,U_863,c_Groups_Ozero__class_Ozero(U_862))
| ~ class_Rings_Olinordered__idom(U_862) ),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_1,plain,
! [V_n,V_m,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__1__mult]) ).
fof(f_302_2,plain,
! [U_866,U_865,U_864] :
( c_Orderings_Oord__class_Oless(U_864,c_Groups_Oone__class_Oone(U_864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_864),U_865),U_866))
| ~ c_Orderings_Oord__class_Oless(U_864,c_Groups_Oone__class_Oone(U_864),U_866)
| ~ c_Orderings_Oord__class_Oless(U_864,c_Groups_Oone__class_Oone(U_864),U_865)
| ~ class_Rings_Olinordered__semidom(U_864) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( c_Orderings_Oord__class_Oless(U_864,c_Groups_Oone__class_Oone(U_864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_864),U_865),U_866))
| ~ c_Orderings_Oord__class_Oless(U_864,c_Groups_Oone__class_Oone(U_864),U_866)
| ~ c_Orderings_Oord__class_Oless(U_864,c_Groups_Oone__class_Oone(U_864),U_865)
| ~ class_Rings_Olinordered__semidom(U_864) ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power]) ).
fof(f_303_2,plain,
! [U_869,U_868,U_867] :
( c_Orderings_Oord__class_Oless(U_867,c_Groups_Ozero__class_Ozero(U_867),hAPP(hAPP(c_Power_Opower__class_Opower(U_867),U_868),U_869))
| ~ c_Orderings_Oord__class_Oless(U_867,c_Groups_Ozero__class_Ozero(U_867),U_868)
| ~ class_Rings_Olinordered__semidom(U_867) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
( c_Orderings_Oord__class_Oless(U_867,c_Groups_Ozero__class_Ozero(U_867),hAPP(hAPP(c_Power_Opower__class_Opower(U_867),U_868),U_869))
| ~ c_Orderings_Oord__class_Oless(U_867,c_Groups_Ozero__class_Ozero(U_867),U_868)
| ~ class_Rings_Olinordered__semidom(U_867) ),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [V_nb_2,V_m_2,V_aa_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_nb_2)
| V_m_2 != V_nb_2 )
& ( V_m_2 = V_nb_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_aa_2),V_nb_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_aa_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).
fof(f_304_2,plain,
! [U_873,U_872,U_871,U_870] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_872) = hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_873)
| U_872 != U_873 )
& ( U_872 = U_873
| hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_872) != hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_873) ) )
| ~ c_Orderings_Oord__class_Oless(U_870,c_Groups_Oone__class_Oone(U_870),U_871)
| ~ class_Rings_Olinordered__semidom(U_870) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
cnf(f_304_3,plain,
( U_872 = U_873
| hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_872) != hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_873)
| ~ c_Orderings_Oord__class_Oless(U_870,c_Groups_Oone__class_Oone(U_870),U_871)
| ~ class_Rings_Olinordered__semidom(U_870) ),
inference(clausify,[status(thm)],[f_304_2]) ).
cnf(f_304_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_872) = hAPP(hAPP(c_Power_Opower__class_Opower(U_870),U_871),U_873)
| U_872 != U_873
| ~ c_Orderings_Oord__class_Oless(U_870,c_Groups_Oone__class_Oone(U_870),U_871)
| ~ class_Rings_Olinordered__semidom(U_870) ),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_one__less__mult]) ).
fof(f_305_2,plain,
! [U_875,U_874] :
( 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_875),U_874))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_875)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_874) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_875),U_874))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_875)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_874) ),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m]) ).
fof(f_306_2,plain,
! [U_877,U_876] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_876,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_876),U_877))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_877)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_876) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_876,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_876),U_877))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_877)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_876) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n]) ).
fof(f_307_2,plain,
! [U_879,U_878] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_878,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_879),U_878))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_879)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_878) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_878,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_879),U_878))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_879)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_878) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [V_nb_2,V_k_2,V_m_2] :
( ( 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_nb_2),V_k_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).
fof(f_308_2,plain,
! [U_882,U_881,U_880] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_880),U_881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_882),U_881))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_880,U_882)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_881) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_880,U_882)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_881)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_880),U_881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_882),U_881)) ) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
( ! [U_888,U_886,U_884] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_884),U_886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_888),U_886))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_884,U_888)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_886) ) )
& ! [U_887,U_885,U_883] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_883,U_887)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_885)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_883),U_885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_887),U_885)) ) ),
inference(miniscope,[status(thm)],[f_308_2]) ).
cnf(f_308_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_883,U_887)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_885)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_883),U_885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_887),U_885)) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_886)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_884),U_886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_888),U_886)) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_884,U_888)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_884),U_886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_888),U_886)) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).
fof(f_309_2,plain,
! [U_891,U_890,U_889] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_889),U_890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_889),U_891))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_890,U_891)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_889) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_890,U_891)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_889)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_889),U_890),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_889),U_891)) ) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
( ! [U_897,U_895,U_893] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_893),U_895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_893),U_897))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_895,U_897)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_893) ) )
& ! [U_896,U_894,U_892] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_894,U_896)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_896)) ) ),
inference(miniscope,[status(thm)],[f_309_2]) ).
cnf(f_309_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_894,U_896)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_896)) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_893)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_893),U_895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_893),U_897)) ),
inference(clausify,[status(thm)],[f_309_3]) ).
cnf(f_309_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_895,U_897)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_893),U_895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_893),U_897)) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_1,plain,
! [V_nb_2,V_m_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2)),V_m_2))
| V_nb_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2)),V_m_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1]) ).
fof(f_310_2,plain,
! [U_899,U_898] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_898),U_899)),U_898))
| U_899 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_899 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_898),U_899)),U_898)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_898) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
( U_899 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_898),U_899)),U_898))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_898) ),
inference(clausify,[status(thm)],[f_310_2]) ).
cnf(f_310_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_898),U_899)),U_898))
| U_899 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_898) ),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
! [V_nb_2,V_m_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_m_2)),V_m_2))
| V_nb_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_nb_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_m_2)),V_m_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2]) ).
fof(f_311_2,plain,
! [U_901,U_900] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_900)),U_900))
| U_901 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_901 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_900)),U_900)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_900) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( U_901 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_900)),U_900))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_900) ),
inference(clausify,[status(thm)],[f_311_2]) ).
cnf(f_311_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_900)),U_900))
| U_901 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_900) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le]) ).
fof(f_312_2,plain,
! [U_904,U_903,U_902] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_903,U_904)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_902)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_902),U_903)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_902),U_904))) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
cnf(f_312_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_903,U_904)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_902)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_902),U_903)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_902),U_904))) ),
inference(clausify,[status(thm)],[f_312_2]) ).
fof(f_313_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
| ~ 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_313_2,plain,
! [U_908,U_907,U_906,U_905] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_908))
| ~ c_Orderings_Oord__class_Oless__eq(U_905,U_907,U_908) )
& ( c_Orderings_Oord__class_Oless__eq(U_905,U_907,U_908)
| ~ c_Orderings_Oord__class_Oless__eq(U_905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_908)) ) )
| ~ c_Orderings_Oord__class_Oless(U_905,c_Groups_Ozero__class_Ozero(U_905),U_906)
| ~ class_Rings_Olinordered__ring__strict(U_905) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_905,U_907,U_908)
| ~ c_Orderings_Oord__class_Oless__eq(U_905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_908))
| ~ c_Orderings_Oord__class_Oless(U_905,c_Groups_Ozero__class_Ozero(U_905),U_906)
| ~ class_Rings_Olinordered__ring__strict(U_905) ),
inference(clausify,[status(thm)],[f_313_2]) ).
cnf(f_313_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_905,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_905),U_906),U_908))
| ~ c_Orderings_Oord__class_Oless__eq(U_905,U_907,U_908)
| ~ c_Orderings_Oord__class_Oless(U_905,c_Groups_Ozero__class_Ozero(U_905),U_906)
| ~ class_Rings_Olinordered__ring__strict(U_905) ),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_aa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2)) ) )
| ~ 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_314_2,plain,
! [U_912,U_911,U_910,U_909] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_912))
| ~ c_Orderings_Oord__class_Oless__eq(U_909,U_912,U_911) )
& ( c_Orderings_Oord__class_Oless__eq(U_909,U_912,U_911)
| ~ c_Orderings_Oord__class_Oless__eq(U_909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_912)) ) )
| ~ c_Orderings_Oord__class_Oless(U_909,U_910,c_Groups_Ozero__class_Ozero(U_909))
| ~ class_Rings_Olinordered__ring__strict(U_909) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_909,U_912,U_911)
| ~ c_Orderings_Oord__class_Oless__eq(U_909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_912))
| ~ c_Orderings_Oord__class_Oless(U_909,U_910,c_Groups_Ozero__class_Ozero(U_909))
| ~ class_Rings_Olinordered__ring__strict(U_909) ),
inference(clausify,[status(thm)],[f_314_2]) ).
cnf(f_314_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_909,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_909),U_910),U_912))
| ~ c_Orderings_Oord__class_Oless__eq(U_909,U_912,U_911)
| ~ c_Orderings_Oord__class_Oless(U_909,U_910,c_Groups_Ozero__class_Ozero(U_909))
| ~ class_Rings_Olinordered__ring__strict(U_909) ),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__mono]) ).
fof(f_315_2,plain,
! [U_917,U_916,U_915,U_914,U_913] :
( c_Orderings_Oord__class_Oless(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917))
| ~ c_Orderings_Oord__class_Oless__eq(U_913,c_Groups_Ozero__class_Ozero(U_913),U_916)
| ~ c_Orderings_Oord__class_Oless(U_913,c_Groups_Ozero__class_Ozero(U_913),U_915)
| ~ c_Orderings_Oord__class_Oless(U_913,U_916,U_917)
| ~ c_Orderings_Oord__class_Oless(U_913,U_914,U_915)
| ~ class_Rings_Olinordered__semiring__strict(U_913) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
( c_Orderings_Oord__class_Oless(U_913,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_914),U_916),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_913),U_915),U_917))
| ~ c_Orderings_Oord__class_Oless__eq(U_913,c_Groups_Ozero__class_Ozero(U_913),U_916)
| ~ c_Orderings_Oord__class_Oless(U_913,c_Groups_Ozero__class_Ozero(U_913),U_915)
| ~ c_Orderings_Oord__class_Oless(U_913,U_916,U_917)
| ~ c_Orderings_Oord__class_Oless(U_913,U_914,U_915)
| ~ class_Rings_Olinordered__semiring__strict(U_913) ),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H]) ).
fof(f_316_2,plain,
! [U_922,U_921,U_920,U_919,U_918] :
( c_Orderings_Oord__class_Oless(U_918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_920),U_922))
| ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_921)
| ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919)
| ~ c_Orderings_Oord__class_Oless(U_918,U_921,U_922)
| ~ c_Orderings_Oord__class_Oless(U_918,U_919,U_920)
| ~ class_Rings_Olinordered__semiring__strict(U_918) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( c_Orderings_Oord__class_Oless(U_918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_920),U_922))
| ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_921)
| ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919)
| ~ c_Orderings_Oord__class_Oless(U_918,U_921,U_922)
| ~ c_Orderings_Oord__class_Oless(U_918,U_919,U_920)
| ~ class_Rings_Olinordered__semiring__strict(U_918) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less]) ).
fof(f_317_2,plain,
! [U_927,U_926,U_925,U_924,U_923] :
( c_Orderings_Oord__class_Oless(U_923,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_923),U_924),U_926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_923),U_925),U_927))
| ~ c_Orderings_Oord__class_Oless(U_923,c_Groups_Ozero__class_Ozero(U_923),U_926)
| ~ c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923),U_924)
| ~ c_Orderings_Oord__class_Oless__eq(U_923,U_926,U_927)
| ~ c_Orderings_Oord__class_Oless(U_923,U_924,U_925)
| ~ class_Rings_Olinordered__semiring__strict(U_923) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( c_Orderings_Oord__class_Oless(U_923,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_923),U_924),U_926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_923),U_925),U_927))
| ~ c_Orderings_Oord__class_Oless(U_923,c_Groups_Ozero__class_Ozero(U_923),U_926)
| ~ c_Orderings_Oord__class_Oless__eq(U_923,c_Groups_Ozero__class_Ozero(U_923),U_924)
| ~ c_Orderings_Oord__class_Oless__eq(U_923,U_926,U_927)
| ~ c_Orderings_Oord__class_Oless(U_923,U_924,U_925)
| ~ class_Rings_Olinordered__semiring__strict(U_923) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less]) ).
fof(f_318_2,plain,
! [U_932,U_931,U_930,U_929,U_928] :
( c_Orderings_Oord__class_Oless(U_928,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_928),U_929),U_931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_928),U_930),U_932))
| ~ c_Orderings_Oord__class_Oless__eq(U_928,c_Groups_Ozero__class_Ozero(U_928),U_931)
| ~ c_Orderings_Oord__class_Oless(U_928,c_Groups_Ozero__class_Ozero(U_928),U_929)
| ~ c_Orderings_Oord__class_Oless(U_928,U_931,U_932)
| ~ c_Orderings_Oord__class_Oless__eq(U_928,U_929,U_930)
| ~ class_Rings_Olinordered__semiring__strict(U_928) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
cnf(f_318_3,plain,
( c_Orderings_Oord__class_Oless(U_928,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_928),U_929),U_931),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_928),U_930),U_932))
| ~ c_Orderings_Oord__class_Oless__eq(U_928,c_Groups_Ozero__class_Ozero(U_928),U_931)
| ~ c_Orderings_Oord__class_Oless(U_928,c_Groups_Ozero__class_Ozero(U_928),U_929)
| ~ c_Orderings_Oord__class_Oless(U_928,U_931,U_932)
| ~ c_Orderings_Oord__class_Oless__eq(U_928,U_929,U_930)
| ~ class_Rings_Olinordered__semiring__strict(U_928) ),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less]) ).
fof(f_319_2,plain,
! [U_936,U_935,U_934,U_933] :
( c_Orderings_Oord__class_Oless(U_933,U_934,U_936)
| ~ c_Orderings_Oord__class_Oless__eq(U_933,c_Groups_Ozero__class_Ozero(U_933),U_935)
| ~ c_Orderings_Oord__class_Oless(U_933,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_933),U_934),U_935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_933),U_936),U_935))
| ~ class_Rings_Olinordered__semiring(U_933) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
cnf(f_319_3,plain,
( c_Orderings_Oord__class_Oless(U_933,U_934,U_936)
| ~ c_Orderings_Oord__class_Oless__eq(U_933,c_Groups_Ozero__class_Ozero(U_933),U_935)
| ~ c_Orderings_Oord__class_Oless(U_933,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_933),U_934),U_935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_933),U_936),U_935))
| ~ class_Rings_Olinordered__semiring(U_933) ),
inference(clausify,[status(thm)],[f_319_2]) ).
fof(f_320_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right]) ).
fof(f_320_2,plain,
! [U_940,U_939,U_938,U_937] :
( c_Orderings_Oord__class_Oless(U_937,U_938,U_940)
| ~ c_Orderings_Oord__class_Oless__eq(U_937,c_Groups_Ozero__class_Ozero(U_937),U_939)
| ~ c_Orderings_Oord__class_Oless(U_937,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_937),U_938),U_939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_937),U_940),U_939))
| ~ class_Rings_Olinordered__semiring__strict(U_937) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( c_Orderings_Oord__class_Oless(U_937,U_938,U_940)
| ~ c_Orderings_Oord__class_Oless__eq(U_937,c_Groups_Ozero__class_Ozero(U_937),U_939)
| ~ c_Orderings_Oord__class_Oless(U_937,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_937),U_938),U_939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_937),U_940),U_939))
| ~ class_Rings_Olinordered__semiring__strict(U_937) ),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less]) ).
fof(f_321_2,plain,
! [U_944,U_943,U_942,U_941] :
( c_Orderings_Oord__class_Oless(U_941,U_943,U_944)
| ~ c_Orderings_Oord__class_Oless__eq(U_941,c_Groups_Ozero__class_Ozero(U_941),U_942)
| ~ c_Orderings_Oord__class_Oless(U_941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_941),U_942),U_943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_941),U_942),U_944))
| ~ class_Rings_Olinordered__semiring(U_941) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( c_Orderings_Oord__class_Oless(U_941,U_943,U_944)
| ~ c_Orderings_Oord__class_Oless__eq(U_941,c_Groups_Ozero__class_Ozero(U_941),U_942)
| ~ c_Orderings_Oord__class_Oless(U_941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_941),U_942),U_943),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_941),U_942),U_944))
| ~ class_Rings_Olinordered__semiring(U_941) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left]) ).
fof(f_322_2,plain,
! [U_948,U_947,U_946,U_945] :
( c_Orderings_Oord__class_Oless(U_945,U_947,U_948)
| ~ c_Orderings_Oord__class_Oless__eq(U_945,c_Groups_Ozero__class_Ozero(U_945),U_946)
| ~ c_Orderings_Oord__class_Oless(U_945,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_945),U_946),U_947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_945),U_946),U_948))
| ~ class_Rings_Olinordered__semiring__strict(U_945) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( c_Orderings_Oord__class_Oless(U_945,U_947,U_948)
| ~ c_Orderings_Oord__class_Oless__eq(U_945,c_Groups_Ozero__class_Ozero(U_945),U_946)
| ~ c_Orderings_Oord__class_Oless(U_945,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_945),U_946),U_947),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_945),U_946),U_948))
| ~ class_Rings_Olinordered__semiring__strict(U_945) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le]) ).
fof(f_323_2,plain,
! [U_952,U_951,U_950,U_949] :
( c_Orderings_Oord__class_Oless__eq(U_949,U_950,U_952)
| ~ c_Orderings_Oord__class_Oless(U_949,c_Groups_Ozero__class_Ozero(U_949),U_951)
| ~ c_Orderings_Oord__class_Oless__eq(U_949,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_952),U_951))
| ~ class_Rings_Olinordered__semiring__strict(U_949) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_949,U_950,U_952)
| ~ c_Orderings_Oord__class_Oless(U_949,c_Groups_Ozero__class_Ozero(U_949),U_951)
| ~ c_Orderings_Oord__class_Oless__eq(U_949,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_952),U_951))
| ~ class_Rings_Olinordered__semiring__strict(U_949) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le]) ).
fof(f_324_2,plain,
! [U_956,U_955,U_954,U_953] :
( c_Orderings_Oord__class_Oless__eq(U_953,U_955,U_956)
| ~ c_Orderings_Oord__class_Oless(U_953,c_Groups_Ozero__class_Ozero(U_953),U_954)
| ~ c_Orderings_Oord__class_Oless__eq(U_953,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),U_955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),U_956))
| ~ class_Rings_Olinordered__semiring__strict(U_953) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
cnf(f_324_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_953,U_955,U_956)
| ~ c_Orderings_Oord__class_Oless(U_953,c_Groups_Ozero__class_Ozero(U_953),U_954)
| ~ c_Orderings_Oord__class_Oless__eq(U_953,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),U_955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),U_956))
| ~ class_Rings_Olinordered__semiring__strict(U_953) ),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).
fof(f_325_2,plain,
! [U_960,U_959,U_958,U_957] :
( c_Orderings_Oord__class_Oless(U_957,U_958,U_960)
| ~ c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),U_960)
| ~ c_Orderings_Oord__class_Oless(U_957,hAPP(hAPP(c_Power_Opower__class_Opower(U_957),U_958),U_959),hAPP(hAPP(c_Power_Opower__class_Opower(U_957),U_960),U_959))
| ~ class_Rings_Olinordered__semidom(U_957) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( c_Orderings_Oord__class_Oless(U_957,U_958,U_960)
| ~ c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),U_960)
| ~ c_Orderings_Oord__class_Oless(U_957,hAPP(hAPP(c_Power_Opower__class_Opower(U_957),U_958),U_959),hAPP(hAPP(c_Power_Opower__class_Opower(U_957),U_960),U_959))
| ~ class_Rings_Olinordered__semidom(U_957) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma]) ).
fof(f_326_2,plain,
! [U_963,U_962,U_961] :
( c_Orderings_Oord__class_Oless(U_961,c_Groups_Oone__class_Oone(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),hAPP(hAPP(c_Power_Opower__class_Opower(U_961),U_962),U_963)))
| ~ c_Orderings_Oord__class_Oless(U_961,c_Groups_Oone__class_Oone(U_961),U_962)
| ~ class_Rings_Olinordered__semidom(U_961) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( c_Orderings_Oord__class_Oless(U_961,c_Groups_Oone__class_Oone(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),hAPP(hAPP(c_Power_Opower__class_Opower(U_961),U_962),U_963)))
| ~ c_Orderings_Oord__class_Oless(U_961,c_Groups_Oone__class_Oone(U_961),U_962)
| ~ class_Rings_Olinordered__semidom(U_961) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc]) ).
fof(f_327_2,plain,
! [U_966,U_965,U_964] :
( c_Orderings_Oord__class_Oless(U_964,hAPP(hAPP(c_Power_Opower__class_Opower(U_964),U_965),U_966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_964),U_965),hAPP(hAPP(c_Power_Opower__class_Opower(U_964),U_965),U_966)))
| ~ c_Orderings_Oord__class_Oless(U_964,c_Groups_Oone__class_Oone(U_964),U_965)
| ~ class_Rings_Olinordered__semidom(U_964) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( c_Orderings_Oord__class_Oless(U_964,hAPP(hAPP(c_Power_Opower__class_Opower(U_964),U_965),U_966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_964),U_965),hAPP(hAPP(c_Power_Opower__class_Opower(U_964),U_965),U_966)))
| ~ c_Orderings_Oord__class_Oless(U_964,c_Groups_Oone__class_Oone(U_964),U_965)
| ~ class_Rings_Olinordered__semidom(U_964) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__gt1]) ).
fof(f_328_2,plain,
! [U_969,U_968,U_967] :
( c_Orderings_Oord__class_Oless(U_967,c_Groups_Oone__class_Oone(U_967),hAPP(hAPP(c_Power_Opower__class_Opower(U_967),U_968),c_Nat_OSuc(U_969)))
| ~ c_Orderings_Oord__class_Oless(U_967,c_Groups_Oone__class_Oone(U_967),U_968)
| ~ class_Rings_Olinordered__semidom(U_967) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( c_Orderings_Oord__class_Oless(U_967,c_Groups_Oone__class_Oone(U_967),hAPP(hAPP(c_Power_Opower__class_Opower(U_967),U_968),c_Nat_OSuc(U_969)))
| ~ c_Orderings_Oord__class_Oless(U_967,c_Groups_Oone__class_Oone(U_967),U_968)
| ~ class_Rings_Olinordered__semidom(U_967) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_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_329_2,plain,
! [U_971,U_970] :
( U_970 = U_971
| c_Nat_OSuc(U_970) != c_Nat_OSuc(U_971) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( U_970 = U_971
| c_Nat_OSuc(U_970) != c_Nat_OSuc(U_971) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_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_330_2,plain,
! [U_973,U_972] :
( ( c_Nat_OSuc(U_972) = c_Nat_OSuc(U_973)
| U_972 != U_973 )
& ( U_972 = U_973
| c_Nat_OSuc(U_972) != c_Nat_OSuc(U_973) ) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
( ! [U_977,U_975] :
( c_Nat_OSuc(U_975) = c_Nat_OSuc(U_977)
| U_975 != U_977 )
& ! [U_976,U_974] :
( U_974 = U_976
| c_Nat_OSuc(U_974) != c_Nat_OSuc(U_976) ) ),
inference(miniscope,[status(thm)],[f_330_2]) ).
cnf(f_330_4,plain,
( U_974 = U_976
| c_Nat_OSuc(U_974) != c_Nat_OSuc(U_976) ),
inference(clausify,[status(thm)],[f_330_3]) ).
cnf(f_330_5,plain,
( c_Nat_OSuc(U_975) = c_Nat_OSuc(U_977)
| U_975 != U_977 ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_1,plain,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_331_2,plain,
! [U_978] : c_Nat_OSuc(U_978) != U_978,
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
c_Nat_OSuc(U_978) != U_978,
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_1,plain,
! [V_n] : V_n != c_Nat_OSuc(V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_332_2,plain,
! [U_979] : U_979 != c_Nat_OSuc(U_979),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
U_979 != c_Nat_OSuc(U_979),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).
fof(f_333_2,plain,
! [U_981,U_980] :
( U_980 = U_981
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_981,U_980)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_980,U_981) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
( U_980 = U_981
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_981,U_980)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_980,U_981) ),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_le__trans]) ).
fof(f_334_2,plain,
! [U_984,U_983,U_982] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_982,U_984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_983,U_984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_982,U_983) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
cnf(f_334_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_982,U_984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_983,U_984)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_982,U_983) ),
inference(clausify,[status(thm)],[f_334_2]) ).
fof(f_335_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| V_m != V_n ),
inference(fof_nnf,[status(thm)],[fact_eq__imp__le]) ).
fof(f_335_2,plain,
! [U_986,U_985] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_985,U_986)
| U_985 != U_986 ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_985,U_986)
| U_985 != U_986 ),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).
fof(f_336_2,plain,
! [U_988,U_987] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_988,U_987)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_987,U_988) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_988,U_987)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_987,U_988) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
inference(fof_nnf,[status(thm)],[fact_le__refl]) ).
fof(f_337_2,plain,
! [U_989] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_989,U_989),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_989,U_989),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_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_338_2,plain,
! [U_991,U_990] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_991) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_991),U_990),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_991) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_991),U_990),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_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_339_2,plain,
! [U_994,U_993,U_992] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),U_993)),U_994) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_993),U_994)),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),U_993)),U_994) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_993),U_994)),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_1,plain,
! [V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1]) ).
fof(f_340_2,plain,
! [U_995] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_995),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| U_995 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_995 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_995),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
( ! [U_997] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_997),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| U_997 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_996] :
( U_996 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_996),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_340_2]) ).
cnf(f_340_4,plain,
( U_996 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_996),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_997),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| U_997 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).
fof(f_341_2,plain,
! [U_1000,U_999,U_998] :
( c_Orderings_Oord__class_Oless(U_998,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_998),U_999),hAPP(hAPP(c_Power_Opower__class_Opower(U_998),U_999),U_1000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_998),U_999),U_1000))
| ~ c_Orderings_Oord__class_Oless(U_998,U_999,c_Groups_Oone__class_Oone(U_998))
| ~ c_Orderings_Oord__class_Oless(U_998,c_Groups_Ozero__class_Ozero(U_998),U_999)
| ~ class_Rings_Olinordered__semidom(U_998) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( c_Orderings_Oord__class_Oless(U_998,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_998),U_999),hAPP(hAPP(c_Power_Opower__class_Opower(U_998),U_999),U_1000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_998),U_999),U_1000))
| ~ c_Orderings_Oord__class_Oless(U_998,U_999,c_Groups_Oone__class_Oone(U_998))
| ~ c_Orderings_Oord__class_Oless(U_998,c_Groups_Ozero__class_Ozero(U_998),U_999)
| ~ class_Rings_Olinordered__semidom(U_998) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one]) ).
fof(f_342_2,plain,
! [U_1003,U_1002,U_1001] :
( c_Orderings_Oord__class_Oless(U_1001,hAPP(hAPP(c_Power_Opower__class_Opower(U_1001),U_1002),c_Nat_OSuc(U_1003)),c_Groups_Oone__class_Oone(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Oone__class_Oone(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,c_Groups_Ozero__class_Ozero(U_1001),U_1002)
| ~ class_Rings_Olinordered__semidom(U_1001) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( c_Orderings_Oord__class_Oless(U_1001,hAPP(hAPP(c_Power_Opower__class_Opower(U_1001),U_1002),c_Nat_OSuc(U_1003)),c_Groups_Oone__class_Oone(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Oone__class_Oone(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,c_Groups_Ozero__class_Ozero(U_1001),U_1002)
| ~ class_Rings_Olinordered__semidom(U_1001) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp]) ).
fof(f_343_2,plain,
! [U_1007,U_1006,U_1005,U_1004] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1006,U_1007)
| ~ c_Orderings_Oord__class_Oless__eq(U_1004,hAPP(hAPP(c_Power_Opower__class_Opower(U_1004),U_1005),U_1006),hAPP(hAPP(c_Power_Opower__class_Opower(U_1004),U_1005),U_1007))
| ~ c_Orderings_Oord__class_Oless(U_1004,c_Groups_Oone__class_Oone(U_1004),U_1005)
| ~ class_Rings_Olinordered__semidom(U_1004) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1006,U_1007)
| ~ c_Orderings_Oord__class_Oless__eq(U_1004,hAPP(hAPP(c_Power_Opower__class_Opower(U_1004),U_1005),U_1006),hAPP(hAPP(c_Power_Opower__class_Opower(U_1004),U_1005),U_1007))
| ~ c_Orderings_Oord__class_Oless(U_1004,c_Groups_Oone__class_Oone(U_1004),U_1005)
| ~ class_Rings_Olinordered__semidom(U_1004) ),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_344_2,plain,
! [U_1011,U_1010,U_1009,U_1008] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1008,hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1010),hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1011))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1010,U_1011) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1010,U_1011)
| ~ c_Orderings_Oord__class_Oless__eq(U_1008,hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1010),hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1011)) ) )
| ~ c_Orderings_Oord__class_Oless(U_1008,c_Groups_Oone__class_Oone(U_1008),U_1009)
| ~ class_Rings_Olinordered__semidom(U_1008) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1010,U_1011)
| ~ c_Orderings_Oord__class_Oless__eq(U_1008,hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1010),hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1011))
| ~ c_Orderings_Oord__class_Oless(U_1008,c_Groups_Oone__class_Oone(U_1008),U_1009)
| ~ class_Rings_Olinordered__semidom(U_1008) ),
inference(clausify,[status(thm)],[f_344_2]) ).
cnf(f_344_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1008,hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1010),hAPP(hAPP(c_Power_Opower__class_Opower(U_1008),U_1009),U_1011))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1010,U_1011)
| ~ c_Orderings_Oord__class_Oless(U_1008,c_Groups_Oone__class_Oone(U_1008),U_1009)
| ~ class_Rings_Olinordered__semidom(U_1008) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).
fof(f_345_2,plain,
! [U_1015,U_1014,U_1013,U_1012] :
( U_1013 = U_1015
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1014)
| ~ c_Orderings_Oord__class_Oless__eq(U_1012,c_Groups_Ozero__class_Ozero(U_1012),U_1015)
| ~ c_Orderings_Oord__class_Oless__eq(U_1012,c_Groups_Ozero__class_Ozero(U_1012),U_1013)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1012),U_1013),U_1014) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1012),U_1015),U_1014)
| ~ class_Rings_Olinordered__semidom(U_1012) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( U_1013 = U_1015
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1014)
| ~ c_Orderings_Oord__class_Oless__eq(U_1012,c_Groups_Ozero__class_Ozero(U_1012),U_1015)
| ~ c_Orderings_Oord__class_Oless__eq(U_1012,c_Groups_Ozero__class_Ozero(U_1012),U_1013)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1012),U_1013),U_1014) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1012),U_1015),U_1014)
| ~ class_Rings_Olinordered__semidom(U_1012) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_1,plain,
! [V_x,V_n,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))
| ( V_x != c_Groups_Oone__class_Oone(T_a)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) )
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power]) ).
fof(f_346_2,plain,
! [U_1018,U_1017,U_1016] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1016),U_1018),hAPP(hAPP(c_Power_Opower__class_Opower(U_1016),U_1018),U_1017)))
| ( U_1018 != c_Groups_Oone__class_Oone(U_1016)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1017) )
| ~ class_Rings_Ocomm__semiring__1(U_1016) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1017)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1016),U_1018),hAPP(hAPP(c_Power_Opower__class_Opower(U_1016),U_1018),U_1017)))
| ~ class_Rings_Ocomm__semiring__1(U_1016) ),
inference(clausify,[status(thm)],[f_346_2]) ).
cnf(f_346_4,plain,
( U_1018 != c_Groups_Oone__class_Oone(U_1016)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1016),U_1018),hAPP(hAPP(c_Power_Opower__class_Opower(U_1016),U_1018),U_1017)))
| ~ class_Rings_Ocomm__semiring__1(U_1016) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_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_347_2,plain,
! [U_1019] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1019),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1019),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_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_348_2,plain,
! [U_1020] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1020),
inference(variable_rename,[status(thm)],[f_348_1]) ).
cnf(f_348_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1020),
inference(clausify,[status(thm)],[f_348_2]) ).
fof(f_349_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_349_2,plain,
! [U_1021] : c_Nat_OSuc(U_1021) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,plain,
c_Nat_OSuc(U_1021) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_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_350_2,plain,
! [U_1022] : c_Nat_OSuc(U_1022) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_350_1]) ).
cnf(f_350_3,plain,
c_Nat_OSuc(U_1022) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_350_2]) ).
fof(f_351_1,plain,
! [V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_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_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1]) ).
fof(f_351_2,plain,
! [U_1023] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1023),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_1023 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( U_1023 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1023),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
( ! [U_1025] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1025),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_1025 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_1024] :
( U_1024 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1024),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(miniscope,[status(thm)],[f_351_2]) ).
cnf(f_351_4,plain,
( U_1024 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1024),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_351_3]) ).
cnf(f_351_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1025),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_1025 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_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_352_2,plain,
! [U_1026] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1026),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1026),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_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_353_2,plain,
! [U_1027] : c_Nat_OSuc(U_1027) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
c_Nat_OSuc(U_1027) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(f_354_2,plain,
! [U_1028] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1028),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1028),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_1,plain,
! [V_nb_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).
fof(f_355_2,plain,
! [U_1029] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1029,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1029 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1029,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
( ! [U_1031] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1031,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1031 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1030] :
( U_1030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1030,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_355_2]) ).
cnf(f_355_4,plain,
( U_1030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1030,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1031,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1031 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_355_3]) ).
fof(f_356_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__leD]) ).
fof(f_356_2,plain,
! [U_1033,U_1032] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1032,U_1033)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1032),U_1033) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1032,U_1033)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1032),U_1033) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_1,plain,
! [V_n,V_m] :
( V_m = c_Nat_OSuc(V_n)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
inference(fof_nnf,[status(thm)],[fact_le__SucE]) ).
fof(f_357_2,plain,
! [U_1035,U_1034] :
( U_1034 = c_Nat_OSuc(U_1035)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1034,U_1035)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1034,c_Nat_OSuc(U_1035)) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( U_1034 = c_Nat_OSuc(U_1035)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1034,U_1035)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1034,c_Nat_OSuc(U_1035)) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_1,plain,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).
fof(f_358_2,plain,
! [U_1037,U_1036] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1036,c_Nat_OSuc(U_1037))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1036,U_1037) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
cnf(f_358_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1036,c_Nat_OSuc(U_1037))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1036,U_1037) ),
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_1,plain,
! [V_m_2,V_nb_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),c_Nat_OSuc(V_m_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_nb_2,V_m_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),c_Nat_OSuc(V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).
fof(f_359_2,plain,
! [U_1039,U_1038] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1038),c_Nat_OSuc(U_1039))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1038,U_1039) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1038,U_1039)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1038),c_Nat_OSuc(U_1039)) ) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
( ! [U_1043,U_1041] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1041),c_Nat_OSuc(U_1043))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1041,U_1043) )
& ! [U_1042,U_1040] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1040,U_1042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1040),c_Nat_OSuc(U_1042)) ) ),
inference(miniscope,[status(thm)],[f_359_2]) ).
cnf(f_359_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1040,U_1042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1040),c_Nat_OSuc(U_1042)) ),
inference(clausify,[status(thm)],[f_359_3]) ).
cnf(f_359_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1041),c_Nat_OSuc(U_1043))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1041,U_1043) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2))
| ( V_m_2 != c_Nat_OSuc(V_nb_2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) )
& ( V_m_2 = c_Nat_OSuc(V_nb_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).
fof(f_360_2,plain,
! [U_1045,U_1044] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1044,c_Nat_OSuc(U_1045))
| ( U_1044 != c_Nat_OSuc(U_1045)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1044,U_1045) ) )
& ( U_1044 = c_Nat_OSuc(U_1045)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1044,U_1045)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1044,c_Nat_OSuc(U_1045)) ) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
( ! [U_1049,U_1047] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1047,c_Nat_OSuc(U_1049))
| ( U_1047 != c_Nat_OSuc(U_1049)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1047,U_1049) ) )
& ! [U_1048,U_1046] :
( U_1046 = c_Nat_OSuc(U_1048)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1046,U_1048)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1046,c_Nat_OSuc(U_1048)) ) ),
inference(miniscope,[status(thm)],[f_360_2]) ).
cnf(f_360_4,plain,
( U_1046 = c_Nat_OSuc(U_1048)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1046,U_1048)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1046,c_Nat_OSuc(U_1048)) ),
inference(clausify,[status(thm)],[f_360_3]) ).
cnf(f_360_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1047,U_1049)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1047,c_Nat_OSuc(U_1049)) ),
inference(clausify,[status(thm)],[f_360_3]) ).
cnf(f_360_6,plain,
( U_1047 != c_Nat_OSuc(U_1049)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1047,c_Nat_OSuc(U_1049)) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_nb_2,V_m_2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_nb_2),V_m_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).
fof(f_361_2,plain,
! [U_1051,U_1050] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1050,U_1051)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1051),U_1050) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1051),U_1050)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1050,U_1051) ) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
( ! [U_1055,U_1053] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1053,U_1055)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1055),U_1053) )
& ! [U_1054,U_1052] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1054),U_1052)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1052,U_1054) ) ),
inference(miniscope,[status(thm)],[f_361_2]) ).
cnf(f_361_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1054),U_1052)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1052,U_1054) ),
inference(clausify,[status(thm)],[f_361_3]) ).
cnf(f_361_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1053,U_1055)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1055),U_1053) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(f_362_2,plain,
! [U_1056] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1056),U_1056),
inference(variable_rename,[status(thm)],[f_362_1]) ).
cnf(f_362_3,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1056),U_1056),
inference(clausify,[status(thm)],[f_362_2]) ).
fof(f_363_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_363_2,plain,
! [U_1057] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1057) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1057) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_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_364_2,plain,
! [U_1058] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1058),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_364_1]) ).
cnf(f_364_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1058),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_364_2]) ).
fof(f_365_1,plain,
! [V_nb_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_nb_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_nb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).
fof(f_365_2,plain,
! [U_1060,U_1059] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1059),U_1060) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1059 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1059),U_1060) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
( ! [U_1064,U_1062] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1062),U_1064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1064 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1063,U_1061] :
( U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1061 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1061),U_1063) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_365_2]) ).
cnf(f_365_4,plain,
( U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1061 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1061),U_1063) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_365_3]) ).
cnf(f_365_5,plain,
( U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1062),U_1064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_365_3]) ).
cnf(f_365_6,plain,
( U_1064 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1062),U_1064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [V_nb_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_nb_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_nb_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_nb_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_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).
fof(f_366_2,plain,
! [U_1067,U_1066,U_1065] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1065),U_1066) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1065),U_1067)
| ( U_1065 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1066 != U_1067 ) )
& ( U_1065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1066 = U_1067
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1065),U_1066) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1065),U_1067) ) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
( ! [U_1073,U_1071,U_1069] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1069),U_1071) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1069),U_1073)
| ( U_1069 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1071 != U_1073 ) )
& ! [U_1072,U_1070,U_1068] :
( U_1068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1070 = U_1072
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1068),U_1070) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1068),U_1072) ) ),
inference(miniscope,[status(thm)],[f_366_2]) ).
cnf(f_366_4,plain,
( U_1068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1070 = U_1072
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1068),U_1070) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1068),U_1072) ),
inference(clausify,[status(thm)],[f_366_3]) ).
cnf(f_366_5,plain,
( U_1071 != U_1073
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1069),U_1071) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1069),U_1073) ),
inference(clausify,[status(thm)],[f_366_3]) ).
cnf(f_366_6,plain,
( U_1069 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1069),U_1071) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1069),U_1073) ),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [V_nb_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_nb_2),V_k_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_nb_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_nb_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_nb_2),V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).
fof(f_367_2,plain,
! [U_1076,U_1075,U_1074] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1074),U_1075) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1076),U_1075)
| ( U_1075 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1074 != U_1076 ) )
& ( U_1075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1074 = U_1076
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1074),U_1075) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1076),U_1075) ) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
( ! [U_1082,U_1080,U_1078] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1078),U_1080) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1082),U_1080)
| ( U_1080 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1078 != U_1082 ) )
& ! [U_1081,U_1079,U_1077] :
( U_1079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1077 = U_1081
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1077),U_1079) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1081),U_1079) ) ),
inference(miniscope,[status(thm)],[f_367_2]) ).
cnf(f_367_4,plain,
( U_1079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1077 = U_1081
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1077),U_1079) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1081),U_1079) ),
inference(clausify,[status(thm)],[f_367_3]) ).
cnf(f_367_5,plain,
( U_1078 != U_1082
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1078),U_1080) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1082),U_1080) ),
inference(clausify,[status(thm)],[f_367_3]) ).
cnf(f_367_6,plain,
( U_1080 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1078),U_1080) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1082),U_1080) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_1,plain,
! [V_nb_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_nb_2)
| V_m_2 != V_nb_2 )
& ( V_m_2 = V_nb_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_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).
fof(f_368_2,plain,
! [U_1085,U_1084,U_1083] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1083)),U_1084) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1083)),U_1085)
| U_1084 != U_1085 )
& ( U_1084 = U_1085
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1083)),U_1084) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1083)),U_1085) ) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
( ! [U_1091,U_1089] :
( ! [U_1087] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1087)),U_1089) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1087)),U_1091)
| U_1089 != U_1091 )
& ! [U_1090,U_1088] :
( ! [U_1086] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1086)),U_1088) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1086)),U_1090)
| U_1088 = U_1090 ) ),
inference(miniscope,[status(thm)],[f_368_2]) ).
cnf(f_368_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1086)),U_1088) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1086)),U_1090)
| U_1088 = U_1090 ),
inference(clausify,[status(thm)],[f_368_3]) ).
cnf(f_368_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1087)),U_1089) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1087)),U_1091)
| U_1089 != U_1091 ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_1,plain,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)),
inference(fof_nnf,[status(thm)],[fact_le__square]) ).
fof(f_369_2,plain,
! [U_1092] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1092,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1092),U_1092)),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1092,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1092),U_1092)),
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_1,plain,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
inference(fof_nnf,[status(thm)],[fact_le__cube]) ).
fof(f_370_2,plain,
! [U_1093] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1093,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1093),U_1093))),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1093,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1093),U_1093))),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono1]) ).
fof(f_371_2,plain,
! [U_1096,U_1095,U_1094] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1094),U_1096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1095),U_1096))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1094,U_1095) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1094),U_1096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1095),U_1096))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1094,U_1095) ),
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).
fof(f_372_2,plain,
! [U_1099,U_1098,U_1097] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1099),U_1097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1099),U_1098))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1097,U_1098) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1099),U_1097),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1099),U_1098))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1097,U_1098) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono]) ).
fof(f_373_2,plain,
! [U_1103,U_1102,U_1101,U_1100] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1100),U_1102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1101),U_1103))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1102,U_1103)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1100,U_1101) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1100),U_1102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1101),U_1103))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1102,U_1103)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1100,U_1101) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_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_374_2,plain,
! [U_1104] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1104) = U_1104,
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1104) = U_1104,
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_1,plain,
! [V_nb_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_nb_2)
| V_nb_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_nb_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_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).
fof(f_375_2,plain,
! [U_1106,U_1105] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1105),U_1106)
| U_1106 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1105 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1106 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1105 = 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_1105),U_1106) ) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
( ! [U_1110,U_1108] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1108),U_1110)
| U_1110 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1108 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1109,U_1107] :
( ( U_1109 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1107 = 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_1107),U_1109) ) ),
inference(miniscope,[status(thm)],[f_375_2]) ).
cnf(f_375_4,plain,
( U_1107 = 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_1107),U_1109) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_5,plain,
( U_1109 = 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_1107),U_1109) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1108),U_1110)
| U_1110 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1108 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_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_376_2,plain,
! [U_1111] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1111),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1111,
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1111),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1111,
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_1,plain,
! [V_nb_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_nb_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_nb_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_nb_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).
fof(f_377_2,plain,
! [U_1113,U_1112] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1112),U_1113) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1113 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1112 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1113 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1112 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1112),U_1113) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
( ! [U_1117,U_1115] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1115),U_1117) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1117 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1115 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1116,U_1114] :
( ( U_1116 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1114 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1114),U_1116) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_377_2]) ).
cnf(f_377_4,plain,
( U_1114 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1114),U_1116) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_377_3]) ).
cnf(f_377_5,plain,
( U_1116 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1114),U_1116) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_377_3]) ).
cnf(f_377_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1115),U_1117) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1117 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1115 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_1,plain,
! [V_nb_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_nb_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_nb_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_nb_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff]) ).
fof(f_378_2,plain,
! [U_1119,U_1118] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1118),U_1119) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1119 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1118 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_1119 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1118 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1118),U_1119) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
( ! [U_1123,U_1121] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1121),U_1123) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1123 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1121 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_1122,U_1120] :
( ( U_1122 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1120 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1120),U_1122) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_378_2]) ).
cnf(f_378_4,plain,
( U_1120 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1120),U_1122) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_378_3]) ).
cnf(f_378_5,plain,
( U_1122 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1120),U_1122) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_378_3]) ).
cnf(f_378_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1121),U_1123) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1123 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1121 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ 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_nb_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1]) ).
fof(f_379_2,plain,
! [U_1126,U_1125,U_1124] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1126))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1125,U_1126) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1125,U_1126)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1126)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1124) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
cnf(f_379_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1125,U_1126)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1126))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1124) ),
inference(clausify,[status(thm)],[f_379_2]) ).
cnf(f_379_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1124),U_1126))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1125,U_1126)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1124) ),
inference(clausify,[status(thm)],[f_379_2]) ).
fof(f_380_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1]) ).
fof(f_380_2,plain,
! [U_1129,U_1128,U_1127] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1129)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1128),U_1129)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1128),U_1129))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1129))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1127) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1128),U_1129))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1129)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1127) ),
inference(clausify,[status(thm)],[f_380_2]) ).
cnf(f_380_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1127),U_1129)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1128),U_1129))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1127) ),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_1,plain,
! [V_b_2,V_aa_2,V_nb_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_nb_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_aa_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_aa_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_nb_2))) ) )
| V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__nat]) ).
fof(f_381_2,plain,
! [U_1132,U_1131,U_1130] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1131),U_1130)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1132),U_1130)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1131),U_1132)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1131),U_1132))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1131),U_1130)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1132),U_1130))) ) )
| U_1130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1131),U_1132))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1131),U_1130)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1132),U_1130)))
| U_1130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_381_2]) ).
cnf(f_381_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1131),U_1130)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1132),U_1130)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1131),U_1132))
| U_1130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_1,plain,
! [V_b,V_n,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__nat]) ).
fof(f_382_2,plain,
! [U_1135,U_1134,U_1133] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1133),U_1135))
| U_1134 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1133),U_1134)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1135),U_1134))) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1133),U_1135))
| U_1134 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1133),U_1134)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1135),U_1134))) ),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [V_nb_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_nb_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
& V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq]) ).
fof(f_383_2,plain,
! [U_1137,U_1136] :
( ( 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_1136),U_1137))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1136)
& U_1137 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1136)
| U_1137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1136),U_1137)) ) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
( ! [U_1141,U_1139] :
( 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_1139),U_1141))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1139)
& U_1141 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1140,U_1138] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1138)
| U_1140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1138),U_1140)) ) ),
inference(miniscope,[status(thm)],[f_383_2]) ).
cnf(f_383_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1138)
| U_1140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1138),U_1140)) ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_5,plain,
( U_1141 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1139),U_1141)) ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1139)
| 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_1139),U_1141)) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2))
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_nb_2))
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj]) ).
fof(f_384_2,plain,
! [U_1144,U_1143,U_1142] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1142),U_1143)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1142),U_1144)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1143),U_1144))
& U_1142 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1143),U_1144))
| U_1142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1142),U_1143)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1142),U_1144))) ) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
( ! [U_1150,U_1148,U_1146] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1146),U_1148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1146),U_1150)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1148),U_1150))
& U_1146 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1149,U_1147,U_1145] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1147),U_1149))
| U_1145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1145),U_1147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1145),U_1149))) ) ),
inference(miniscope,[status(thm)],[f_384_2]) ).
cnf(f_384_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1147),U_1149))
| U_1145 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1145),U_1147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1145),U_1149))) ),
inference(clausify,[status(thm)],[f_384_3]) ).
cnf(f_384_5,plain,
( U_1146 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1146),U_1148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1146),U_1150))) ),
inference(clausify,[status(thm)],[f_384_3]) ).
cnf(f_384_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1148),U_1150))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1146),U_1148)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1146),U_1150))) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_1,plain,
! [V_nb_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_nb_2)
| V_m_2 != V_nb_2 )
& ( V_m_2 = V_nb_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_nb_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1]) ).
fof(f_385_2,plain,
! [U_1153,U_1152,U_1151] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1152) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1153)
| U_1152 != U_1153 )
& ( U_1152 = U_1153
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1152) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1153) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1151) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
cnf(f_385_3,plain,
( U_1152 = U_1153
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1152) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1153)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1151) ),
inference(clausify,[status(thm)],[f_385_2]) ).
cnf(f_385_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1152) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1151),U_1153)
| U_1152 != U_1153
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1151) ),
inference(clausify,[status(thm)],[f_385_2]) ).
fof(f_386_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ 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_nb_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1]) ).
fof(f_386_2,plain,
! [U_1156,U_1155,U_1154] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1156))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1155,U_1156) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1155,U_1156)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1156)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1154) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
cnf(f_386_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1155,U_1156)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1156))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1154) ),
inference(clausify,[status(thm)],[f_386_2]) ).
cnf(f_386_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1154),U_1156))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1155,U_1156)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1154) ),
inference(clausify,[status(thm)],[f_386_2]) ).
fof(f_387_1,plain,
! [V_b,V_n,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__int]) ).
fof(f_387_2,plain,
! [U_1159,U_1158,U_1157] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1157),U_1159))
| U_1158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1157),U_1158)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1159),U_1158))) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1157),U_1159))
| U_1158 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1157),U_1158)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1159),U_1158))) ),
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_1,plain,
! [V_b_2,V_aa_2,V_nb_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_nb_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_aa_2),V_nb_2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_nb_2))) ) )
| V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__int]) ).
fof(f_388_2,plain,
! [U_1162,U_1161,U_1160] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1161),U_1160)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1162),U_1160)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1161),U_1162)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1161),U_1162))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1161),U_1160)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1162),U_1160))) ) )
| U_1160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1161),U_1162))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1161),U_1160)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1162),U_1160)))
| U_1160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_388_2]) ).
cnf(f_388_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1161),U_1160)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1162),U_1160)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1161),U_1162))
| U_1160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_1,plain,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Otop__greatest]) ).
fof(f_389_2,plain,
! [U_1163] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1163),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1163),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_1,plain,
! [V_nb_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_nb_2)
| ( V_m_2 != V_nb_2
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_m_2 = V_nb_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_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).
fof(f_390_2,plain,
! [U_1166,U_1165,U_1164] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1164),U_1165) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1164),U_1166)
| ( U_1165 != U_1166
& U_1164 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1165 = U_1166
| U_1164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1164),U_1165) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1164),U_1166) ) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
( ! [U_1172,U_1170,U_1168] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1168),U_1170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1168),U_1172)
| ( U_1170 != U_1172
& U_1168 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1171,U_1169,U_1167] :
( U_1169 = U_1171
| U_1167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1167),U_1169) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1167),U_1171) ) ),
inference(miniscope,[status(thm)],[f_390_2]) ).
cnf(f_390_4,plain,
( U_1169 = U_1171
| U_1167 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1167),U_1169) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1167),U_1171) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_5,plain,
( U_1168 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1168),U_1170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1168),U_1172) ),
inference(clausify,[status(thm)],[f_390_3]) ).
cnf(f_390_6,plain,
( U_1170 != U_1172
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1168),U_1170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1168),U_1172) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_1,plain,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)),
inference(fof_nnf,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Obot__least]) ).
fof(f_391_2,plain,
! [U_1173] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1173)),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1173)),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_1,plain,
! [V_x] :
( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one]) ).
fof(f_392_2,plain,
! [U_1174] :
( U_1174 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1174 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1174,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
( U_1174 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1174 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1174,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_dvd__pos__nat]) ).
fof(f_393_2,plain,
! [U_1176,U_1175] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1176)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1176),U_1175))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1175) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1176)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_1176),U_1175))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1175) ),
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_1,plain,
! [V_p,T_a] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_psize__def]) ).
fof(f_394_2,plain,
! [U_1178,U_1177] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1177,U_1178) = c_Nat_OSuc(c_Polynomial_Odegree(U_1177,U_1178))
| U_1178 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1177)) )
& ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1177,U_1178) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1178 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1177)) ) )
| ~ class_Groups_Ozero(U_1177) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
cnf(f_394_3,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1177,U_1178) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1178 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1177))
| ~ class_Groups_Ozero(U_1177) ),
inference(clausify,[status(thm)],[f_394_2]) ).
cnf(f_394_4,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1177,U_1178) = c_Nat_OSuc(c_Polynomial_Odegree(U_1177,U_1178))
| U_1178 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1177))
| ~ class_Groups_Ozero(U_1177) ),
inference(clausify,[status(thm)],[f_394_2]) ).
fof(f_395_1,plain,
! [V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__refl]) ).
fof(f_395_2,plain,
! [U_1180,U_1179] :
( c_Orderings_Oord__class_Oless__eq(U_1179,U_1180,U_1180)
| ~ class_Orderings_Opreorder(U_1179) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1179,U_1180,U_1180)
| ~ class_Orderings_Opreorder(U_1179) ),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_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_396_2,plain,
! [U_1181] :
( c_Power_Opower__class_Opower(U_1181) = c_Power_Opower_Opower(U_1181,c_Groups_Oone__class_Oone(U_1181),c_Groups_Otimes__class_Otimes(U_1181))
| ~ class_Power_Opower(U_1181) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( c_Power_Opower__class_Opower(U_1181) = c_Power_Opower_Opower(U_1181,c_Groups_Oone__class_Oone(U_1181),c_Groups_Otimes__class_Otimes(U_1181))
| ~ class_Power_Opower(U_1181) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_1,plain,
! [V_q,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(T_a,V_p)),c_Polynomial_Odegree(T_a,V_q)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__pcompose__le]) ).
fof(f_397_2,plain,
! [U_1184,U_1183,U_1182] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1182,c_Polynomial_Opcompose(U_1182,U_1183,U_1184)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(U_1182,U_1183)),c_Polynomial_Odegree(U_1182,U_1184)))
| ~ class_Rings_Ocomm__semiring__0(U_1182) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1182,c_Polynomial_Opcompose(U_1182,U_1183,U_1184)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Polynomial_Odegree(U_1182,U_1183)),c_Polynomial_Odegree(U_1182,U_1184)))
| ~ class_Rings_Ocomm__semiring__0(U_1182) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_1,plain,
! [V_q,T_a] :
( c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pcompose__0]) ).
fof(f_398_2,plain,
! [U_1186,U_1185] :
( c_Polynomial_Opcompose(U_1185,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1185)),U_1186) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1185))
| ~ class_Rings_Ocomm__semiring__0(U_1185) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
( c_Polynomial_Opcompose(U_1185,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1185)),U_1186) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1185))
| ~ class_Rings_Ocomm__semiring__0(U_1185) ),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__pcompose]) ).
fof(f_399_2,plain,
! [U_1190,U_1189,U_1188,U_1187] :
( hAPP(c_Polynomial_Opoly(U_1187,c_Polynomial_Opcompose(U_1187,U_1188,U_1189)),U_1190) = hAPP(c_Polynomial_Opoly(U_1187,U_1188),hAPP(c_Polynomial_Opoly(U_1187,U_1189),U_1190))
| ~ class_Rings_Ocomm__semiring__0(U_1187) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
cnf(f_399_3,plain,
( hAPP(c_Polynomial_Opoly(U_1187,c_Polynomial_Opcompose(U_1187,U_1188,U_1189)),U_1190) = hAPP(c_Polynomial_Opoly(U_1187,U_1188),hAPP(c_Polynomial_Opoly(U_1187,U_1189),U_1190))
| ~ class_Rings_Ocomm__semiring__0(U_1187) ),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_1,plain,
! [V_aa_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(f_400_2,plain,
! [U_1194,U_1193,U_1192,U_1191] : hAPP(hAPP(c_Power_Opower_Opower(U_1191,U_1192,U_1193),U_1194),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1192,
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_1191,U_1192,U_1193),U_1194),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1192,
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_1,plain,
! [V_nb_2,V_aa_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),c_Nat_OSuc(V_nb_2)) = hAPP(hAPP(V_times_2,V_aa_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_aa_2),V_nb_2)),
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(f_401_2,plain,
! [U_1199,U_1198,U_1197,U_1196,U_1195] : hAPP(hAPP(c_Power_Opower_Opower(U_1195,U_1196,U_1197),U_1198),c_Nat_OSuc(U_1199)) = hAPP(hAPP(U_1197,U_1198),hAPP(hAPP(c_Power_Opower_Opower(U_1195,U_1196,U_1197),U_1198),U_1199)),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_1195,U_1196,U_1197),U_1198),c_Nat_OSuc(U_1199)) = hAPP(hAPP(U_1197,U_1198),hAPP(hAPP(c_Power_Opower_Opower(U_1195,U_1196,U_1197),U_1198),U_1199)),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__cases]) ).
fof(f_402_2,plain,
! [U_1202,U_1201,U_1200] :
( c_Orderings_Oord__class_Oless__eq(U_1200,U_1202,U_1201)
| c_Orderings_Oord__class_Oless__eq(U_1200,U_1201,U_1202)
| ~ class_Orderings_Olinorder(U_1200) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
cnf(f_402_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1200,U_1202,U_1201)
| c_Orderings_Oord__class_Oless__eq(U_1200,U_1201,U_1202)
| ~ class_Orderings_Olinorder(U_1200) ),
inference(clausify,[status(thm)],[f_402_2]) ).
fof(f_403_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_403_2,plain,
! [U_1207,U_1206,U_1205,U_1204,U_1203] :
( c_Orderings_Oord__class_Oless__eq(U_1203,hAPP(U_1205,U_1207),hAPP(U_1206,U_1207))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1204,U_1203),U_1205,U_1206)
| ~ class_Orderings_Oord(U_1203) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1203,hAPP(U_1205,U_1207),hAPP(U_1206,U_1207))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1204,U_1203),U_1205,U_1206)
| ~ class_Orderings_Oord(U_1203) ),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).
fof(f_404_2,plain,
! [U_1211,U_1210,U_1209,U_1208] :
( c_Orderings_Oord__class_Oless__eq(U_1208,U_1211,U_1210)
| ~ c_Orderings_Oord__class_Oless__eq(U_1208,U_1211,U_1209)
| ~ c_Orderings_Oord__class_Oless__eq(U_1208,U_1209,U_1210)
| ~ class_Orderings_Oorder(U_1208) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
cnf(f_404_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1208,U_1211,U_1210)
| ~ c_Orderings_Oord__class_Oless__eq(U_1208,U_1211,U_1209)
| ~ c_Orderings_Oord__class_Oless__eq(U_1208,U_1209,U_1210)
| ~ class_Orderings_Oorder(U_1208) ),
inference(clausify,[status(thm)],[f_404_2]) ).
fof(f_405_1,plain,
! [V_x,V_y,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I5_J]) ).
fof(f_405_2,plain,
! [U_1214,U_1213,U_1212] :
( U_1214 = U_1213
| ~ c_Orderings_Oord__class_Oless__eq(U_1212,U_1214,U_1213)
| ~ c_Orderings_Oord__class_Oless__eq(U_1212,U_1213,U_1214)
| ~ class_Orderings_Oorder(U_1212) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
( U_1214 = U_1213
| ~ c_Orderings_Oord__class_Oless__eq(U_1212,U_1214,U_1213)
| ~ c_Orderings_Oord__class_Oless__eq(U_1212,U_1213,U_1214)
| ~ class_Orderings_Oorder(U_1212) ),
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__trans]) ).
fof(f_406_2,plain,
! [U_1218,U_1217,U_1216,U_1215] :
( c_Orderings_Oord__class_Oless__eq(U_1215,U_1216,U_1218)
| ~ c_Orderings_Oord__class_Oless__eq(U_1215,U_1217,U_1218)
| ~ c_Orderings_Oord__class_Oless__eq(U_1215,U_1216,U_1217)
| ~ class_Orderings_Opreorder(U_1215) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1215,U_1216,U_1218)
| ~ c_Orderings_Oord__class_Oless__eq(U_1215,U_1217,U_1218)
| ~ c_Orderings_Oord__class_Oless__eq(U_1215,U_1216,U_1217)
| ~ class_Orderings_Opreorder(U_1215) ),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym]) ).
fof(f_407_2,plain,
! [U_1221,U_1220,U_1219] :
( U_1220 = U_1221
| ~ c_Orderings_Oord__class_Oless__eq(U_1219,U_1221,U_1220)
| ~ c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221)
| ~ class_Orderings_Oorder(U_1219) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
cnf(f_407_3,plain,
( U_1220 = U_1221
| ~ c_Orderings_Oord__class_Oless__eq(U_1219,U_1221,U_1220)
| ~ c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221)
| ~ class_Orderings_Oorder(U_1219) ),
inference(clausify,[status(thm)],[f_407_2]) ).
fof(f_408_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I4_J]) ).
fof(f_408_2,plain,
! [U_1225,U_1224,U_1223,U_1222] :
( c_Orderings_Oord__class_Oless__eq(U_1222,U_1225,U_1224)
| U_1223 != U_1225
| ~ c_Orderings_Oord__class_Oless__eq(U_1222,U_1223,U_1224)
| ~ class_Orderings_Oorder(U_1222) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
cnf(f_408_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1222,U_1225,U_1224)
| U_1223 != U_1225
| ~ c_Orderings_Oord__class_Oless__eq(U_1222,U_1223,U_1224)
| ~ class_Orderings_Oorder(U_1222) ),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__le__eq__trans]) ).
fof(f_409_2,plain,
! [U_1229,U_1228,U_1227,U_1226] :
( c_Orderings_Oord__class_Oless__eq(U_1226,U_1227,U_1229)
| U_1228 != U_1229
| ~ c_Orderings_Oord__class_Oless__eq(U_1226,U_1227,U_1228)
| ~ class_Orderings_Oord(U_1226) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1226,U_1227,U_1229)
| U_1228 != U_1229
| ~ c_Orderings_Oord__class_Oless__eq(U_1226,U_1227,U_1228)
| ~ class_Orderings_Oord(U_1226) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I3_J]) ).
fof(f_410_2,plain,
! [U_1233,U_1232,U_1231,U_1230] :
( c_Orderings_Oord__class_Oless__eq(U_1230,U_1233,U_1231)
| ~ c_Orderings_Oord__class_Oless__eq(U_1230,U_1233,U_1232)
| U_1231 != U_1232
| ~ class_Orderings_Oorder(U_1230) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
cnf(f_410_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1230,U_1233,U_1231)
| ~ c_Orderings_Oord__class_Oless__eq(U_1230,U_1233,U_1232)
| U_1231 != U_1232
| ~ class_Orderings_Oorder(U_1230) ),
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__le__trans]) ).
fof(f_411_2,plain,
! [U_1237,U_1236,U_1235,U_1234] :
( c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1237)
| ~ c_Orderings_Oord__class_Oless__eq(U_1234,U_1236,U_1237)
| U_1235 != U_1236
| ~ class_Orderings_Oord(U_1234) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1237)
| ~ c_Orderings_Oord__class_Oless__eq(U_1234,U_1236,U_1237)
| U_1235 != U_1236
| ~ class_Orderings_Oord(U_1234) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_412_2,plain,
! [U_1240,U_1239,U_1238] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1238,U_1240,U_1239)
| U_1240 != U_1239 )
& ( U_1240 = U_1239
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1240,U_1239) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1239,U_1240)
| ~ class_Orderings_Oorder(U_1238) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( U_1240 = U_1239
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1240,U_1239)
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1239,U_1240)
| ~ class_Orderings_Oorder(U_1238) ),
inference(clausify,[status(thm)],[f_412_2]) ).
cnf(f_412_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1238,U_1240,U_1239)
| U_1240 != U_1239
| ~ c_Orderings_Oord__class_Oless__eq(U_1238,U_1239,U_1240)
| ~ class_Orderings_Oorder(U_1238) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_413_2,plain,
! [U_1245,U_1244,U_1243,U_1242,U_1241] :
( c_Orderings_Oord__class_Oless__eq(U_1241,hAPP(U_1243,U_1245),hAPP(U_1244,U_1245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1242,U_1241),U_1243,U_1244)
| ~ class_Orderings_Oord(U_1241) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
cnf(f_413_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1241,hAPP(U_1243,U_1245),hAPP(U_1244,U_1245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1242,U_1241),U_1243,U_1244)
| ~ class_Orderings_Oord(U_1241) ),
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| V_x != V_y
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__refl]) ).
fof(f_414_2,plain,
! [U_1248,U_1247,U_1246] :
( c_Orderings_Oord__class_Oless__eq(U_1246,U_1247,U_1248)
| U_1247 != U_1248
| ~ class_Orderings_Opreorder(U_1246) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1246,U_1247,U_1248)
| U_1247 != U_1248
| ~ class_Orderings_Opreorder(U_1246) ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_415_2,plain,
! [U_1251,U_1250,U_1249] :
( ( ( U_1250 = U_1251
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1251,U_1250)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,U_1251) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1249,U_1251,U_1250)
& c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,U_1251) )
| U_1250 != U_1251 ) )
| ~ class_Orderings_Oorder(U_1249) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,U_1251)
| U_1250 != U_1251
| ~ class_Orderings_Oorder(U_1249) ),
inference(clausify,[status(thm)],[f_415_2]) ).
cnf(f_415_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1249,U_1251,U_1250)
| U_1250 != U_1251
| ~ class_Orderings_Oorder(U_1249) ),
inference(clausify,[status(thm)],[f_415_2]) ).
cnf(f_415_5,plain,
( U_1250 = U_1251
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1251,U_1250)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,U_1251)
| ~ class_Orderings_Oorder(U_1249) ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__linear]) ).
fof(f_416_2,plain,
! [U_1254,U_1253,U_1252] :
( c_Orderings_Oord__class_Oless__eq(U_1252,U_1254,U_1253)
| c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,U_1254)
| ~ class_Orderings_Olinorder(U_1252) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1252,U_1254,U_1253)
| c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,U_1254)
| ~ class_Orderings_Olinorder(U_1252) ),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ? [B_x] : ~ c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) )
& ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_417_2,plain,
! [U_1260,U_1259,U_1258,U_1257] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1258,U_1257),U_1259,U_1260)
| ? [U_1256] : ~ c_Orderings_Oord__class_Oless__eq(U_1257,hAPP(U_1259,U_1256),hAPP(U_1260,U_1256)) )
& ( ! [U_1255] : c_Orderings_Oord__class_Oless__eq(U_1257,hAPP(U_1259,U_1255),hAPP(U_1260,U_1255))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1258,U_1257),U_1259,U_1260) ) )
| ~ class_Orderings_Oord(U_1257) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
! [U_1260,U_1259,U_1258,U_1257] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1258,U_1257),U_1259,U_1260)
| ~ c_Orderings_Oord__class_Oless__eq(U_1257,hAPP(U_1259,sK5(U_1260,U_1259,U_1258,U_1257)),hAPP(U_1260,sK5(U_1260,U_1259,U_1258,U_1257))) )
& ( ! [U_1255] : c_Orderings_Oord__class_Oless__eq(U_1257,hAPP(U_1259,U_1255),hAPP(U_1260,U_1255))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1258,U_1257),U_1259,U_1260) ) )
| ~ class_Orderings_Oord(U_1257) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_1256,sK5(U_1260,U_1259,U_1258,U_1257))],[f_417_2]) ).
cnf(f_417_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1257,hAPP(U_1259,U_1255),hAPP(U_1260,U_1255))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1258,U_1257),U_1259,U_1260)
| ~ class_Orderings_Oord(U_1257) ),
inference(clausify,[status(thm)],[f_417_3]) ).
cnf(f_417_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1258,U_1257),U_1259,U_1260)
| ~ c_Orderings_Oord__class_Oless__eq(U_1257,hAPP(U_1259,sK5(U_1260,U_1259,U_1258,U_1257)),hAPP(U_1260,sK5(U_1260,U_1259,U_1258,U_1257)))
| ~ class_Orderings_Oord(U_1257) ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__cases]) ).
fof(f_418_2,plain,
! [U_1263,U_1262,U_1261] :
( c_Orderings_Oord__class_Oless(U_1261,U_1263,U_1262)
| U_1262 = U_1263
| c_Orderings_Oord__class_Oless(U_1261,U_1262,U_1263)
| ~ class_Orderings_Olinorder(U_1261) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
cnf(f_418_3,plain,
( c_Orderings_Oord__class_Oless(U_1261,U_1263,U_1262)
| U_1262 = U_1263
| c_Orderings_Oord__class_Oless(U_1261,U_1262,U_1263)
| ~ class_Orderings_Olinorder(U_1261) ),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym]) ).
fof(f_419_2,plain,
! [U_1266,U_1265,U_1264] :
( ~ c_Orderings_Oord__class_Oless(U_1264,U_1266,U_1265)
| ~ c_Orderings_Oord__class_Oless(U_1264,U_1265,U_1266)
| ~ class_Orderings_Opreorder(U_1264) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1264,U_1266,U_1265)
| ~ c_Orderings_Oord__class_Oless(U_1264,U_1265,U_1266)
| ~ class_Orderings_Opreorder(U_1264) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I10_J]) ).
fof(f_420_2,plain,
! [U_1270,U_1269,U_1268,U_1267] :
( c_Orderings_Oord__class_Oless(U_1267,U_1270,U_1269)
| ~ c_Orderings_Oord__class_Oless(U_1267,U_1270,U_1268)
| ~ c_Orderings_Oord__class_Oless(U_1267,U_1268,U_1269)
| ~ class_Orderings_Oorder(U_1267) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
( c_Orderings_Oord__class_Oless(U_1267,U_1270,U_1269)
| ~ c_Orderings_Oord__class_Oless(U_1267,U_1270,U_1268)
| ~ c_Orderings_Oord__class_Oless(U_1267,U_1268,U_1269)
| ~ class_Orderings_Oorder(U_1267) ),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__trans]) ).
fof(f_421_2,plain,
! [U_1274,U_1273,U_1272,U_1271] :
( c_Orderings_Oord__class_Oless(U_1271,U_1272,U_1274)
| ~ c_Orderings_Oord__class_Oless(U_1271,U_1273,U_1274)
| ~ c_Orderings_Oord__class_Oless(U_1271,U_1272,U_1273)
| ~ class_Orderings_Opreorder(U_1271) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
( c_Orderings_Oord__class_Oless(U_1271,U_1272,U_1274)
| ~ c_Orderings_Oord__class_Oless(U_1271,U_1273,U_1274)
| ~ c_Orderings_Oord__class_Oless(U_1271,U_1272,U_1273)
| ~ class_Orderings_Opreorder(U_1271) ),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I2_J]) ).
fof(f_422_2,plain,
! [U_1278,U_1277,U_1276,U_1275] :
( c_Orderings_Oord__class_Oless(U_1275,U_1278,U_1277)
| U_1276 != U_1278
| ~ c_Orderings_Oord__class_Oless(U_1275,U_1276,U_1277)
| ~ class_Orderings_Oorder(U_1275) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
( c_Orderings_Oord__class_Oless(U_1275,U_1278,U_1277)
| U_1276 != U_1278
| ~ c_Orderings_Oord__class_Oless(U_1275,U_1276,U_1277)
| ~ class_Orderings_Oorder(U_1275) ),
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| V_b != V_c
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__less__eq__trans]) ).
fof(f_423_2,plain,
! [U_1282,U_1281,U_1280,U_1279] :
( c_Orderings_Oord__class_Oless(U_1279,U_1280,U_1282)
| U_1281 != U_1282
| ~ c_Orderings_Oord__class_Oless(U_1279,U_1280,U_1281)
| ~ class_Orderings_Oord(U_1279) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
cnf(f_423_3,plain,
( c_Orderings_Oord__class_Oless(U_1279,U_1280,U_1282)
| U_1281 != U_1282
| ~ c_Orderings_Oord__class_Oless(U_1279,U_1280,U_1281)
| ~ class_Orderings_Oord(U_1279) ),
inference(clausify,[status(thm)],[f_423_2]) ).
fof(f_424_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
| V_a != V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I1_J]) ).
fof(f_424_2,plain,
! [U_1286,U_1285,U_1284,U_1283] :
( c_Orderings_Oord__class_Oless(U_1283,U_1286,U_1284)
| ~ c_Orderings_Oord__class_Oless(U_1283,U_1286,U_1285)
| U_1284 != U_1285
| ~ class_Orderings_Oorder(U_1283) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
cnf(f_424_3,plain,
( c_Orderings_Oord__class_Oless(U_1283,U_1286,U_1284)
| ~ c_Orderings_Oord__class_Oless(U_1283,U_1286,U_1285)
| U_1284 != U_1285
| ~ class_Orderings_Oorder(U_1283) ),
inference(clausify,[status(thm)],[f_424_2]) ).
fof(f_425_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| V_a != V_b
| ~ class_Orderings_Oord(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ord__eq__less__trans]) ).
fof(f_425_2,plain,
! [U_1290,U_1289,U_1288,U_1287] :
( c_Orderings_Oord__class_Oless(U_1287,U_1288,U_1290)
| ~ c_Orderings_Oord__class_Oless(U_1287,U_1289,U_1290)
| U_1288 != U_1289
| ~ class_Orderings_Oord(U_1287) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
( c_Orderings_Oord__class_Oless(U_1287,U_1288,U_1290)
| ~ c_Orderings_Oord__class_Oless(U_1287,U_1289,U_1290)
| U_1288 != U_1289
| ~ class_Orderings_Oord(U_1287) ),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_1,plain,
! [V_a,V_b,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I9_J]) ).
fof(f_426_2,plain,
! [U_1293,U_1292,U_1291] :
( ~ c_Orderings_Oord__class_Oless(U_1291,U_1293,U_1292)
| ~ c_Orderings_Oord__class_Oless(U_1291,U_1292,U_1293)
| ~ class_Orderings_Oorder(U_1291) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1291,U_1293,U_1292)
| ~ c_Orderings_Oord__class_Oless(U_1291,U_1292,U_1293)
| ~ class_Orderings_Oorder(U_1291) ),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_1,plain,
! [V_b,V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__asym_H]) ).
fof(f_427_2,plain,
! [U_1296,U_1295,U_1294] :
( ~ c_Orderings_Oord__class_Oless(U_1294,U_1296,U_1295)
| ~ c_Orderings_Oord__class_Oless(U_1294,U_1295,U_1296)
| ~ class_Orderings_Opreorder(U_1294) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
cnf(f_427_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1294,U_1296,U_1295)
| ~ c_Orderings_Oord__class_Oless(U_1294,U_1295,U_1296)
| ~ class_Orderings_Opreorder(U_1294) ),
inference(clausify,[status(thm)],[f_427_2]) ).
fof(f_428_1,plain,
! [V_y,V_x,T_a] :
( V_y != V_x
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2]) ).
fof(f_428_2,plain,
! [U_1299,U_1298,U_1297] :
( U_1299 != U_1298
| ~ c_Orderings_Oord__class_Oless(U_1297,U_1298,U_1299)
| ~ class_Orderings_Oorder(U_1297) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
cnf(f_428_3,plain,
( U_1299 != U_1298
| ~ c_Orderings_Oord__class_Oless(U_1297,U_1298,U_1299)
| ~ class_Orderings_Oorder(U_1297) ),
inference(clausify,[status(thm)],[f_428_2]) ).
fof(f_429_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq]) ).
fof(f_429_2,plain,
! [U_1302,U_1301,U_1300] :
( U_1301 != U_1302
| ~ c_Orderings_Oord__class_Oless(U_1300,U_1301,U_1302)
| ~ class_Orderings_Oorder(U_1300) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
( U_1301 != U_1302
| ~ c_Orderings_Oord__class_Oless(U_1300,U_1301,U_1302)
| ~ class_Orderings_Oorder(U_1300) ),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(f_430_2,plain,
! [U_1305,U_1304,U_1303] :
( ~ c_Orderings_Oord__class_Oless(U_1303,U_1305,U_1304)
| ~ c_Orderings_Oord__class_Oless(U_1303,U_1304,U_1305)
| ~ class_Orderings_Opreorder(U_1303) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1303,U_1305,U_1304)
| ~ c_Orderings_Oord__class_Oless(U_1303,U_1304,U_1305)
| ~ class_Orderings_Opreorder(U_1303) ),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__not__sym]) ).
fof(f_431_2,plain,
! [U_1308,U_1307,U_1306] :
( ~ c_Orderings_Oord__class_Oless(U_1306,U_1308,U_1307)
| ~ c_Orderings_Oord__class_Oless(U_1306,U_1307,U_1308)
| ~ class_Orderings_Opreorder(U_1306) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1306,U_1308,U_1307)
| ~ c_Orderings_Oord__class_Oless(U_1306,U_1307,U_1308)
| ~ class_Orderings_Opreorder(U_1306) ),
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_1,plain,
! [V_y,V_x,T_a] :
( V_x != V_y
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__neq]) ).
fof(f_432_2,plain,
! [U_1311,U_1310,U_1309] :
( U_1310 != U_1311
| ~ c_Orderings_Oord__class_Oless(U_1309,U_1310,U_1311)
| ~ class_Orderings_Oorder(U_1309) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
( U_1310 != U_1311
| ~ c_Orderings_Oord__class_Oless(U_1309,U_1310,U_1311)
| ~ class_Orderings_Oorder(U_1309) ),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| V_x = V_y
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neqE]) ).
fof(f_433_2,plain,
! [U_1314,U_1313,U_1312] :
( c_Orderings_Oord__class_Oless(U_1312,U_1314,U_1313)
| c_Orderings_Oord__class_Oless(U_1312,U_1313,U_1314)
| U_1313 = U_1314
| ~ class_Orderings_Olinorder(U_1312) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( c_Orderings_Oord__class_Oless(U_1312,U_1314,U_1313)
| c_Orderings_Oord__class_Oless(U_1312,U_1313,U_1314)
| U_1313 = U_1314
| ~ class_Orderings_Olinorder(U_1312) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_434_2,plain,
! [U_1317,U_1316,U_1315] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_1315,U_1317,U_1316)
| U_1317 != U_1316 )
& ( U_1317 = U_1316
| c_Orderings_Oord__class_Oless(U_1315,U_1317,U_1316) ) )
| c_Orderings_Oord__class_Oless(U_1315,U_1316,U_1317)
| ~ class_Orderings_Olinorder(U_1315) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
cnf(f_434_3,plain,
( U_1317 = U_1316
| c_Orderings_Oord__class_Oless(U_1315,U_1317,U_1316)
| c_Orderings_Oord__class_Oless(U_1315,U_1316,U_1317)
| ~ class_Orderings_Olinorder(U_1315) ),
inference(clausify,[status(thm)],[f_434_2]) ).
cnf(f_434_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_1315,U_1317,U_1316)
| U_1317 != U_1316
| c_Orderings_Oord__class_Oless(U_1315,U_1316,U_1317)
| ~ class_Orderings_Olinorder(U_1315) ),
inference(clausify,[status(thm)],[f_434_2]) ).
fof(f_435_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__less__linear]) ).
fof(f_435_2,plain,
! [U_1320,U_1319,U_1318] :
( c_Orderings_Oord__class_Oless(U_1318,U_1320,U_1319)
| U_1319 = U_1320
| c_Orderings_Oord__class_Oless(U_1318,U_1319,U_1320)
| ~ class_Orderings_Olinorder(U_1318) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
( c_Orderings_Oord__class_Oless(U_1318,U_1320,U_1319)
| U_1319 = U_1320
| c_Orderings_Oord__class_Oless(U_1318,U_1319,U_1320)
| ~ class_Orderings_Olinorder(U_1318) ),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_436_2,plain,
! [U_1323,U_1322,U_1321] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_1321,U_1322,U_1323)
| ( U_1322 != U_1323
& ~ c_Orderings_Oord__class_Oless(U_1321,U_1323,U_1322) ) )
& ( U_1322 = U_1323
| c_Orderings_Oord__class_Oless(U_1321,U_1323,U_1322)
| c_Orderings_Oord__class_Oless(U_1321,U_1322,U_1323) ) )
| ~ class_Orderings_Olinorder(U_1321) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
( U_1322 = U_1323
| c_Orderings_Oord__class_Oless(U_1321,U_1323,U_1322)
| c_Orderings_Oord__class_Oless(U_1321,U_1322,U_1323)
| ~ class_Orderings_Olinorder(U_1321) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_1321,U_1323,U_1322)
| ~ c_Orderings_Oord__class_Oless(U_1321,U_1322,U_1323)
| ~ class_Orderings_Olinorder(U_1321) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_5,plain,
( U_1322 != U_1323
| ~ c_Orderings_Oord__class_Oless(U_1321,U_1322,U_1323)
| ~ class_Orderings_Olinorder(U_1321) ),
inference(clausify,[status(thm)],[f_436_2]) ).
fof(f_437_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 != V_y_2
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_437_2,plain,
! [U_1326,U_1325,U_1324] :
( ( ( U_1325 != U_1326
| ( ~ c_Orderings_Oord__class_Oless(U_1324,U_1326,U_1325)
& ~ c_Orderings_Oord__class_Oless(U_1324,U_1325,U_1326) ) )
& ( c_Orderings_Oord__class_Oless(U_1324,U_1326,U_1325)
| c_Orderings_Oord__class_Oless(U_1324,U_1325,U_1326)
| U_1325 = U_1326 ) )
| ~ class_Orderings_Olinorder(U_1324) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
( c_Orderings_Oord__class_Oless(U_1324,U_1326,U_1325)
| c_Orderings_Oord__class_Oless(U_1324,U_1325,U_1326)
| U_1325 = U_1326
| ~ class_Orderings_Olinorder(U_1324) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_1324,U_1325,U_1326)
| U_1325 != U_1326
| ~ class_Orderings_Olinorder(U_1324) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_5,plain,
( ~ c_Orderings_Oord__class_Oless(U_1324,U_1326,U_1325)
| U_1325 != U_1326
| ~ class_Orderings_Olinorder(U_1324) ),
inference(clausify,[status(thm)],[f_437_2]) ).
fof(f_438_1,plain,
! [V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__irrefl]) ).
fof(f_438_2,plain,
! [U_1328,U_1327] :
( ~ c_Orderings_Oord__class_Oless(U_1327,U_1328,U_1328)
| ~ class_Orderings_Opreorder(U_1327) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1327,U_1328,U_1328)
| ~ class_Orderings_Opreorder(U_1327) ),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_1,plain,
! [V_pb_2,T_a] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pb_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_439_2,plain,
! [U_1330,U_1329] :
( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1329,U_1330) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1330 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1329)) )
& ( U_1330 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1329))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1329,U_1330) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Groups_Ozero(U_1329) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( U_1330 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1329))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1329,U_1330) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(U_1329) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_4,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_1329,U_1330) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1330 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1329))
| ~ class_Groups_Ozero(U_1329) ),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_440_2,plain,
! [U_1333,U_1332,U_1331] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_1331,U_1332,U_1333)
| ~ c_Orderings_Oord__class_Oless__eq(U_1331,U_1333,U_1332) )
& ( c_Orderings_Oord__class_Oless__eq(U_1331,U_1333,U_1332)
| c_Orderings_Oord__class_Oless(U_1331,U_1332,U_1333) ) )
| ~ class_Orderings_Olinorder(U_1331) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1331,U_1333,U_1332)
| c_Orderings_Oord__class_Oless(U_1331,U_1332,U_1333)
| ~ class_Orderings_Olinorder(U_1331) ),
inference(clausify,[status(thm)],[f_440_2]) ).
cnf(f_440_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_1331,U_1332,U_1333)
| ~ c_Orderings_Oord__class_Oless__eq(U_1331,U_1333,U_1332)
| ~ class_Orderings_Olinorder(U_1331) ),
inference(clausify,[status(thm)],[f_440_2]) ).
fof(f_441_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_441_2,plain,
! [U_1336,U_1335,U_1334] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1334,U_1335,U_1336)
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,U_1335) )
& ( c_Orderings_Oord__class_Oless(U_1334,U_1336,U_1335)
| c_Orderings_Oord__class_Oless__eq(U_1334,U_1335,U_1336) ) )
| ~ class_Orderings_Olinorder(U_1334) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
cnf(f_441_3,plain,
( c_Orderings_Oord__class_Oless(U_1334,U_1336,U_1335)
| c_Orderings_Oord__class_Oless__eq(U_1334,U_1335,U_1336)
| ~ class_Orderings_Olinorder(U_1334) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1334,U_1335,U_1336)
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,U_1335)
| ~ class_Orderings_Olinorder(U_1334) ),
inference(clausify,[status(thm)],[f_441_2]) ).
fof(f_442_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear]) ).
fof(f_442_2,plain,
! [U_1339,U_1338,U_1337] :
( c_Orderings_Oord__class_Oless(U_1337,U_1339,U_1338)
| c_Orderings_Oord__class_Oless__eq(U_1337,U_1338,U_1339)
| ~ class_Orderings_Olinorder(U_1337) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
cnf(f_442_3,plain,
( c_Orderings_Oord__class_Oless(U_1337,U_1339,U_1338)
| c_Orderings_Oord__class_Oless__eq(U_1337,U_1338,U_1339)
| ~ class_Orderings_Olinorder(U_1337) ),
inference(clausify,[status(thm)],[f_442_2]) ).
fof(f_443_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_443_2,plain,
! [U_1342,U_1341,U_1340] :
( ( ( c_Orderings_Oord__class_Oless(U_1340,U_1341,U_1342)
| U_1341 = U_1342
| ~ c_Orderings_Oord__class_Oless__eq(U_1340,U_1341,U_1342) )
& ( ( U_1341 != U_1342
& c_Orderings_Oord__class_Oless__eq(U_1340,U_1341,U_1342) )
| ~ c_Orderings_Oord__class_Oless(U_1340,U_1341,U_1342) ) )
| ~ class_Orderings_Oorder(U_1340) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
cnf(f_443_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1340,U_1341,U_1342)
| ~ c_Orderings_Oord__class_Oless(U_1340,U_1341,U_1342)
| ~ class_Orderings_Oorder(U_1340) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_4,plain,
( U_1341 != U_1342
| ~ c_Orderings_Oord__class_Oless(U_1340,U_1341,U_1342)
| ~ class_Orderings_Oorder(U_1340) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_5,plain,
( c_Orderings_Oord__class_Oless(U_1340,U_1341,U_1342)
| U_1341 = U_1342
| ~ c_Orderings_Oord__class_Oless__eq(U_1340,U_1341,U_1342)
| ~ class_Orderings_Oorder(U_1340) ),
inference(clausify,[status(thm)],[f_443_2]) ).
fof(f_444_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_444_2,plain,
! [U_1345,U_1344,U_1343] :
( ( ( c_Orderings_Oord__class_Oless(U_1343,U_1344,U_1345)
| c_Orderings_Oord__class_Oless__eq(U_1343,U_1345,U_1344)
| ~ c_Orderings_Oord__class_Oless__eq(U_1343,U_1344,U_1345) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1343,U_1345,U_1344)
& c_Orderings_Oord__class_Oless__eq(U_1343,U_1344,U_1345) )
| ~ c_Orderings_Oord__class_Oless(U_1343,U_1344,U_1345) ) )
| ~ class_Orderings_Opreorder(U_1343) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1343,U_1344,U_1345)
| ~ c_Orderings_Oord__class_Oless(U_1343,U_1344,U_1345)
| ~ class_Orderings_Opreorder(U_1343) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1343,U_1345,U_1344)
| ~ c_Orderings_Oord__class_Oless(U_1343,U_1344,U_1345)
| ~ class_Orderings_Opreorder(U_1343) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_5,plain,
( c_Orderings_Oord__class_Oless(U_1343,U_1344,U_1345)
| c_Orderings_Oord__class_Oless__eq(U_1343,U_1345,U_1344)
| ~ c_Orderings_Oord__class_Oless__eq(U_1343,U_1344,U_1345)
| ~ class_Orderings_Opreorder(U_1343) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_445_2,plain,
! [U_1348,U_1347,U_1346] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1346,U_1347,U_1348)
| ( U_1347 != U_1348
& ~ c_Orderings_Oord__class_Oless(U_1346,U_1347,U_1348) ) )
& ( U_1347 = U_1348
| c_Orderings_Oord__class_Oless(U_1346,U_1347,U_1348)
| ~ c_Orderings_Oord__class_Oless__eq(U_1346,U_1347,U_1348) ) )
| ~ class_Orderings_Oorder(U_1346) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
( U_1347 = U_1348
| c_Orderings_Oord__class_Oless(U_1346,U_1347,U_1348)
| ~ c_Orderings_Oord__class_Oless__eq(U_1346,U_1347,U_1348)
| ~ class_Orderings_Oorder(U_1346) ),
inference(clausify,[status(thm)],[f_445_2]) ).
cnf(f_445_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_1346,U_1347,U_1348)
| c_Orderings_Oord__class_Oless__eq(U_1346,U_1347,U_1348)
| ~ class_Orderings_Oorder(U_1346) ),
inference(clausify,[status(thm)],[f_445_2]) ).
cnf(f_445_5,plain,
( U_1347 != U_1348
| c_Orderings_Oord__class_Oless__eq(U_1346,U_1347,U_1348)
| ~ class_Orderings_Oorder(U_1346) ),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leI]) ).
fof(f_446_2,plain,
! [U_1351,U_1350,U_1349] :
( c_Orderings_Oord__class_Oless__eq(U_1349,U_1351,U_1350)
| c_Orderings_Oord__class_Oless(U_1349,U_1350,U_1351)
| ~ class_Orderings_Olinorder(U_1349) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1349,U_1351,U_1350)
| c_Orderings_Oord__class_Oless(U_1349,U_1350,U_1351)
| ~ class_Orderings_Olinorder(U_1349) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_1,plain,
! [V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__leE]) ).
fof(f_447_2,plain,
! [U_1354,U_1353,U_1352] :
( c_Orderings_Oord__class_Oless(U_1352,U_1354,U_1353)
| c_Orderings_Oord__class_Oless__eq(U_1352,U_1353,U_1354)
| ~ class_Orderings_Olinorder(U_1352) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( c_Orderings_Oord__class_Oless(U_1352,U_1354,U_1353)
| c_Orderings_Oord__class_Oless__eq(U_1352,U_1353,U_1354)
| ~ class_Orderings_Olinorder(U_1352) ),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_448_2,plain,
! [U_1357,U_1356,U_1355] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1355,U_1356,U_1357)
| U_1356 != U_1357 )
& ( U_1356 = U_1357
| ~ c_Orderings_Oord__class_Oless__eq(U_1355,U_1356,U_1357) ) )
| c_Orderings_Oord__class_Oless(U_1355,U_1356,U_1357)
| ~ class_Orderings_Olinorder(U_1355) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
cnf(f_448_3,plain,
( U_1356 = U_1357
| ~ c_Orderings_Oord__class_Oless__eq(U_1355,U_1356,U_1357)
| c_Orderings_Oord__class_Oless(U_1355,U_1356,U_1357)
| ~ class_Orderings_Olinorder(U_1355) ),
inference(clausify,[status(thm)],[f_448_2]) ).
cnf(f_448_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1355,U_1356,U_1357)
| U_1356 != U_1357
| c_Orderings_Oord__class_Oless(U_1355,U_1356,U_1357)
| ~ class_Orderings_Olinorder(U_1355) ),
inference(clausify,[status(thm)],[f_448_2]) ).
fof(f_449_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans]) ).
fof(f_449_2,plain,
! [U_1360,U_1359,U_1358] :
( c_Orderings_Oord__class_Oless(U_1358,U_1359,U_1360)
| ~ c_Orderings_Oord__class_Oless__eq(U_1358,U_1359,U_1360)
| U_1359 = U_1360
| ~ class_Orderings_Oorder(U_1358) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
cnf(f_449_3,plain,
( c_Orderings_Oord__class_Oless(U_1358,U_1359,U_1360)
| ~ c_Orderings_Oord__class_Oless__eq(U_1358,U_1359,U_1360)
| U_1359 = U_1360
| ~ class_Orderings_Oorder(U_1358) ),
inference(clausify,[status(thm)],[f_449_2]) ).
fof(f_450_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| V_a = V_b
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I12_J]) ).
fof(f_450_2,plain,
! [U_1363,U_1362,U_1361] :
( c_Orderings_Oord__class_Oless(U_1361,U_1363,U_1362)
| ~ c_Orderings_Oord__class_Oless__eq(U_1361,U_1363,U_1362)
| U_1362 = U_1363
| ~ class_Orderings_Oorder(U_1361) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,plain,
( c_Orderings_Oord__class_Oless(U_1361,U_1363,U_1362)
| ~ c_Orderings_Oord__class_Oless__eq(U_1361,U_1363,U_1362)
| U_1362 = U_1363
| ~ class_Orderings_Oorder(U_1361) ),
inference(clausify,[status(thm)],[f_450_2]) ).
fof(f_451_1,plain,
! [V_x,V_y,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leD]) ).
fof(f_451_2,plain,
! [U_1366,U_1365,U_1364] :
( ~ c_Orderings_Oord__class_Oless(U_1364,U_1366,U_1365)
| ~ c_Orderings_Oord__class_Oless__eq(U_1364,U_1365,U_1366)
| ~ class_Orderings_Olinorder(U_1364) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1364,U_1366,U_1365)
| ~ c_Orderings_Oord__class_Oless__eq(U_1364,U_1365,U_1366)
| ~ class_Orderings_Olinorder(U_1364) ),
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__imp__le]) ).
fof(f_452_2,plain,
! [U_1369,U_1368,U_1367] :
( c_Orderings_Oord__class_Oless__eq(U_1367,U_1368,U_1369)
| ~ c_Orderings_Oord__class_Oless(U_1367,U_1368,U_1369)
| ~ class_Orderings_Opreorder(U_1367) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1367,U_1368,U_1369)
| ~ c_Orderings_Oord__class_Oless(U_1367,U_1368,U_1369)
| ~ class_Orderings_Opreorder(U_1367) ),
inference(clausify,[status(thm)],[f_452_2]) ).
fof(f_453_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_453_2,plain,
! [U_1372,U_1371,U_1370] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_1370,U_1371,U_1372)
| U_1371 != U_1372 )
& ( U_1371 = U_1372
| c_Orderings_Oord__class_Oless(U_1370,U_1371,U_1372) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1370,U_1371,U_1372)
| ~ class_Orderings_Olinorder(U_1370) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,plain,
( U_1371 = U_1372
| c_Orderings_Oord__class_Oless(U_1370,U_1371,U_1372)
| ~ c_Orderings_Oord__class_Oless__eq(U_1370,U_1371,U_1372)
| ~ class_Orderings_Olinorder(U_1370) ),
inference(clausify,[status(thm)],[f_453_2]) ).
cnf(f_453_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_1370,U_1371,U_1372)
| U_1371 != U_1372
| ~ c_Orderings_Oord__class_Oless__eq(U_1370,U_1371,U_1372)
| ~ class_Orderings_Olinorder(U_1370) ),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq]) ).
fof(f_454_2,plain,
! [U_1375,U_1374,U_1373] :
( U_1374 = U_1375
| c_Orderings_Oord__class_Oless(U_1373,U_1374,U_1375)
| ~ c_Orderings_Oord__class_Oless__eq(U_1373,U_1374,U_1375)
| ~ class_Orderings_Oorder(U_1373) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
( U_1374 = U_1375
| c_Orderings_Oord__class_Oless(U_1373,U_1374,U_1375)
| ~ c_Orderings_Oord__class_Oless__eq(U_1373,U_1374,U_1375)
| ~ class_Orderings_Oorder(U_1373) ),
inference(clausify,[status(thm)],[f_454_2]) ).
fof(f_455_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| V_a = V_b
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans]) ).
fof(f_455_2,plain,
! [U_1378,U_1377,U_1376] :
( c_Orderings_Oord__class_Oless(U_1376,U_1377,U_1378)
| U_1377 = U_1378
| ~ c_Orderings_Oord__class_Oless__eq(U_1376,U_1377,U_1378)
| ~ class_Orderings_Oorder(U_1376) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
cnf(f_455_3,plain,
( c_Orderings_Oord__class_Oless(U_1376,U_1377,U_1378)
| U_1377 = U_1378
| ~ c_Orderings_Oord__class_Oless__eq(U_1376,U_1377,U_1378)
| ~ class_Orderings_Oorder(U_1376) ),
inference(clausify,[status(thm)],[f_455_2]) ).
fof(f_456_1,plain,
! [V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| V_a = V_b
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I11_J]) ).
fof(f_456_2,plain,
! [U_1381,U_1380,U_1379] :
( c_Orderings_Oord__class_Oless(U_1379,U_1380,U_1381)
| U_1381 = U_1380
| ~ c_Orderings_Oord__class_Oless__eq(U_1379,U_1380,U_1381)
| ~ class_Orderings_Oorder(U_1379) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
cnf(f_456_3,plain,
( c_Orderings_Oord__class_Oless(U_1379,U_1380,U_1381)
| U_1381 = U_1380
| ~ c_Orderings_Oord__class_Oless__eq(U_1379,U_1380,U_1381)
| ~ class_Orderings_Oorder(U_1379) ),
inference(clausify,[status(thm)],[f_456_2]) ).
fof(f_457_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le__trans]) ).
fof(f_457_2,plain,
! [U_1385,U_1384,U_1383,U_1382] :
( c_Orderings_Oord__class_Oless(U_1382,U_1383,U_1385)
| ~ c_Orderings_Oord__class_Oless__eq(U_1382,U_1384,U_1385)
| ~ c_Orderings_Oord__class_Oless(U_1382,U_1383,U_1384)
| ~ class_Orderings_Opreorder(U_1382) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
cnf(f_457_3,plain,
( c_Orderings_Oord__class_Oless(U_1382,U_1383,U_1385)
| ~ c_Orderings_Oord__class_Oless__eq(U_1382,U_1384,U_1385)
| ~ c_Orderings_Oord__class_Oless(U_1382,U_1383,U_1384)
| ~ class_Orderings_Opreorder(U_1382) ),
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I7_J]) ).
fof(f_458_2,plain,
! [U_1389,U_1388,U_1387,U_1386] :
( c_Orderings_Oord__class_Oless(U_1386,U_1389,U_1388)
| ~ c_Orderings_Oord__class_Oless__eq(U_1386,U_1389,U_1387)
| ~ c_Orderings_Oord__class_Oless(U_1386,U_1387,U_1388)
| ~ class_Orderings_Oorder(U_1386) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
cnf(f_458_3,plain,
( c_Orderings_Oord__class_Oless(U_1386,U_1389,U_1388)
| ~ c_Orderings_Oord__class_Oless__eq(U_1386,U_1389,U_1387)
| ~ c_Orderings_Oord__class_Oless(U_1386,U_1387,U_1388)
| ~ class_Orderings_Oorder(U_1386) ),
inference(clausify,[status(thm)],[f_458_2]) ).
fof(f_459_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less__trans]) ).
fof(f_459_2,plain,
! [U_1393,U_1392,U_1391,U_1390] :
( c_Orderings_Oord__class_Oless(U_1390,U_1391,U_1393)
| ~ c_Orderings_Oord__class_Oless(U_1390,U_1392,U_1393)
| ~ c_Orderings_Oord__class_Oless__eq(U_1390,U_1391,U_1392)
| ~ class_Orderings_Opreorder(U_1390) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
cnf(f_459_3,plain,
( c_Orderings_Oord__class_Oless(U_1390,U_1391,U_1393)
| ~ c_Orderings_Oord__class_Oless(U_1390,U_1392,U_1393)
| ~ c_Orderings_Oord__class_Oless__eq(U_1390,U_1391,U_1392)
| ~ class_Orderings_Opreorder(U_1390) ),
inference(clausify,[status(thm)],[f_459_2]) ).
fof(f_460_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_xt1_I8_J]) ).
fof(f_460_2,plain,
! [U_1397,U_1396,U_1395,U_1394] :
( c_Orderings_Oord__class_Oless(U_1394,U_1397,U_1396)
| ~ c_Orderings_Oord__class_Oless(U_1394,U_1397,U_1395)
| ~ c_Orderings_Oord__class_Oless__eq(U_1394,U_1395,U_1396)
| ~ class_Orderings_Oorder(U_1394) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( c_Orderings_Oord__class_Oless(U_1394,U_1397,U_1396)
| ~ c_Orderings_Oord__class_Oless(U_1394,U_1397,U_1395)
| ~ c_Orderings_Oord__class_Oless__eq(U_1394,U_1395,U_1396)
| ~ class_Orderings_Oorder(U_1394) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_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_461_2,plain,
! [U_1400,U_1399,U_1398] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1398),U_1399)),U_1400) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1400)),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1398),U_1399)),U_1400) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1400)),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).
fof(f_462_2,plain,
! [U_1402,U_1401] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1401,U_1402)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1401,U_1402) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
cnf(f_462_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1401,U_1402)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1401,U_1402) ),
inference(clausify,[status(thm)],[f_462_2]) ).
fof(f_463_1,plain,
! [V_pb_2,V_aa_2,T_a] :
( ( ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ~ c_Polynomial_Opos__poly(T_a,V_pb_2) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
& V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_Polynomial_Opos__poly(T_a,V_pb_2)
| ~ c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pb_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons]) ).
fof(f_463_2,plain,
! [U_1405,U_1404,U_1403] :
( ( ( c_Polynomial_Opos__poly(U_1403,c_Polynomial_OpCons(U_1403,U_1404,U_1405))
| ( ( ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1404)
| U_1405 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1403)) )
& ~ c_Polynomial_Opos__poly(U_1403,U_1405) ) )
& ( ( c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1404)
& U_1405 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1403)) )
| c_Polynomial_Opos__poly(U_1403,U_1405)
| ~ c_Polynomial_Opos__poly(U_1403,c_Polynomial_OpCons(U_1403,U_1404,U_1405)) ) )
| ~ class_Rings_Olinordered__idom(U_1403) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( U_1405 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1403))
| c_Polynomial_Opos__poly(U_1403,U_1405)
| ~ c_Polynomial_Opos__poly(U_1403,c_Polynomial_OpCons(U_1403,U_1404,U_1405))
| ~ class_Rings_Olinordered__idom(U_1403) ),
inference(clausify,[status(thm)],[f_463_2]) ).
cnf(f_463_4,plain,
( c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1404)
| c_Polynomial_Opos__poly(U_1403,U_1405)
| ~ c_Polynomial_Opos__poly(U_1403,c_Polynomial_OpCons(U_1403,U_1404,U_1405))
| ~ class_Rings_Olinordered__idom(U_1403) ),
inference(clausify,[status(thm)],[f_463_2]) ).
cnf(f_463_5,plain,
( ~ c_Polynomial_Opos__poly(U_1403,U_1405)
| c_Polynomial_Opos__poly(U_1403,c_Polynomial_OpCons(U_1403,U_1404,U_1405))
| ~ class_Rings_Olinordered__idom(U_1403) ),
inference(clausify,[status(thm)],[f_463_2]) ).
cnf(f_463_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1404)
| U_1405 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1403))
| c_Polynomial_Opos__poly(U_1403,c_Polynomial_OpCons(U_1403,U_1404,U_1405))
| ~ class_Rings_Olinordered__idom(U_1403) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).
fof(f_464_2,plain,
! [U_1408,U_1407,U_1406] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1406,c_Groups_Ouminus__class_Ouminus(U_1406,U_1407),c_Groups_Ouminus__class_Ouminus(U_1406,U_1408))
| ~ c_Orderings_Oord__class_Oless__eq(U_1406,U_1408,U_1407) )
& ( c_Orderings_Oord__class_Oless__eq(U_1406,U_1408,U_1407)
| ~ c_Orderings_Oord__class_Oless__eq(U_1406,c_Groups_Ouminus__class_Ouminus(U_1406,U_1407),c_Groups_Ouminus__class_Ouminus(U_1406,U_1408)) ) )
| ~ class_Lattices_Oboolean__algebra(U_1406) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1406,U_1408,U_1407)
| ~ c_Orderings_Oord__class_Oless__eq(U_1406,c_Groups_Ouminus__class_Ouminus(U_1406,U_1407),c_Groups_Ouminus__class_Ouminus(U_1406,U_1408))
| ~ class_Lattices_Oboolean__algebra(U_1406) ),
inference(clausify,[status(thm)],[f_464_2]) ).
cnf(f_464_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1406,c_Groups_Ouminus__class_Ouminus(U_1406,U_1407),c_Groups_Ouminus__class_Ouminus(U_1406,U_1408))
| ~ c_Orderings_Oord__class_Oless__eq(U_1406,U_1408,U_1407)
| ~ class_Lattices_Oboolean__algebra(U_1406) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__mono]) ).
fof(f_465_2,plain,
! [U_1411,U_1410,U_1409] :
( c_Orderings_Oord__class_Oless__eq(U_1409,c_Groups_Ouminus__class_Ouminus(U_1409,U_1411),c_Groups_Ouminus__class_Ouminus(U_1409,U_1410))
| ~ c_Orderings_Oord__class_Oless__eq(U_1409,U_1410,U_1411)
| ~ class_Lattices_Oboolean__algebra(U_1409) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1409,c_Groups_Ouminus__class_Ouminus(U_1409,U_1411),c_Groups_Ouminus__class_Ouminus(U_1409,U_1410))
| ~ c_Orderings_Oord__class_Oless__eq(U_1409,U_1410,U_1411)
| ~ class_Lattices_Oboolean__algebra(U_1409) ),
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
| c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_466_2,plain,
! [U_1415,U_1414,U_1413,U_1412] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_1413,U_1412),U_1414,U_1415)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1415,U_1414)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1414,U_1415) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1415,U_1414)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1414,U_1415) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1413,U_1412),U_1414,U_1415) ) )
| ~ class_Orderings_Oord(U_1412) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
cnf(f_466_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1414,U_1415)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1413,U_1412),U_1414,U_1415)
| ~ class_Orderings_Oord(U_1412) ),
inference(clausify,[status(thm)],[f_466_2]) ).
cnf(f_466_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1415,U_1414)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_1413,U_1412),U_1414,U_1415)
| ~ class_Orderings_Oord(U_1412) ),
inference(clausify,[status(thm)],[f_466_2]) ).
cnf(f_466_5,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_1413,U_1412),U_1414,U_1415)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1415,U_1414)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1413,U_1412),U_1414,U_1415)
| ~ class_Orderings_Oord(U_1412) ),
inference(clausify,[status(thm)],[f_466_2]) ).
fof(f_467_1,plain,
! [T_a] :
( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__pos__poly__0]) ).
fof(f_467_2,plain,
! [U_1416] :
( ~ c_Polynomial_Opos__poly(U_1416,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1416)))
| ~ class_Rings_Olinordered__idom(U_1416) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( ~ c_Polynomial_Opos__poly(U_1416,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1416)))
| ~ class_Rings_Olinordered__idom(U_1416) ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))
| ~ c_Polynomial_Opos__poly(T_a,V_q)
| ~ c_Polynomial_Opos__poly(T_a,V_p)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__mult]) ).
fof(f_468_2,plain,
! [U_1419,U_1418,U_1417] :
( c_Polynomial_Opos__poly(U_1417,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1417)),U_1418),U_1419))
| ~ c_Polynomial_Opos__poly(U_1417,U_1419)
| ~ c_Polynomial_Opos__poly(U_1417,U_1418)
| ~ class_Rings_Olinordered__idom(U_1417) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( c_Polynomial_Opos__poly(U_1417,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1417)),U_1418),U_1419))
| ~ c_Polynomial_Opos__poly(U_1417,U_1419)
| ~ c_Polynomial_Opos__poly(U_1417,U_1418)
| ~ class_Rings_Olinordered__idom(U_1417) ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__idem]) ).
fof(f_469_2,plain,
! [U_1422,U_1421,U_1420] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1420),U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1420),U_1421),U_1422)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1420),U_1421),U_1422)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1420) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1420),U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1420),U_1421),U_1422)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1420),U_1421),U_1422)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1420) ),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__idem]) ).
fof(f_470_2,plain,
! [U_1424,U_1423] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1424),U_1424) = U_1424
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1423) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1424),U_1424) = U_1424
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1423) ),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times_Oidem]) ).
fof(f_471_2,plain,
! [U_1426,U_1425] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1426) = U_1426
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1425) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1426) = U_1426
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1425) ),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).
fof(f_472_2,plain,
! [U_1429,U_1428,U_1427] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1427,U_1428) = c_Groups_Ouminus__class_Ouminus(U_1427,U_1429)
| U_1428 != U_1429 )
& ( U_1428 = U_1429
| c_Groups_Ouminus__class_Ouminus(U_1427,U_1428) != c_Groups_Ouminus__class_Ouminus(U_1427,U_1429) ) )
| ~ class_Lattices_Oboolean__algebra(U_1427) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
cnf(f_472_3,plain,
( U_1428 = U_1429
| c_Groups_Ouminus__class_Ouminus(U_1427,U_1428) != c_Groups_Ouminus__class_Ouminus(U_1427,U_1429)
| ~ class_Lattices_Oboolean__algebra(U_1427) ),
inference(clausify,[status(thm)],[f_472_2]) ).
cnf(f_472_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1427,U_1428) = c_Groups_Ouminus__class_Ouminus(U_1427,U_1429)
| U_1428 != U_1429
| ~ class_Lattices_Oboolean__algebra(U_1427) ),
inference(clausify,[status(thm)],[f_472_2]) ).
fof(f_473_1,plain,
! [V_x_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).
fof(f_473_2,plain,
! [U_1433,U_1432,U_1431,U_1430] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1431,U_1430),U_1432),U_1433) = c_Groups_Ouminus__class_Ouminus(U_1430,hAPP(U_1432,U_1433))
| ~ class_Groups_Ouminus(U_1430) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
cnf(f_473_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1431,U_1430),U_1432),U_1433) = c_Groups_Ouminus__class_Ouminus(U_1430,hAPP(U_1432,U_1433))
| ~ class_Groups_Ouminus(U_1430) ),
inference(clausify,[status(thm)],[f_473_2]) ).
fof(f_474_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__compl]) ).
fof(f_474_2,plain,
! [U_1435,U_1434] :
( c_Groups_Ouminus__class_Ouminus(U_1434,c_Groups_Ouminus__class_Ouminus(U_1434,U_1435)) = U_1435
| ~ class_Lattices_Oboolean__algebra(U_1434) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1434,c_Groups_Ouminus__class_Ouminus(U_1434,U_1435)) = U_1435
| ~ class_Lattices_Oboolean__algebra(U_1434) ),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg]) ).
fof(f_475_2,plain,
! [U_1437,U_1436] :
( U_1436 = U_1437
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1437),U_1436))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1436),U_1437))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1437)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1436) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
cnf(f_475_3,plain,
( U_1436 = U_1437
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1437),U_1436))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1436),U_1437))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1437)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1436) ),
inference(clausify,[status(thm)],[f_475_2]) ).
fof(f_476_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
| V_k = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel]) ).
fof(f_476_2,plain,
! [U_1440,U_1439,U_1438] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1439),U_1440))
| U_1438 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1438),U_1439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1438),U_1440))) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
cnf(f_476_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1439),U_1440))
| U_1438 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1438),U_1439)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1438),U_1440))) ),
inference(clausify,[status(thm)],[f_476_2]) ).
fof(f_477_1,plain,
! [V_n,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le]) ).
fof(f_477_2,plain,
! [U_1442,U_1441] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1441,U_1442)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1442)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1441),U_1442)) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
cnf(f_477_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1441,U_1442)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1442)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1441),U_1442)) ),
inference(clausify,[status(thm)],[f_477_2]) ).
fof(f_478_1,plain,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__not__zless]) ).
fof(f_478_2,plain,
! [U_1444,U_1443] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1444),U_1443))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1443,U_1444)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1443) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
cnf(f_478_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1444),U_1443))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1443,U_1444)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1443) ),
inference(clausify,[status(thm)],[f_478_2]) ).
fof(f_479_1,plain,
! [V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| c_Polynomial_Opos__poly(T_a,V_p)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__total]) ).
fof(f_479_2,plain,
! [U_1446,U_1445] :
( c_Polynomial_Opos__poly(U_1445,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1445),U_1446))
| c_Polynomial_Opos__poly(U_1445,U_1446)
| U_1446 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1445))
| ~ class_Rings_Olinordered__idom(U_1445) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
cnf(f_479_3,plain,
( c_Polynomial_Opos__poly(U_1445,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1445),U_1446))
| c_Polynomial_Opos__poly(U_1445,U_1446)
| U_1446 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1445))
| ~ class_Rings_Olinordered__idom(U_1445) ),
inference(clausify,[status(thm)],[f_479_2]) ).
fof(f_480_1,plain,
! [V_x,V_p,V_n,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,c_Groups_Oone__class_Oone(T_a),V_n)),V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__replicate__append]) ).
fof(f_480_2,plain,
! [U_1450,U_1449,U_1448,U_1447] :
( hAPP(c_Polynomial_Opoly(U_1447,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1447)),c_Polynomial_Omonom(U_1447,c_Groups_Oone__class_Oone(U_1447),U_1448)),U_1449)),U_1450) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1447),hAPP(hAPP(c_Power_Opower__class_Opower(U_1447),U_1450),U_1448)),hAPP(c_Polynomial_Opoly(U_1447,U_1449),U_1450))
| ~ class_Rings_Ocomm__ring__1(U_1447) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( hAPP(c_Polynomial_Opoly(U_1447,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1447)),c_Polynomial_Omonom(U_1447,c_Groups_Oone__class_Oone(U_1447),U_1448)),U_1449)),U_1450) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1447),hAPP(hAPP(c_Power_Opower__class_Opower(U_1447),U_1450),U_1448)),hAPP(c_Polynomial_Opoly(U_1447,U_1449),U_1450))
| ~ class_Rings_Ocomm__ring__1(U_1447) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_1,plain,
! [V_pb_2,V_aa_2,T_a,V_z_2,V_f_2,T_b] :
( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pb_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pb_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pb_2))
| hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) != V_z_2
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_poly__rec__pCons]) ).
fof(f_481_2,plain,
! [U_1456,U_1455,U_1454,U_1453,U_1452,U_1451] :
( c_Polynomial_Opoly__rec(U_1454,U_1451,U_1453,U_1452,c_Polynomial_OpCons(U_1451,U_1455,U_1456)) = hAPP(hAPP(hAPP(U_1452,U_1455),U_1456),c_Polynomial_Opoly__rec(U_1454,U_1451,U_1453,U_1452,U_1456))
| hAPP(hAPP(hAPP(U_1452,c_Groups_Ozero__class_Ozero(U_1451)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1451))),U_1453) != U_1453
| ~ class_Groups_Ozero(U_1451) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
( c_Polynomial_Opoly__rec(U_1454,U_1451,U_1453,U_1452,c_Polynomial_OpCons(U_1451,U_1455,U_1456)) = hAPP(hAPP(hAPP(U_1452,U_1455),U_1456),c_Polynomial_Opoly__rec(U_1454,U_1451,U_1453,U_1452,U_1456))
| hAPP(hAPP(hAPP(U_1452,c_Groups_Ozero__class_Ozero(U_1451)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1451))),U_1453) != U_1453
| ~ class_Groups_Ozero(U_1451) ),
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_1,plain,
! [V_c_2,V_pb_2,T_a] :
( ( ( c_Polynomial_Osynthetic__div(T_a,V_pb_2,V_c_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Odegree(T_a,V_pb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_Odegree(T_a,V_pb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(T_a,V_pb_2,V_c_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_synthetic__div__eq__0__iff]) ).
fof(f_482_2,plain,
! [U_1459,U_1458,U_1457] :
( ( ( c_Polynomial_Osynthetic__div(U_1457,U_1458,U_1459) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1457))
| c_Polynomial_Odegree(U_1457,U_1458) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Polynomial_Odegree(U_1457,U_1458) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(U_1457,U_1458,U_1459) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1457)) ) )
| ~ class_Rings_Ocomm__semiring__0(U_1457) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
cnf(f_482_3,plain,
( c_Polynomial_Odegree(U_1457,U_1458) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Polynomial_Osynthetic__div(U_1457,U_1458,U_1459) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1457))
| ~ class_Rings_Ocomm__semiring__0(U_1457) ),
inference(clausify,[status(thm)],[f_482_2]) ).
cnf(f_482_4,plain,
( c_Polynomial_Osynthetic__div(U_1457,U_1458,U_1459) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1457))
| c_Polynomial_Odegree(U_1457,U_1458) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__0(U_1457) ),
inference(clausify,[status(thm)],[f_482_2]) ).
fof(f_483_1,plain,
! [V_n,V_p,T_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__zero__or__degree__less]) ).
fof(f_483_2,plain,
! [U_1462,U_1461,U_1460] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1460,U_1461),U_1462)
| U_1461 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1460))
| hAPP(c_Polynomial_Ocoeff(U_1460,U_1461),U_1462) != c_Groups_Ozero__class_Ozero(U_1460)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1460,U_1461),U_1462)
| ~ class_Groups_Ozero(U_1460) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1460,U_1461),U_1462)
| U_1461 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1460))
| hAPP(c_Polynomial_Ocoeff(U_1460,U_1461),U_1462) != c_Groups_Ozero__class_Ozero(U_1460)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1460,U_1461),U_1462)
| ~ class_Groups_Ozero(U_1460) ),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_1,plain,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).
fof(f_484_2,plain,
! [U_1463] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1463,U_1463),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1463,U_1463),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_1,plain,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).
fof(f_485_2,plain,
! [U_1465,U_1464] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1465,U_1464)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1464,U_1465) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1465,U_1464)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1464,U_1465) ),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).
fof(f_486_2,plain,
! [U_1468,U_1467,U_1466] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1466,U_1468)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1467,U_1468)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1466,U_1467) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1466,U_1468)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1467,U_1468)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1466,U_1467) ),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_1,plain,
! [V_w,V_z] :
( V_z = V_w
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).
fof(f_487_2,plain,
! [U_1470,U_1469] :
( U_1469 = U_1470
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1470,U_1469)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1469,U_1470) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
( U_1469 = U_1470
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1470,U_1469)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1469,U_1470) ),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_1,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).
cnf(f_488_2,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_488_1]) ).
fof(f_489_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_489_2,plain,
! [U_1471] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1471) = U_1471,
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1471) = U_1471,
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_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_490_2,plain,
! [U_1472] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1472),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1472,
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1472),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1472,
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_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_491_2,plain,
! [U_1474,U_1473] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1473),U_1474) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1474),U_1473),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1473),U_1474) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1474),U_1473),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_1,plain,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
inference(fof_nnf,[status(thm)],[fact_zmult__zminus]) ).
fof(f_492_2,plain,
! [U_1476,U_1475] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1475)),U_1476) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1475),U_1476)),
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1475)),U_1476) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1475),U_1476)),
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_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_493_2,plain,
! [U_1479,U_1478,U_1477] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1477),U_1478)),U_1479) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1478),U_1479)),
inference(variable_rename,[status(thm)],[f_493_1]) ).
cnf(f_493_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1477),U_1478)),U_1479) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1478),U_1479)),
inference(clausify,[status(thm)],[f_493_2]) ).
fof(f_494_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_494_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_494_1]) ).
fof(f_495_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
| V_x = V_y
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).
fof(f_495_2,plain,
! [U_1481,U_1480] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1481,U_1480)
| U_1480 = U_1481
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1480,U_1481) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1481,U_1480)
| U_1480 = U_1481
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1480,U_1481) ),
inference(clausify,[status(thm)],[f_495_2]) ).
fof(f_496_1,plain,
! [V_w_2,V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
| V_z_2 = V_w_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
& ( ( V_z_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_496_2,plain,
! [U_1483,U_1482] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1482,U_1483)
| U_1482 = U_1483
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1482,U_1483) )
& ( ( U_1482 != U_1483
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1482,U_1483) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1482,U_1483) ) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
( ! [U_1487,U_1485] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1485,U_1487)
| U_1485 = U_1487
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1485,U_1487) )
& ! [U_1486,U_1484] :
( ( U_1484 != U_1486
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1484,U_1486) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1484,U_1486) ) ),
inference(miniscope,[status(thm)],[f_496_2]) ).
cnf(f_496_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1484,U_1486)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1484,U_1486) ),
inference(clausify,[status(thm)],[f_496_3]) ).
cnf(f_496_5,plain,
( U_1484 != U_1486
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1484,U_1486) ),
inference(clausify,[status(thm)],[f_496_3]) ).
cnf(f_496_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1485,U_1487)
| U_1485 = U_1487
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1485,U_1487) ),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).
fof(f_497_2,plain,
! [U_1490,U_1489,U_1488] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1490),U_1488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1490),U_1489))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1490)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1488,U_1489) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1490),U_1488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1490),U_1489))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1490)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1488,U_1489) ),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_1,plain,
! [V_nb_2,V_m_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_nb_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_nb_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( V_nb_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_nb_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).
fof(f_498_2,plain,
! [U_1492,U_1491] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1491),U_1492) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1492 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1491 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_1492 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_1491 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1491),U_1492) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1491) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
( U_1491 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1491),U_1492) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1491) ),
inference(clausify,[status(thm)],[f_498_2]) ).
cnf(f_498_4,plain,
( U_1492 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1491),U_1492) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1491) ),
inference(clausify,[status(thm)],[f_498_2]) ).
cnf(f_498_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1491),U_1492) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1492 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1491 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1491) ),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2) ) ),
inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).
fof(f_499_2,plain,
! [U_1493] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1493)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1493) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1493)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1493) ) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
( ! [U_1495] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1495)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1495) )
& ! [U_1494] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1494) ) ),
inference(miniscope,[status(thm)],[f_499_2]) ).
cnf(f_499_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1494) ),
inference(clausify,[status(thm)],[f_499_3]) ).
cnf(f_499_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1495)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1495) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).
cnf(f_500_2,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_500_1]) ).
fof(f_501_1,plain,
! [V_a,V_n,V_m,T_a] :
( ( ( hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| V_m = V_n )
& ( hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n) = V_a
| V_m != V_n ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__monom]) ).
fof(f_501_2,plain,
! [U_1499,U_1498,U_1497,U_1496] :
( ( ( hAPP(c_Polynomial_Ocoeff(U_1496,c_Polynomial_Omonom(U_1496,U_1499,U_1497)),U_1498) = c_Groups_Ozero__class_Ozero(U_1496)
| U_1497 = U_1498 )
& ( hAPP(c_Polynomial_Ocoeff(U_1496,c_Polynomial_Omonom(U_1496,U_1499,U_1497)),U_1498) = U_1499
| U_1497 != U_1498 ) )
| ~ class_Groups_Ozero(U_1496) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
cnf(f_501_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1496,c_Polynomial_Omonom(U_1496,U_1499,U_1497)),U_1498) = U_1499
| U_1497 != U_1498
| ~ class_Groups_Ozero(U_1496) ),
inference(clausify,[status(thm)],[f_501_2]) ).
cnf(f_501_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1496,c_Polynomial_Omonom(U_1496,U_1499,U_1497)),U_1498) = c_Groups_Ozero__class_Ozero(U_1496)
| U_1497 = U_1498
| ~ class_Groups_Ozero(U_1496) ),
inference(clausify,[status(thm)],[f_501_2]) ).
fof(f_502_1,plain,
! [V_qb_2,V_pb_2,T_a] :
( ( ( V_pb_2 = V_qb_2
| ? [B_n] : hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),B_n) != hAPP(c_Polynomial_Ocoeff(T_a,V_qb_2),B_n) )
& ( ! [B_n] : hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),B_n) = hAPP(c_Polynomial_Ocoeff(T_a,V_qb_2),B_n)
| V_pb_2 != V_qb_2 ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_expand__poly__eq]) ).
fof(f_502_2,plain,
! [U_1504,U_1503,U_1502] :
( ( ( U_1503 = U_1504
| ? [U_1501] : hAPP(c_Polynomial_Ocoeff(U_1502,U_1503),U_1501) != hAPP(c_Polynomial_Ocoeff(U_1502,U_1504),U_1501) )
& ( ! [U_1500] : hAPP(c_Polynomial_Ocoeff(U_1502,U_1503),U_1500) = hAPP(c_Polynomial_Ocoeff(U_1502,U_1504),U_1500)
| U_1503 != U_1504 ) )
| ~ class_Groups_Ozero(U_1502) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
! [U_1504,U_1503,U_1502] :
( ( ( U_1503 = U_1504
| hAPP(c_Polynomial_Ocoeff(U_1502,U_1503),sK6(U_1504,U_1503,U_1502)) != hAPP(c_Polynomial_Ocoeff(U_1502,U_1504),sK6(U_1504,U_1503,U_1502)) )
& ( ! [U_1500] : hAPP(c_Polynomial_Ocoeff(U_1502,U_1503),U_1500) = hAPP(c_Polynomial_Ocoeff(U_1502,U_1504),U_1500)
| U_1503 != U_1504 ) )
| ~ class_Groups_Ozero(U_1502) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_1501,sK6(U_1504,U_1503,U_1502))],[f_502_2]) ).
cnf(f_502_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1502,U_1503),U_1500) = hAPP(c_Polynomial_Ocoeff(U_1502,U_1504),U_1500)
| U_1503 != U_1504
| ~ class_Groups_Ozero(U_1502) ),
inference(clausify,[status(thm)],[f_502_3]) ).
cnf(f_502_5,plain,
( U_1503 = U_1504
| hAPP(c_Polynomial_Ocoeff(U_1502,U_1503),sK6(U_1504,U_1503,U_1502)) != hAPP(c_Polynomial_Ocoeff(U_1502,U_1504),sK6(U_1504,U_1503,U_1502))
| ~ class_Groups_Ozero(U_1502) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Polynomial_Ocoeff(T_a,V_x_2) = c_Polynomial_Ocoeff(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Polynomial_Ocoeff(T_a,V_x_2) != c_Polynomial_Ocoeff(T_a,V_y_2) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__inject]) ).
fof(f_503_2,plain,
! [U_1507,U_1506,U_1505] :
( ( ( c_Polynomial_Ocoeff(U_1505,U_1506) = c_Polynomial_Ocoeff(U_1505,U_1507)
| U_1506 != U_1507 )
& ( U_1506 = U_1507
| c_Polynomial_Ocoeff(U_1505,U_1506) != c_Polynomial_Ocoeff(U_1505,U_1507) ) )
| ~ class_Groups_Ozero(U_1505) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
cnf(f_503_3,plain,
( U_1506 = U_1507
| c_Polynomial_Ocoeff(U_1505,U_1506) != c_Polynomial_Ocoeff(U_1505,U_1507)
| ~ class_Groups_Ozero(U_1505) ),
inference(clausify,[status(thm)],[f_503_2]) ).
cnf(f_503_4,plain,
( c_Polynomial_Ocoeff(U_1505,U_1506) = c_Polynomial_Ocoeff(U_1505,U_1507)
| U_1506 != U_1507
| ~ class_Groups_Ozero(U_1505) ),
inference(clausify,[status(thm)],[f_503_2]) ).
fof(f_504_1,plain,
! [V_b_2,V_nb_2,V_aa_2,T_a] :
( ( ( c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) = c_Polynomial_Omonom(T_a,V_b_2,V_nb_2)
| V_aa_2 != V_b_2 )
& ( V_aa_2 = V_b_2
| c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) != c_Polynomial_Omonom(T_a,V_b_2,V_nb_2) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_monom__eq__iff]) ).
fof(f_504_2,plain,
! [U_1511,U_1510,U_1509,U_1508] :
( ( ( c_Polynomial_Omonom(U_1508,U_1509,U_1510) = c_Polynomial_Omonom(U_1508,U_1511,U_1510)
| U_1509 != U_1511 )
& ( U_1509 = U_1511
| c_Polynomial_Omonom(U_1508,U_1509,U_1510) != c_Polynomial_Omonom(U_1508,U_1511,U_1510) ) )
| ~ class_Groups_Ozero(U_1508) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
cnf(f_504_3,plain,
( U_1509 = U_1511
| c_Polynomial_Omonom(U_1508,U_1509,U_1510) != c_Polynomial_Omonom(U_1508,U_1511,U_1510)
| ~ class_Groups_Ozero(U_1508) ),
inference(clausify,[status(thm)],[f_504_2]) ).
cnf(f_504_4,plain,
( c_Polynomial_Omonom(U_1508,U_1509,U_1510) = c_Polynomial_Omonom(U_1508,U_1511,U_1510)
| U_1509 != U_1511
| ~ class_Groups_Ozero(U_1508) ),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_1,plain,
! [V_n,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__0]) ).
fof(f_505_2,plain,
! [U_1513,U_1512] :
( hAPP(c_Polynomial_Ocoeff(U_1512,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1512))),U_1513) = c_Groups_Ozero__class_Ozero(U_1512)
| ~ class_Groups_Ozero(U_1512) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
cnf(f_505_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1512,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1512))),U_1513) = c_Groups_Ozero__class_Ozero(U_1512)
| ~ class_Groups_Ozero(U_1512) ),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_1,plain,
! [V_p,V_a,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_a
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__pCons__0]) ).
fof(f_506_2,plain,
! [U_1516,U_1515,U_1514] :
( hAPP(c_Polynomial_Ocoeff(U_1514,c_Polynomial_OpCons(U_1514,U_1515,U_1516)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1515
| ~ class_Groups_Ozero(U_1514) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
cnf(f_506_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1514,c_Polynomial_OpCons(U_1514,U_1515,U_1516)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1515
| ~ class_Groups_Ozero(U_1514) ),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_1,plain,
! [V_n,V_p,V_a,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(V_n)) = hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__pCons__Suc]) ).
fof(f_507_2,plain,
! [U_1520,U_1519,U_1518,U_1517] :
( hAPP(c_Polynomial_Ocoeff(U_1517,c_Polynomial_OpCons(U_1517,U_1518,U_1519)),c_Nat_OSuc(U_1520)) = hAPP(c_Polynomial_Ocoeff(U_1517,U_1519),U_1520)
| ~ class_Groups_Ozero(U_1517) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
cnf(f_507_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1517,c_Polynomial_OpCons(U_1517,U_1518,U_1519)),c_Nat_OSuc(U_1520)) = hAPP(c_Polynomial_Ocoeff(U_1517,U_1519),U_1520)
| ~ class_Groups_Ozero(U_1517) ),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_1,plain,
! [V_c,T_a] :
( c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_synthetic__div__0]) ).
fof(f_508_2,plain,
! [U_1522,U_1521] :
( c_Polynomial_Osynthetic__div(U_1521,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1521)),U_1522) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1521))
| ~ class_Rings_Ocomm__semiring__0(U_1521) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
( c_Polynomial_Osynthetic__div(U_1521,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1521)),U_1522) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1521))
| ~ class_Rings_Ocomm__semiring__0(U_1521) ),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_1,plain,
! [V_n,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__minus]) ).
fof(f_509_2,plain,
! [U_1525,U_1524,U_1523] :
( hAPP(c_Polynomial_Ocoeff(U_1523,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1523),U_1524)),U_1525) = c_Groups_Ouminus__class_Ouminus(U_1523,hAPP(c_Polynomial_Ocoeff(U_1523,U_1524),U_1525))
| ~ class_Groups_Oab__group__add(U_1523) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
cnf(f_509_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1523,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1523),U_1524)),U_1525) = c_Groups_Ouminus__class_Ouminus(U_1523,hAPP(c_Polynomial_Ocoeff(U_1523,U_1524),U_1525))
| ~ class_Groups_Oab__group__add(U_1523) ),
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_1,plain,
! [V_q,V_p,T_a] :
( V_p = V_q
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_q),V_p))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_p),V_q))
| hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) != hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__dvd__antisym]) ).
fof(f_510_2,plain,
! [U_1528,U_1527,U_1526] :
( U_1527 = U_1528
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1526)),U_1528),U_1527))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1526)),U_1527),U_1528))
| hAPP(c_Polynomial_Ocoeff(U_1526,U_1527),c_Polynomial_Odegree(U_1526,U_1527)) != hAPP(c_Polynomial_Ocoeff(U_1526,U_1528),c_Polynomial_Odegree(U_1526,U_1528))
| ~ class_Rings_Oidom(U_1526) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
cnf(f_510_3,plain,
( U_1527 = U_1528
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1526)),U_1528),U_1527))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1526)),U_1527),U_1528))
| hAPP(c_Polynomial_Ocoeff(U_1526,U_1527),c_Polynomial_Odegree(U_1526,U_1527)) != hAPP(c_Polynomial_Ocoeff(U_1526,U_1528),c_Polynomial_Odegree(U_1526,U_1528))
| ~ class_Rings_Oidom(U_1526) ),
inference(clausify,[status(thm)],[f_510_2]) ).
fof(f_511_1,plain,
! [V_n,T_a] :
( c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_monom__eq__0]) ).
fof(f_511_2,plain,
! [U_1530,U_1529] :
( c_Polynomial_Omonom(U_1529,c_Groups_Ozero__class_Ozero(U_1529),U_1530) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1529))
| ~ class_Groups_Ozero(U_1529) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
cnf(f_511_3,plain,
( c_Polynomial_Omonom(U_1529,c_Groups_Ozero__class_Ozero(U_1529),U_1530) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1529))
| ~ class_Groups_Ozero(U_1529) ),
inference(clausify,[status(thm)],[f_511_2]) ).
fof(f_512_1,plain,
! [V_nb_2,V_aa_2,T_a] :
( ( ( c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Polynomial_Omonom(T_a,V_aa_2,V_nb_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_monom__eq__0__iff]) ).
fof(f_512_2,plain,
! [U_1533,U_1532,U_1531] :
( ( ( c_Polynomial_Omonom(U_1531,U_1532,U_1533) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1531))
| U_1532 != c_Groups_Ozero__class_Ozero(U_1531) )
& ( U_1532 = c_Groups_Ozero__class_Ozero(U_1531)
| c_Polynomial_Omonom(U_1531,U_1532,U_1533) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1531)) ) )
| ~ class_Groups_Ozero(U_1531) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
cnf(f_512_3,plain,
( U_1532 = c_Groups_Ozero__class_Ozero(U_1531)
| c_Polynomial_Omonom(U_1531,U_1532,U_1533) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1531))
| ~ class_Groups_Ozero(U_1531) ),
inference(clausify,[status(thm)],[f_512_2]) ).
cnf(f_512_4,plain,
( c_Polynomial_Omonom(U_1531,U_1532,U_1533) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1531))
| U_1532 != c_Groups_Ozero__class_Ozero(U_1531)
| ~ class_Groups_Ozero(U_1531) ),
inference(clausify,[status(thm)],[f_512_2]) ).
fof(f_513_1,plain,
! [V_n,V_a,T_a] :
( c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)) = V_n
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__monom__eq]) ).
fof(f_513_2,plain,
! [U_1536,U_1535,U_1534] :
( c_Polynomial_Odegree(U_1534,c_Polynomial_Omonom(U_1534,U_1535,U_1536)) = U_1536
| U_1535 = c_Groups_Ozero__class_Ozero(U_1534)
| ~ class_Groups_Ozero(U_1534) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
( c_Polynomial_Odegree(U_1534,c_Polynomial_Omonom(U_1534,U_1535,U_1536)) = U_1536
| U_1535 = c_Groups_Ozero__class_Ozero(U_1534)
| ~ class_Groups_Ozero(U_1534) ),
inference(clausify,[status(thm)],[f_513_2]) ).
fof(f_514_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_n)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__monom__le]) ).
fof(f_514_2,plain,
! [U_1539,U_1538,U_1537] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1537,c_Polynomial_Omonom(U_1537,U_1538,U_1539)),U_1539)
| ~ class_Groups_Ozero(U_1537) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1537,c_Polynomial_Omonom(U_1537,U_1538,U_1539)),U_1539)
| ~ class_Groups_Ozero(U_1537) ),
inference(clausify,[status(thm)],[f_514_2]) ).
fof(f_515_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__monom]) ).
fof(f_515_2,plain,
! [U_1542,U_1541,U_1540] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1540),c_Polynomial_Omonom(U_1540,U_1541,U_1542)) = c_Polynomial_Omonom(U_1540,c_Groups_Ouminus__class_Ouminus(U_1540,U_1541),U_1542)
| ~ class_Groups_Oab__group__add(U_1540) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
cnf(f_515_3,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1540),c_Polynomial_Omonom(U_1540,U_1541,U_1542)) = c_Polynomial_Omonom(U_1540,c_Groups_Ouminus__class_Ouminus(U_1540,U_1541),U_1542)
| ~ class_Groups_Oab__group__add(U_1540) ),
inference(clausify,[status(thm)],[f_515_2]) ).
fof(f_516_1,plain,
! [V_n,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__eq__0]) ).
fof(f_516_2,plain,
! [U_1545,U_1544,U_1543] :
( hAPP(c_Polynomial_Ocoeff(U_1543,U_1544),U_1545) = c_Groups_Ozero__class_Ozero(U_1543)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1543,U_1544),U_1545)
| ~ class_Groups_Ozero(U_1543) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
cnf(f_516_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1543,U_1544),U_1545) = c_Groups_Ozero__class_Ozero(U_1543)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1543,U_1544),U_1545)
| ~ class_Groups_Ozero(U_1543) ),
inference(clausify,[status(thm)],[f_516_2]) ).
fof(f_517_1,plain,
! [V_n,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))
| hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__degree]) ).
fof(f_517_2,plain,
! [U_1548,U_1547,U_1546] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1548,c_Polynomial_Odegree(U_1546,U_1547))
| hAPP(c_Polynomial_Ocoeff(U_1546,U_1547),U_1548) = c_Groups_Ozero__class_Ozero(U_1546)
| ~ class_Groups_Ozero(U_1546) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1548,c_Polynomial_Odegree(U_1546,U_1547))
| hAPP(c_Polynomial_Ocoeff(U_1546,U_1547),U_1548) = c_Groups_Ozero__class_Ozero(U_1546)
| ~ class_Groups_Ozero(U_1546) ),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_1,plain,
! [V_pb_2,T_a] :
( ( ( hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2)) = c_Groups_Ozero__class_Ozero(T_a)
| V_pb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_pb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leading__coeff__0__iff]) ).
fof(f_518_2,plain,
! [U_1550,U_1549] :
( ( ( hAPP(c_Polynomial_Ocoeff(U_1549,U_1550),c_Polynomial_Odegree(U_1549,U_1550)) = c_Groups_Ozero__class_Ozero(U_1549)
| U_1550 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1549)) )
& ( U_1550 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1549))
| hAPP(c_Polynomial_Ocoeff(U_1549,U_1550),c_Polynomial_Odegree(U_1549,U_1550)) != c_Groups_Ozero__class_Ozero(U_1549) ) )
| ~ class_Groups_Ozero(U_1549) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
cnf(f_518_3,plain,
( U_1550 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1549))
| hAPP(c_Polynomial_Ocoeff(U_1549,U_1550),c_Polynomial_Odegree(U_1549,U_1550)) != c_Groups_Ozero__class_Ozero(U_1549)
| ~ class_Groups_Ozero(U_1549) ),
inference(clausify,[status(thm)],[f_518_2]) ).
cnf(f_518_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1549,U_1550),c_Polynomial_Odegree(U_1549,U_1550)) = c_Groups_Ozero__class_Ozero(U_1549)
| U_1550 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1549))
| ~ class_Groups_Ozero(U_1549) ),
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_1,plain,
! [V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)) != c_Groups_Ozero__class_Ozero(T_a)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_leading__coeff__neq__0]) ).
fof(f_519_2,plain,
! [U_1552,U_1551] :
( hAPP(c_Polynomial_Ocoeff(U_1551,U_1552),c_Polynomial_Odegree(U_1551,U_1552)) != c_Groups_Ozero__class_Ozero(U_1551)
| U_1552 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1551))
| ~ class_Groups_Ozero(U_1551) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
cnf(f_519_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1551,U_1552),c_Polynomial_Odegree(U_1551,U_1552)) != c_Groups_Ozero__class_Ozero(U_1551)
| U_1552 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1551))
| ~ class_Groups_Ozero(U_1551) ),
inference(clausify,[status(thm)],[f_519_2]) ).
fof(f_520_1,plain,
! [V_n,V_a,T_a] :
( c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n)) = c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_monom__Suc]) ).
fof(f_520_2,plain,
! [U_1555,U_1554,U_1553] :
( c_Polynomial_Omonom(U_1553,U_1554,c_Nat_OSuc(U_1555)) = c_Polynomial_OpCons(U_1553,c_Groups_Ozero__class_Ozero(U_1553),c_Polynomial_Omonom(U_1553,U_1554,U_1555))
| ~ class_Groups_Ozero(U_1553) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
cnf(f_520_3,plain,
( c_Polynomial_Omonom(U_1553,U_1554,c_Nat_OSuc(U_1555)) = c_Polynomial_OpCons(U_1553,c_Groups_Ozero__class_Ozero(U_1553),c_Polynomial_Omonom(U_1553,U_1554,U_1555))
| ~ class_Groups_Ozero(U_1553) ),
inference(clausify,[status(thm)],[f_520_2]) ).
fof(f_521_1,plain,
! [V_x,V_n,V_a,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__monom]) ).
fof(f_521_2,plain,
! [U_1559,U_1558,U_1557,U_1556] :
( hAPP(c_Polynomial_Opoly(U_1556,c_Polynomial_Omonom(U_1556,U_1557,U_1558)),U_1559) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),hAPP(hAPP(c_Power_Opower__class_Opower(U_1556),U_1559),U_1558))
| ~ class_Rings_Ocomm__semiring__1(U_1556) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
cnf(f_521_3,plain,
( hAPP(c_Polynomial_Opoly(U_1556,c_Polynomial_Omonom(U_1556,U_1557,U_1558)),U_1559) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),hAPP(hAPP(c_Power_Opower__class_Opower(U_1556),U_1559),U_1558))
| ~ class_Rings_Ocomm__semiring__1(U_1556) ),
inference(clausify,[status(thm)],[f_521_2]) ).
fof(f_522_1,plain,
! [V_a,T_a] :
( c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_monom__0]) ).
fof(f_522_2,plain,
! [U_1561,U_1560] :
( c_Polynomial_Omonom(U_1560,U_1561,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(U_1560,U_1561,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1560)))
| ~ class_Groups_Ozero(U_1560) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( c_Polynomial_Omonom(U_1560,U_1561,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(U_1560,U_1561,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1560)))
| ~ class_Groups_Ozero(U_1560) ),
inference(clausify,[status(thm)],[f_522_2]) ).
fof(f_523_1,plain,
! [V_c,V_p,V_a,T_a] :
( c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons]) ).
fof(f_523_2,plain,
! [U_1565,U_1564,U_1563,U_1562] :
( c_Polynomial_Osynthetic__div(U_1562,c_Polynomial_OpCons(U_1562,U_1563,U_1564),U_1565) = c_Polynomial_OpCons(U_1562,hAPP(c_Polynomial_Opoly(U_1562,U_1564),U_1565),c_Polynomial_Osynthetic__div(U_1562,U_1564,U_1565))
| ~ class_Rings_Ocomm__semiring__0(U_1562) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
cnf(f_523_3,plain,
( c_Polynomial_Osynthetic__div(U_1562,c_Polynomial_OpCons(U_1562,U_1563,U_1564),U_1565) = c_Polynomial_OpCons(U_1562,hAPP(c_Polynomial_Opoly(U_1562,U_1564),U_1565),c_Polynomial_Osynthetic__div(U_1562,U_1564,U_1565))
| ~ class_Rings_Ocomm__semiring__0(U_1562) ),
inference(clausify,[status(thm)],[f_523_2]) ).
fof(f_524_1,plain,
! [T_a,V_z_2,V_f_2,T_b] :
( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2
| hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) != V_z_2
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_poly__rec__0]) ).
fof(f_524_2,plain,
! [U_1569,U_1568,U_1567,U_1566] :
( c_Polynomial_Opoly__rec(U_1569,U_1566,U_1568,U_1567,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1566))) = U_1568
| hAPP(hAPP(hAPP(U_1567,c_Groups_Ozero__class_Ozero(U_1566)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1566))),U_1568) != U_1568
| ~ class_Groups_Ozero(U_1566) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
cnf(f_524_3,plain,
( c_Polynomial_Opoly__rec(U_1569,U_1566,U_1568,U_1567,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1566))) = U_1568
| hAPP(hAPP(hAPP(U_1567,c_Groups_Ozero__class_Ozero(U_1566)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1566))),U_1568) != U_1568
| ~ class_Groups_Ozero(U_1566) ),
inference(clausify,[status(thm)],[f_524_2]) ).
fof(f_525_1,plain,
! [V_n,T_a] :
( ( ( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n) = c_Groups_Oone__class_Oone(T_a)
| V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__1]) ).
fof(f_525_2,plain,
! [U_1571,U_1570] :
( ( ( hAPP(c_Polynomial_Ocoeff(U_1570,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1570))),U_1571) = c_Groups_Ozero__class_Ozero(U_1570)
| U_1571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Polynomial_Ocoeff(U_1570,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1570))),U_1571) = c_Groups_Oone__class_Oone(U_1570)
| U_1571 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Ocomm__semiring__1(U_1570) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1570,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1570))),U_1571) = c_Groups_Oone__class_Oone(U_1570)
| U_1571 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__1(U_1570) ),
inference(clausify,[status(thm)],[f_525_2]) ).
cnf(f_525_4,plain,
( hAPP(c_Polynomial_Ocoeff(U_1570,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1570))),U_1571) = c_Groups_Ozero__class_Ozero(U_1570)
| U_1571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Ocomm__semiring__1(U_1570) ),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_1,plain,
! [V_pb_2,T_a] :
( ( ( c_Polynomial_Opos__poly(T_a,V_pb_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2))) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pb_2),c_Polynomial_Odegree(T_a,V_pb_2)))
| ~ c_Polynomial_Opos__poly(T_a,V_pb_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__def]) ).
fof(f_526_2,plain,
! [U_1573,U_1572] :
( ( ( c_Polynomial_Opos__poly(U_1572,U_1573)
| ~ c_Orderings_Oord__class_Oless(U_1572,c_Groups_Ozero__class_Ozero(U_1572),hAPP(c_Polynomial_Ocoeff(U_1572,U_1573),c_Polynomial_Odegree(U_1572,U_1573))) )
& ( c_Orderings_Oord__class_Oless(U_1572,c_Groups_Ozero__class_Ozero(U_1572),hAPP(c_Polynomial_Ocoeff(U_1572,U_1573),c_Polynomial_Odegree(U_1572,U_1573)))
| ~ c_Polynomial_Opos__poly(U_1572,U_1573) ) )
| ~ class_Rings_Olinordered__idom(U_1572) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
cnf(f_526_3,plain,
( c_Orderings_Oord__class_Oless(U_1572,c_Groups_Ozero__class_Ozero(U_1572),hAPP(c_Polynomial_Ocoeff(U_1572,U_1573),c_Polynomial_Odegree(U_1572,U_1573)))
| ~ c_Polynomial_Opos__poly(U_1572,U_1573)
| ~ class_Rings_Olinordered__idom(U_1572) ),
inference(clausify,[status(thm)],[f_526_2]) ).
cnf(f_526_4,plain,
( c_Polynomial_Opos__poly(U_1572,U_1573)
| ~ c_Orderings_Oord__class_Oless(U_1572,c_Groups_Ozero__class_Ozero(U_1572),hAPP(c_Polynomial_Ocoeff(U_1572,U_1573),c_Polynomial_Odegree(U_1572,U_1573)))
| ~ class_Rings_Olinordered__idom(U_1572) ),
inference(clausify,[status(thm)],[f_526_2]) ).
fof(f_527_1,plain,
! [V_n,V_a,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),V_n)),V_n) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__linear__power]) ).
fof(f_527_2,plain,
! [U_1576,U_1575,U_1574] :
( hAPP(c_Polynomial_Ocoeff(U_1574,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1574)),c_Polynomial_OpCons(U_1574,U_1575,c_Polynomial_OpCons(U_1574,c_Groups_Oone__class_Oone(U_1574),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1574))))),U_1576)),U_1576) = c_Groups_Oone__class_Oone(U_1574)
| ~ class_Rings_Ocomm__semiring__1(U_1574) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1574,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1574)),c_Polynomial_OpCons(U_1574,U_1575,c_Polynomial_OpCons(U_1574,c_Groups_Oone__class_Oone(U_1574),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1574))))),U_1576)),U_1576) = c_Groups_Oone__class_Oone(U_1574)
| ~ class_Rings_Ocomm__semiring__1(U_1574) ),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_1,plain,
! [V_pb_2,V_aa_2,V_f_2,V_z_2,T_a,T_b] :
( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pb_2)) = hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pb_2),c_If(T_a,c_fequal(V_pb_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pb_2)))
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_poly__rec_Osimps]) ).
fof(f_528_2,plain,
! [U_1582,U_1581,U_1580,U_1579,U_1578,U_1577] :
( c_Polynomial_Opoly__rec(U_1578,U_1577,U_1579,U_1580,c_Polynomial_OpCons(U_1577,U_1581,U_1582)) = hAPP(hAPP(hAPP(U_1580,U_1581),U_1582),c_If(U_1578,c_fequal(U_1582,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1577))),U_1579,c_Polynomial_Opoly__rec(U_1578,U_1577,U_1579,U_1580,U_1582)))
| ~ class_Groups_Ozero(U_1577) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
cnf(f_528_3,plain,
( c_Polynomial_Opoly__rec(U_1578,U_1577,U_1579,U_1580,c_Polynomial_OpCons(U_1577,U_1581,U_1582)) = hAPP(hAPP(hAPP(U_1580,U_1581),U_1582),c_If(U_1578,c_fequal(U_1582,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1577))),U_1579,c_Polynomial_Opoly__rec(U_1578,U_1577,U_1579,U_1580,U_1582)))
| ~ class_Groups_Ozero(U_1577) ),
inference(clausify,[status(thm)],[f_528_2]) ).
fof(f_529_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).
fof(f_529_2,plain,
! [U_1584,U_1583] :
( 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_1583),U_1584))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1583) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
cnf(f_529_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1583),U_1584))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1583) ),
inference(clausify,[status(thm)],[f_529_2]) ).
fof(f_530_1,plain,
! [V_t_2,V_m_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2)) ) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mono]) ).
fof(f_530_2,plain,
! [U_1587,U_1586,U_1585] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1586),U_1587))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1586)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1587))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1586)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1587)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1586),U_1587)) ) )
| U_1585 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
cnf(f_530_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1586)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1587)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1586),U_1587))
| U_1585 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_530_2]) ).
cnf(f_530_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1586),U_1587))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1586)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1585),U_1587)))
| U_1585 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_530_2]) ).
fof(f_531_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).
fof(f_531_2,plain,
! [U_1589,U_1588] :
( 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_1588),U_1589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1588) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
cnf(f_531_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1588),U_1589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1589)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1588) ),
inference(clausify,[status(thm)],[f_531_2]) ).
fof(f_532_1,plain,
! [V_p,V_c,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H]) ).
fof(f_532_2,plain,
! [U_1592,U_1591,U_1590] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1590)),c_Polynomial_OpCons(U_1590,c_Groups_Ouminus__class_Ouminus(U_1590,U_1591),c_Polynomial_OpCons(U_1590,c_Groups_Oone__class_Oone(U_1590),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1590))))),c_Polynomial_Osynthetic__div(U_1590,U_1592,U_1591)),c_Polynomial_OpCons(U_1590,hAPP(c_Polynomial_Opoly(U_1590,U_1592),U_1591),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1590)))) = U_1592
| ~ class_Rings_Ocomm__ring__1(U_1590) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
cnf(f_532_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1590)),c_Polynomial_OpCons(U_1590,c_Groups_Ouminus__class_Ouminus(U_1590,U_1591),c_Polynomial_OpCons(U_1590,c_Groups_Oone__class_Oone(U_1590),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1590))))),c_Polynomial_Osynthetic__div(U_1590,U_1592,U_1591)),c_Polynomial_OpCons(U_1590,hAPP(c_Polynomial_Opoly(U_1590,U_1592),U_1591),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1590)))) = U_1592
| ~ class_Rings_Ocomm__ring__1(U_1590) ),
inference(clausify,[status(thm)],[f_532_2]) ).
fof(f_533_1,plain,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).
fof(f_533_2,plain,
! [U_1593] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1593)) = U_1593,
inference(variable_rename,[status(thm)],[f_533_1]) ).
cnf(f_533_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1593)) = U_1593,
inference(clausify,[status(thm)],[f_533_2]) ).
fof(f_534_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_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_534_2,plain,
! [U_1595,U_1594] :
( ( ( c_Groups_Oplus__class_Oplus(U_1594,U_1595,U_1595) = c_Groups_Ozero__class_Ozero(U_1594)
| U_1595 != c_Groups_Ozero__class_Ozero(U_1594) )
& ( U_1595 = c_Groups_Ozero__class_Ozero(U_1594)
| c_Groups_Oplus__class_Oplus(U_1594,U_1595,U_1595) != c_Groups_Ozero__class_Ozero(U_1594) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1594) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
cnf(f_534_3,plain,
( U_1595 = c_Groups_Ozero__class_Ozero(U_1594)
| c_Groups_Oplus__class_Oplus(U_1594,U_1595,U_1595) != c_Groups_Ozero__class_Ozero(U_1594)
| ~ class_Groups_Olinordered__ab__group__add(U_1594) ),
inference(clausify,[status(thm)],[f_534_2]) ).
cnf(f_534_4,plain,
( c_Groups_Oplus__class_Oplus(U_1594,U_1595,U_1595) = c_Groups_Ozero__class_Ozero(U_1594)
| U_1595 != c_Groups_Ozero__class_Ozero(U_1594)
| ~ class_Groups_Olinordered__ab__group__add(U_1594) ),
inference(clausify,[status(thm)],[f_534_2]) ).
fof(f_535_1,plain,
! [V_b_2,V_c_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),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_535_2,plain,
! [U_1599,U_1598,U_1597,U_1596] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1596,c_Groups_Oplus__class_Oplus(U_1596,U_1597,U_1598),c_Groups_Oplus__class_Oplus(U_1596,U_1599,U_1598))
| ~ c_Orderings_Oord__class_Oless__eq(U_1596,U_1597,U_1599) )
& ( c_Orderings_Oord__class_Oless__eq(U_1596,U_1597,U_1599)
| ~ c_Orderings_Oord__class_Oless__eq(U_1596,c_Groups_Oplus__class_Oplus(U_1596,U_1597,U_1598),c_Groups_Oplus__class_Oplus(U_1596,U_1599,U_1598)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1596) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1596,U_1597,U_1599)
| ~ c_Orderings_Oord__class_Oless__eq(U_1596,c_Groups_Oplus__class_Oplus(U_1596,U_1597,U_1598),c_Groups_Oplus__class_Oplus(U_1596,U_1599,U_1598))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1596) ),
inference(clausify,[status(thm)],[f_535_2]) ).
cnf(f_535_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1596,c_Groups_Oplus__class_Oplus(U_1596,U_1597,U_1598),c_Groups_Oplus__class_Oplus(U_1596,U_1599,U_1598))
| ~ c_Orderings_Oord__class_Oless__eq(U_1596,U_1597,U_1599)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1596) ),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),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_536_2,plain,
! [U_1603,U_1602,U_1601,U_1600] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1600,c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1602),c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1603))
| ~ c_Orderings_Oord__class_Oless__eq(U_1600,U_1602,U_1603) )
& ( c_Orderings_Oord__class_Oless__eq(U_1600,U_1602,U_1603)
| ~ c_Orderings_Oord__class_Oless__eq(U_1600,c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1602),c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1603)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1600) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
cnf(f_536_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1600,U_1602,U_1603)
| ~ c_Orderings_Oord__class_Oless__eq(U_1600,c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1602),c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1603))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1600) ),
inference(clausify,[status(thm)],[f_536_2]) ).
cnf(f_536_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1600,c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1602),c_Groups_Oplus__class_Oplus(U_1600,U_1601,U_1603))
| ~ c_Orderings_Oord__class_Oless__eq(U_1600,U_1602,U_1603)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1600) ),
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__mono]) ).
fof(f_537_2,plain,
! [U_1607,U_1606,U_1605,U_1604] :
( c_Orderings_Oord__class_Oless__eq(U_1604,c_Groups_Oplus__class_Oplus(U_1604,U_1605,U_1607),c_Groups_Oplus__class_Oplus(U_1604,U_1606,U_1607))
| ~ c_Orderings_Oord__class_Oless__eq(U_1604,U_1605,U_1606)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1604) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
cnf(f_537_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1604,c_Groups_Oplus__class_Oplus(U_1604,U_1605,U_1607),c_Groups_Oplus__class_Oplus(U_1604,U_1606,U_1607))
| ~ c_Orderings_Oord__class_Oless__eq(U_1604,U_1605,U_1606)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1604) ),
inference(clausify,[status(thm)],[f_537_2]) ).
fof(f_538_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__mono]) ).
fof(f_538_2,plain,
! [U_1611,U_1610,U_1609,U_1608] :
( c_Orderings_Oord__class_Oless__eq(U_1608,c_Groups_Oplus__class_Oplus(U_1608,U_1611,U_1609),c_Groups_Oplus__class_Oplus(U_1608,U_1611,U_1610))
| ~ c_Orderings_Oord__class_Oless__eq(U_1608,U_1609,U_1610)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1608) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
cnf(f_538_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1608,c_Groups_Oplus__class_Oplus(U_1608,U_1611,U_1609),c_Groups_Oplus__class_Oplus(U_1608,U_1611,U_1610))
| ~ c_Orderings_Oord__class_Oless__eq(U_1608,U_1609,U_1610)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1608) ),
inference(clausify,[status(thm)],[f_538_2]) ).
fof(f_539_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__mono]) ).
fof(f_539_2,plain,
! [U_1616,U_1615,U_1614,U_1613,U_1612] :
( c_Orderings_Oord__class_Oless__eq(U_1612,c_Groups_Oplus__class_Oplus(U_1612,U_1613,U_1615),c_Groups_Oplus__class_Oplus(U_1612,U_1614,U_1616))
| ~ c_Orderings_Oord__class_Oless__eq(U_1612,U_1615,U_1616)
| ~ c_Orderings_Oord__class_Oless__eq(U_1612,U_1613,U_1614)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1612) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
cnf(f_539_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1612,c_Groups_Oplus__class_Oplus(U_1612,U_1613,U_1615),c_Groups_Oplus__class_Oplus(U_1612,U_1614,U_1616))
| ~ c_Orderings_Oord__class_Oless__eq(U_1612,U_1615,U_1616)
| ~ c_Orderings_Oord__class_Oless__eq(U_1612,U_1613,U_1614)
| ~ class_Groups_Oordered__ab__semigroup__add(U_1612) ),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right]) ).
fof(f_540_2,plain,
! [U_1620,U_1619,U_1618,U_1617] :
( c_Orderings_Oord__class_Oless__eq(U_1617,U_1618,U_1620)
| ~ c_Orderings_Oord__class_Oless__eq(U_1617,c_Groups_Oplus__class_Oplus(U_1617,U_1618,U_1619),c_Groups_Oplus__class_Oplus(U_1617,U_1620,U_1619))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1617) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
cnf(f_540_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1617,U_1618,U_1620)
| ~ c_Orderings_Oord__class_Oless__eq(U_1617,c_Groups_Oplus__class_Oplus(U_1617,U_1618,U_1619),c_Groups_Oplus__class_Oplus(U_1617,U_1620,U_1619))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1617) ),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left]) ).
fof(f_541_2,plain,
! [U_1624,U_1623,U_1622,U_1621] :
( c_Orderings_Oord__class_Oless__eq(U_1621,U_1623,U_1624)
| ~ c_Orderings_Oord__class_Oless__eq(U_1621,c_Groups_Oplus__class_Oplus(U_1621,U_1622,U_1623),c_Groups_Oplus__class_Oplus(U_1621,U_1622,U_1624))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1621) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
cnf(f_541_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1621,U_1623,U_1624)
| ~ c_Orderings_Oord__class_Oless__eq(U_1621,c_Groups_Oplus__class_Oplus(U_1621,U_1622,U_1623),c_Groups_Oplus__class_Oplus(U_1621,U_1622,U_1624))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1621) ),
inference(clausify,[status(thm)],[f_541_2]) ).
fof(f_542_1,plain,
! [V_p,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J]) ).
fof(f_542_2,plain,
! [U_1626,U_1625] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1625),U_1626,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1625))) = U_1626
| ~ class_Groups_Ocomm__monoid__add(U_1625) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
cnf(f_542_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1625),U_1626,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1625))) = U_1626
| ~ class_Groups_Ocomm__monoid__add(U_1625) ),
inference(clausify,[status(thm)],[f_542_2]) ).
fof(f_543_1,plain,
! [V_q,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J]) ).
fof(f_543_2,plain,
! [U_1628,U_1627] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1627),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1627)),U_1628) = U_1628
| ~ class_Groups_Ocomm__monoid__add(U_1627) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
cnf(f_543_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1627),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1627)),U_1628) = U_1628
| ~ class_Groups_Ocomm__monoid__add(U_1627) ),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_1,plain,
! [V_r,V_q,V_p,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left]) ).
fof(f_544_2,plain,
! [U_1632,U_1631,U_1630,U_1629] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1629)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1629),U_1630,U_1631)),U_1632) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1629)),U_1630),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1629)),U_1631),U_1632))
| ~ class_Rings_Ocomm__semiring__0(U_1629) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1629)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1629),U_1630,U_1631)),U_1632) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1629)),U_1630),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1629)),U_1631),U_1632))
| ~ class_Rings_Ocomm__semiring__0(U_1629) ),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
! [V_aa_2,V_b_2,T_a] :
( ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_b_2 != c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).
fof(f_545_2,plain,
! [U_1635,U_1634,U_1633] :
( ( ( U_1634 = c_Groups_Oplus__class_Oplus(U_1633,U_1634,U_1635)
| U_1635 != c_Groups_Ozero__class_Ozero(U_1633) )
& ( U_1635 = c_Groups_Ozero__class_Ozero(U_1633)
| U_1634 != c_Groups_Oplus__class_Oplus(U_1633,U_1634,U_1635) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1633) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
cnf(f_545_3,plain,
( U_1635 = c_Groups_Ozero__class_Ozero(U_1633)
| U_1634 != c_Groups_Oplus__class_Oplus(U_1633,U_1634,U_1635)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1633) ),
inference(clausify,[status(thm)],[f_545_2]) ).
cnf(f_545_4,plain,
( U_1634 = c_Groups_Oplus__class_Oplus(U_1633,U_1634,U_1635)
| U_1635 != c_Groups_Ozero__class_Ozero(U_1633)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1633) ),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).
fof(f_546_2,plain,
! [U_1637,U_1636] :
( c_Groups_Oplus__class_Oplus(U_1636,U_1637,c_Groups_Ozero__class_Ozero(U_1636)) = U_1637
| ~ class_Rings_Ocomm__semiring__1(U_1636) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
cnf(f_546_3,plain,
( c_Groups_Oplus__class_Oplus(U_1636,U_1637,c_Groups_Ozero__class_Ozero(U_1636)) = U_1637
| ~ class_Rings_Ocomm__semiring__1(U_1636) ),
inference(clausify,[status(thm)],[f_546_2]) ).
fof(f_547_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).
fof(f_547_2,plain,
! [U_1639,U_1638] :
( c_Groups_Oplus__class_Oplus(U_1638,c_Groups_Ozero__class_Ozero(U_1638),U_1639) = U_1639
| ~ class_Rings_Ocomm__semiring__1(U_1638) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
cnf(f_547_3,plain,
( c_Groups_Oplus__class_Oplus(U_1638,c_Groups_Ozero__class_Ozero(U_1638),U_1639) = U_1639
| ~ class_Rings_Ocomm__semiring__1(U_1638) ),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral]) ).
fof(f_548_2,plain,
! [U_1641,U_1640] :
( c_Groups_Oplus__class_Oplus(U_1640,U_1641,c_Groups_Ozero__class_Ozero(U_1640)) = U_1641
| ~ class_Groups_Ocomm__monoid__add(U_1640) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
cnf(f_548_3,plain,
( c_Groups_Oplus__class_Oplus(U_1640,U_1641,c_Groups_Ozero__class_Ozero(U_1640)) = U_1641
| ~ class_Groups_Ocomm__monoid__add(U_1640) ),
inference(clausify,[status(thm)],[f_548_2]) ).
fof(f_549_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__right]) ).
fof(f_549_2,plain,
! [U_1643,U_1642] :
( c_Groups_Oplus__class_Oplus(U_1642,U_1643,c_Groups_Ozero__class_Ozero(U_1642)) = U_1643
| ~ class_Groups_Omonoid__add(U_1642) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
cnf(f_549_3,plain,
( c_Groups_Oplus__class_Oplus(U_1642,U_1643,c_Groups_Ozero__class_Ozero(U_1642)) = U_1643
| ~ class_Groups_Omonoid__add(U_1642) ),
inference(clausify,[status(thm)],[f_549_2]) ).
fof(f_550_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).
fof(f_550_2,plain,
! [U_1645,U_1644] :
( ( ( c_Groups_Ozero__class_Ozero(U_1644) = c_Groups_Oplus__class_Oplus(U_1644,U_1645,U_1645)
| U_1645 != c_Groups_Ozero__class_Ozero(U_1644) )
& ( U_1645 = c_Groups_Ozero__class_Ozero(U_1644)
| c_Groups_Ozero__class_Ozero(U_1644) != c_Groups_Oplus__class_Oplus(U_1644,U_1645,U_1645) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1644) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
cnf(f_550_3,plain,
( U_1645 = c_Groups_Ozero__class_Ozero(U_1644)
| c_Groups_Ozero__class_Ozero(U_1644) != c_Groups_Oplus__class_Oplus(U_1644,U_1645,U_1645)
| ~ class_Groups_Olinordered__ab__group__add(U_1644) ),
inference(clausify,[status(thm)],[f_550_2]) ).
cnf(f_550_4,plain,
( c_Groups_Ozero__class_Ozero(U_1644) = c_Groups_Oplus__class_Oplus(U_1644,U_1645,U_1645)
| U_1645 != c_Groups_Ozero__class_Ozero(U_1644)
| ~ class_Groups_Olinordered__ab__group__add(U_1644) ),
inference(clausify,[status(thm)],[f_550_2]) ).
fof(f_551_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0]) ).
fof(f_551_2,plain,
! [U_1647,U_1646] :
( c_Groups_Oplus__class_Oplus(U_1646,c_Groups_Ozero__class_Ozero(U_1646),U_1647) = U_1647
| ~ class_Groups_Ocomm__monoid__add(U_1646) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
cnf(f_551_3,plain,
( c_Groups_Oplus__class_Oplus(U_1646,c_Groups_Ozero__class_Ozero(U_1646),U_1647) = U_1647
| ~ class_Groups_Ocomm__monoid__add(U_1646) ),
inference(clausify,[status(thm)],[f_551_2]) ).
fof(f_552_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
| ~ class_Groups_Omonoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__0__left]) ).
fof(f_552_2,plain,
! [U_1649,U_1648] :
( c_Groups_Oplus__class_Oplus(U_1648,c_Groups_Ozero__class_Ozero(U_1648),U_1649) = U_1649
| ~ class_Groups_Omonoid__add(U_1648) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
cnf(f_552_3,plain,
( c_Groups_Oplus__class_Oplus(U_1648,c_Groups_Ozero__class_Ozero(U_1648),U_1649) = U_1649
| ~ class_Groups_Omonoid__add(U_1648) ),
inference(clausify,[status(thm)],[f_552_2]) ).
fof(f_553_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left]) ).
fof(f_553_2,plain,
! [U_1653,U_1652,U_1651,U_1650] :
( c_Orderings_Oord__class_Oless(U_1650,U_1652,U_1653)
| ~ c_Orderings_Oord__class_Oless(U_1650,c_Groups_Oplus__class_Oplus(U_1650,U_1651,U_1652),c_Groups_Oplus__class_Oplus(U_1650,U_1651,U_1653))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1650) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
cnf(f_553_3,plain,
( c_Orderings_Oord__class_Oless(U_1650,U_1652,U_1653)
| ~ c_Orderings_Oord__class_Oless(U_1650,c_Groups_Oplus__class_Oplus(U_1650,U_1651,U_1652),c_Groups_Oplus__class_Oplus(U_1650,U_1651,U_1653))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1650) ),
inference(clausify,[status(thm)],[f_553_2]) ).
fof(f_554_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right]) ).
fof(f_554_2,plain,
! [U_1657,U_1656,U_1655,U_1654] :
( c_Orderings_Oord__class_Oless(U_1654,U_1655,U_1657)
| ~ c_Orderings_Oord__class_Oless(U_1654,c_Groups_Oplus__class_Oplus(U_1654,U_1655,U_1656),c_Groups_Oplus__class_Oplus(U_1654,U_1657,U_1656))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1654) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
cnf(f_554_3,plain,
( c_Orderings_Oord__class_Oless(U_1654,U_1655,U_1657)
| ~ c_Orderings_Oord__class_Oless(U_1654,c_Groups_Oplus__class_Oplus(U_1654,U_1655,U_1656),c_Groups_Oplus__class_Oplus(U_1654,U_1657,U_1656))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1654) ),
inference(clausify,[status(thm)],[f_554_2]) ).
fof(f_555_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__mono]) ).
fof(f_555_2,plain,
! [U_1662,U_1661,U_1660,U_1659,U_1658] :
( c_Orderings_Oord__class_Oless(U_1658,c_Groups_Oplus__class_Oplus(U_1658,U_1659,U_1661),c_Groups_Oplus__class_Oplus(U_1658,U_1660,U_1662))
| ~ c_Orderings_Oord__class_Oless(U_1658,U_1661,U_1662)
| ~ c_Orderings_Oord__class_Oless(U_1658,U_1659,U_1660)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1658) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
cnf(f_555_3,plain,
( c_Orderings_Oord__class_Oless(U_1658,c_Groups_Oplus__class_Oplus(U_1658,U_1659,U_1661),c_Groups_Oplus__class_Oplus(U_1658,U_1660,U_1662))
| ~ c_Orderings_Oord__class_Oless(U_1658,U_1661,U_1662)
| ~ c_Orderings_Oord__class_Oless(U_1658,U_1659,U_1660)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1658) ),
inference(clausify,[status(thm)],[f_555_2]) ).
fof(f_556_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono]) ).
fof(f_556_2,plain,
! [U_1666,U_1665,U_1664,U_1663] :
( c_Orderings_Oord__class_Oless(U_1663,c_Groups_Oplus__class_Oplus(U_1663,U_1666,U_1664),c_Groups_Oplus__class_Oplus(U_1663,U_1666,U_1665))
| ~ c_Orderings_Oord__class_Oless(U_1663,U_1664,U_1665)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1663) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
cnf(f_556_3,plain,
( c_Orderings_Oord__class_Oless(U_1663,c_Groups_Oplus__class_Oplus(U_1663,U_1666,U_1664),c_Groups_Oplus__class_Oplus(U_1663,U_1666,U_1665))
| ~ c_Orderings_Oord__class_Oless(U_1663,U_1664,U_1665)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1663) ),
inference(clausify,[status(thm)],[f_556_2]) ).
fof(f_557_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono]) ).
fof(f_557_2,plain,
! [U_1670,U_1669,U_1668,U_1667] :
( c_Orderings_Oord__class_Oless(U_1667,c_Groups_Oplus__class_Oplus(U_1667,U_1668,U_1670),c_Groups_Oplus__class_Oplus(U_1667,U_1669,U_1670))
| ~ c_Orderings_Oord__class_Oless(U_1667,U_1668,U_1669)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1667) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
cnf(f_557_3,plain,
( c_Orderings_Oord__class_Oless(U_1667,c_Groups_Oplus__class_Oplus(U_1667,U_1668,U_1670),c_Groups_Oplus__class_Oplus(U_1667,U_1669,U_1670))
| ~ c_Orderings_Oord__class_Oless(U_1667,U_1668,U_1669)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1667) ),
inference(clausify,[status(thm)],[f_557_2]) ).
fof(f_558_1,plain,
! [V_b_2,V_aa_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),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_558_2,plain,
! [U_1674,U_1673,U_1672,U_1671] :
( ( ( c_Orderings_Oord__class_Oless(U_1671,c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1673),c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1674))
| ~ c_Orderings_Oord__class_Oless(U_1671,U_1673,U_1674) )
& ( c_Orderings_Oord__class_Oless(U_1671,U_1673,U_1674)
| ~ c_Orderings_Oord__class_Oless(U_1671,c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1673),c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1674)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1671) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
cnf(f_558_3,plain,
( c_Orderings_Oord__class_Oless(U_1671,U_1673,U_1674)
| ~ c_Orderings_Oord__class_Oless(U_1671,c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1673),c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1674))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1671) ),
inference(clausify,[status(thm)],[f_558_2]) ).
cnf(f_558_4,plain,
( c_Orderings_Oord__class_Oless(U_1671,c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1673),c_Groups_Oplus__class_Oplus(U_1671,U_1672,U_1674))
| ~ c_Orderings_Oord__class_Oless(U_1671,U_1673,U_1674)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1671) ),
inference(clausify,[status(thm)],[f_558_2]) ).
fof(f_559_1,plain,
! [V_b_2,V_c_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),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_559_2,plain,
! [U_1678,U_1677,U_1676,U_1675] :
( ( ( c_Orderings_Oord__class_Oless(U_1675,c_Groups_Oplus__class_Oplus(U_1675,U_1676,U_1677),c_Groups_Oplus__class_Oplus(U_1675,U_1678,U_1677))
| ~ c_Orderings_Oord__class_Oless(U_1675,U_1676,U_1678) )
& ( c_Orderings_Oord__class_Oless(U_1675,U_1676,U_1678)
| ~ c_Orderings_Oord__class_Oless(U_1675,c_Groups_Oplus__class_Oplus(U_1675,U_1676,U_1677),c_Groups_Oplus__class_Oplus(U_1675,U_1678,U_1677)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1675) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
cnf(f_559_3,plain,
( c_Orderings_Oord__class_Oless(U_1675,U_1676,U_1678)
| ~ c_Orderings_Oord__class_Oless(U_1675,c_Groups_Oplus__class_Oplus(U_1675,U_1676,U_1677),c_Groups_Oplus__class_Oplus(U_1675,U_1678,U_1677))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1675) ),
inference(clausify,[status(thm)],[f_559_2]) ).
cnf(f_559_4,plain,
( c_Orderings_Oord__class_Oless(U_1675,c_Groups_Oplus__class_Oplus(U_1675,U_1676,U_1677),c_Groups_Oplus__class_Oplus(U_1675,U_1678,U_1677))
| ~ c_Orderings_Oord__class_Oless(U_1675,U_1676,U_1678)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1675) ),
inference(clausify,[status(thm)],[f_559_2]) ).
fof(f_560_1,plain,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
| ( V_y_2 != V_z_2
& V_w_2 != V_x_2 ) )
& ( V_y_2 = V_z_2
| V_w_2 = V_x_2
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).
fof(f_560_2,plain,
! [U_1683,U_1682,U_1681,U_1680,U_1679] :
( ( ( c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1683)) = c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1681))
| ( U_1681 != U_1683
& U_1680 != U_1682 ) )
& ( U_1681 = U_1683
| U_1680 = U_1682
| c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1683)) != c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1681)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1679) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
cnf(f_560_3,plain,
( U_1681 = U_1683
| U_1680 = U_1682
| c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1683)) != c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1681))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1679) ),
inference(clausify,[status(thm)],[f_560_2]) ).
cnf(f_560_4,plain,
( U_1680 != U_1682
| c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1683)) = c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1681))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1679) ),
inference(clausify,[status(thm)],[f_560_2]) ).
cnf(f_560_5,plain,
( U_1681 != U_1683
| c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1683)) = c_Groups_Oplus__class_Oplus(U_1679,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1680),U_1683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1679),U_1682),U_1681))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1679) ),
inference(clausify,[status(thm)],[f_560_2]) ).
fof(f_561_1,plain,
! [V_c,V_b,V_e,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c)
| ~ class_Rings_Osemiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_combine__common__factor]) ).
fof(f_561_2,plain,
! [U_1688,U_1687,U_1686,U_1685,U_1684] :
( c_Groups_Oplus__class_Oplus(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1685),U_1686),c_Groups_Oplus__class_Oplus(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1687),U_1686),U_1688)) = c_Groups_Oplus__class_Oplus(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),c_Groups_Oplus__class_Oplus(U_1684,U_1685,U_1687)),U_1686),U_1688)
| ~ class_Rings_Osemiring(U_1684) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
cnf(f_561_3,plain,
( c_Groups_Oplus__class_Oplus(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1685),U_1686),c_Groups_Oplus__class_Oplus(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1687),U_1686),U_1688)) = c_Groups_Oplus__class_Oplus(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),c_Groups_Oplus__class_Oplus(U_1684,U_1685,U_1687)),U_1686),U_1688)
| ~ class_Rings_Osemiring(U_1684) ),
inference(clausify,[status(thm)],[f_561_2]) ).
fof(f_562_1,plain,
! [V_b,V_m,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_562_2,plain,
! [U_1692,U_1691,U_1690,U_1689] :
( c_Groups_Oplus__class_Oplus(U_1689,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1689),U_1690),U_1691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1689),U_1692),U_1691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1689),c_Groups_Oplus__class_Oplus(U_1689,U_1690,U_1692)),U_1691)
| ~ class_Rings_Ocomm__semiring__1(U_1689) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
cnf(f_562_3,plain,
( c_Groups_Oplus__class_Oplus(U_1689,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1689),U_1690),U_1691),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1689),U_1692),U_1691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1689),c_Groups_Oplus__class_Oplus(U_1689,U_1690,U_1692)),U_1691)
| ~ class_Rings_Ocomm__semiring__1(U_1689) ),
inference(clausify,[status(thm)],[f_562_2]) ).
fof(f_563_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).
fof(f_563_2,plain,
! [U_1696,U_1695,U_1694,U_1693] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1693),c_Groups_Oplus__class_Oplus(U_1693,U_1694,U_1695)),U_1696) = c_Groups_Oplus__class_Oplus(U_1693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1693),U_1694),U_1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1693),U_1695),U_1696))
| ~ class_Rings_Ocomm__semiring__1(U_1693) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
cnf(f_563_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1693),c_Groups_Oplus__class_Oplus(U_1693,U_1694,U_1695)),U_1696) = c_Groups_Oplus__class_Oplus(U_1693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1693),U_1694),U_1696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1693),U_1695),U_1696))
| ~ class_Rings_Ocomm__semiring__1(U_1693) ),
inference(clausify,[status(thm)],[f_563_2]) ).
fof(f_564_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Ocomm__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib]) ).
fof(f_564_2,plain,
! [U_1700,U_1699,U_1698,U_1697] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),c_Groups_Oplus__class_Oplus(U_1697,U_1698,U_1699)),U_1700) = c_Groups_Oplus__class_Oplus(U_1697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1698),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1699),U_1700))
| ~ class_Rings_Ocomm__semiring(U_1697) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
cnf(f_564_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),c_Groups_Oplus__class_Oplus(U_1697,U_1698,U_1699)),U_1700) = c_Groups_Oplus__class_Oplus(U_1697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1698),U_1700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1699),U_1700))
| ~ class_Rings_Ocomm__semiring(U_1697) ),
inference(clausify,[status(thm)],[f_564_2]) ).
fof(f_565_1,plain,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( ( ( ( V_c_2 != V_d_2
& V_aa_2 != V_b_2 )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) )
& ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_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_aa_2 = V_b_2 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).
fof(f_565_2,plain,
! [U_1705,U_1704,U_1703,U_1702,U_1701] :
( ( ( ( U_1704 != U_1705
& U_1702 != U_1703 )
| c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1705)) = c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1704)) )
& ( c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1705)) != c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1704))
| U_1704 = U_1705
| U_1702 = U_1703 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1701) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
cnf(f_565_3,plain,
( c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1705)) != c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1704))
| U_1704 = U_1705
| U_1702 = U_1703
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1701) ),
inference(clausify,[status(thm)],[f_565_2]) ).
cnf(f_565_4,plain,
( U_1702 != U_1703
| c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1705)) = c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1704))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1701) ),
inference(clausify,[status(thm)],[f_565_2]) ).
cnf(f_565_5,plain,
( U_1704 != U_1705
| c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1705)) = c_Groups_Oplus__class_Oplus(U_1701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1702),U_1705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1701),U_1703),U_1704))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1701) ),
inference(clausify,[status(thm)],[f_565_2]) ).
fof(f_566_1,plain,
! [V_z,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_566_2,plain,
! [U_1709,U_1708,U_1707,U_1706] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1706),U_1707),c_Groups_Oplus__class_Oplus(U_1706,U_1708,U_1709)) = c_Groups_Oplus__class_Oplus(U_1706,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1706),U_1707),U_1708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1706),U_1707),U_1709))
| ~ class_Rings_Ocomm__semiring__1(U_1706) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
cnf(f_566_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1706),U_1707),c_Groups_Oplus__class_Oplus(U_1706,U_1708,U_1709)) = c_Groups_Oplus__class_Oplus(U_1706,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1706),U_1707),U_1708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1706),U_1707),U_1709))
| ~ class_Rings_Ocomm__semiring__1(U_1706) ),
inference(clausify,[status(thm)],[f_566_2]) ).
fof(f_567_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd]) ).
fof(f_567_2,plain,
! [U_1713,U_1712,U_1711,U_1710] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1710),c_Groups_Oplus__class_Oplus(U_1710,U_1711,U_1712)),U_1713) = c_Groups_Oplus__class_Oplus(U_1710,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1710),U_1711),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1710),U_1712),U_1713))
| ~ class_RealVector_Oreal__normed__algebra(U_1710) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
cnf(f_567_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1710),c_Groups_Oplus__class_Oplus(U_1710,U_1711,U_1712)),U_1713) = c_Groups_Oplus__class_Oplus(U_1710,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1710),U_1711),U_1713),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1710),U_1712),U_1713))
| ~ class_RealVector_Oreal__normed__algebra(U_1710) ),
inference(clausify,[status(thm)],[f_567_2]) ).
fof(f_568_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left]) ).
fof(f_568_2,plain,
! [U_1717,U_1716,U_1715,U_1714] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),c_Groups_Oplus__class_Oplus(U_1714,U_1715,U_1716)),U_1717) = c_Groups_Oplus__class_Oplus(U_1714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1716),U_1717))
| ~ class_RealVector_Oreal__normed__algebra(U_1714) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
cnf(f_568_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),c_Groups_Oplus__class_Oplus(U_1714,U_1715,U_1716)),U_1717) = c_Groups_Oplus__class_Oplus(U_1714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1715),U_1717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1714),U_1716),U_1717))
| ~ class_RealVector_Oreal__normed__algebra(U_1714) ),
inference(clausify,[status(thm)],[f_568_2]) ).
fof(f_569_1,plain,
! [V_y,V_x,V_xa,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd]) ).
fof(f_569_2,plain,
! [U_1721,U_1720,U_1719,U_1718] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),c_Groups_Oplus__class_Oplus(U_1718,U_1720,U_1721)) = c_Groups_Oplus__class_Oplus(U_1718,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),U_1720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),U_1721))
| ~ class_RealVector_Oreal__normed__algebra(U_1718) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
cnf(f_569_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),c_Groups_Oplus__class_Oplus(U_1718,U_1720,U_1721)) = c_Groups_Oplus__class_Oplus(U_1718,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),U_1720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1718),U_1719),U_1721))
| ~ class_RealVector_Oreal__normed__algebra(U_1718) ),
inference(clausify,[status(thm)],[f_569_2]) ).
fof(f_570_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right]) ).
fof(f_570_2,plain,
! [U_1725,U_1724,U_1723,U_1722] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1722),U_1723),c_Groups_Oplus__class_Oplus(U_1722,U_1724,U_1725)) = c_Groups_Oplus__class_Oplus(U_1722,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1722),U_1723),U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1722),U_1723),U_1725))
| ~ class_RealVector_Oreal__normed__algebra(U_1722) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
cnf(f_570_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1722),U_1723),c_Groups_Oplus__class_Oplus(U_1722,U_1724,U_1725)) = c_Groups_Oplus__class_Oplus(U_1722,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1722),U_1723),U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1722),U_1723),U_1725))
| ~ class_RealVector_Oreal__normed__algebra(U_1722) ),
inference(clausify,[status(thm)],[f_570_2]) ).
fof(f_571_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__cancel]) ).
fof(f_571_2,plain,
! [U_1728,U_1727,U_1726] :
( c_Groups_Oplus__class_Oplus(U_1726,c_Groups_Ouminus__class_Ouminus(U_1726,U_1727),c_Groups_Oplus__class_Oplus(U_1726,U_1727,U_1728)) = U_1728
| ~ class_Groups_Ogroup__add(U_1726) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
cnf(f_571_3,plain,
( c_Groups_Oplus__class_Oplus(U_1726,c_Groups_Ouminus__class_Ouminus(U_1726,U_1727),c_Groups_Oplus__class_Oplus(U_1726,U_1727,U_1728)) = U_1728
| ~ class_Groups_Ogroup__add(U_1726) ),
inference(clausify,[status(thm)],[f_571_2]) ).
fof(f_572_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__minus__cancel]) ).
fof(f_572_2,plain,
! [U_1731,U_1730,U_1729] :
( c_Groups_Oplus__class_Oplus(U_1729,U_1730,c_Groups_Oplus__class_Oplus(U_1729,c_Groups_Ouminus__class_Ouminus(U_1729,U_1730),U_1731)) = U_1731
| ~ class_Groups_Ogroup__add(U_1729) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
cnf(f_572_3,plain,
( c_Groups_Oplus__class_Oplus(U_1729,U_1730,c_Groups_Oplus__class_Oplus(U_1729,c_Groups_Ouminus__class_Ouminus(U_1729,U_1730),U_1731)) = U_1731
| ~ class_Groups_Ogroup__add(U_1729) ),
inference(clausify,[status(thm)],[f_572_2]) ).
fof(f_573_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add]) ).
fof(f_573_2,plain,
! [U_1734,U_1733,U_1732] :
( c_Groups_Ouminus__class_Ouminus(U_1732,c_Groups_Oplus__class_Oplus(U_1732,U_1733,U_1734)) = c_Groups_Oplus__class_Oplus(U_1732,c_Groups_Ouminus__class_Ouminus(U_1732,U_1734),c_Groups_Ouminus__class_Ouminus(U_1732,U_1733))
| ~ class_Groups_Ogroup__add(U_1732) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
cnf(f_573_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1732,c_Groups_Oplus__class_Oplus(U_1732,U_1733,U_1734)) = c_Groups_Oplus__class_Oplus(U_1732,c_Groups_Ouminus__class_Ouminus(U_1732,U_1734),c_Groups_Ouminus__class_Ouminus(U_1732,U_1733))
| ~ class_Groups_Ogroup__add(U_1732) ),
inference(clausify,[status(thm)],[f_573_2]) ).
fof(f_574_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__distrib]) ).
fof(f_574_2,plain,
! [U_1737,U_1736,U_1735] :
( c_Groups_Ouminus__class_Ouminus(U_1735,c_Groups_Oplus__class_Oplus(U_1735,U_1736,U_1737)) = c_Groups_Oplus__class_Oplus(U_1735,c_Groups_Ouminus__class_Ouminus(U_1735,U_1736),c_Groups_Ouminus__class_Ouminus(U_1735,U_1737))
| ~ class_Groups_Oab__group__add(U_1735) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
cnf(f_574_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1735,c_Groups_Oplus__class_Oplus(U_1735,U_1736,U_1737)) = c_Groups_Oplus__class_Oplus(U_1735,c_Groups_Ouminus__class_Ouminus(U_1735,U_1736),c_Groups_Ouminus__class_Ouminus(U_1735,U_1737))
| ~ class_Groups_Oab__group__add(U_1735) ),
inference(clausify,[status(thm)],[f_574_2]) ).
fof(f_575_1,plain,
! [V_n,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__add]) ).
fof(f_575_2,plain,
! [U_1741,U_1740,U_1739,U_1738] :
( hAPP(c_Polynomial_Ocoeff(U_1738,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1738),U_1739,U_1740)),U_1741) = c_Groups_Oplus__class_Oplus(U_1738,hAPP(c_Polynomial_Ocoeff(U_1738,U_1739),U_1741),hAPP(c_Polynomial_Ocoeff(U_1738,U_1740),U_1741))
| ~ class_Groups_Ocomm__monoid__add(U_1738) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
cnf(f_575_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1738,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1738),U_1739,U_1740)),U_1741) = c_Groups_Oplus__class_Oplus(U_1738,hAPP(c_Polynomial_Ocoeff(U_1738,U_1739),U_1741),hAPP(c_Polynomial_Ocoeff(U_1738,U_1740),U_1741))
| ~ class_Groups_Ocomm__monoid__add(U_1738) ),
inference(clausify,[status(thm)],[f_575_2]) ).
fof(f_576_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n)
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__monom]) ).
fof(f_576_2,plain,
! [U_1745,U_1744,U_1743,U_1742] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1742),c_Polynomial_Omonom(U_1742,U_1743,U_1744),c_Polynomial_Omonom(U_1742,U_1745,U_1744)) = c_Polynomial_Omonom(U_1742,c_Groups_Oplus__class_Oplus(U_1742,U_1743,U_1745),U_1744)
| ~ class_Groups_Ocomm__monoid__add(U_1742) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
cnf(f_576_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1742),c_Polynomial_Omonom(U_1742,U_1743,U_1744),c_Polynomial_Omonom(U_1742,U_1745,U_1744)) = c_Polynomial_Omonom(U_1742,c_Groups_Oplus__class_Oplus(U_1742,U_1743,U_1745),U_1744)
| ~ class_Groups_Ocomm__monoid__add(U_1742) ),
inference(clausify,[status(thm)],[f_576_2]) ).
fof(f_577_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__add]) ).
fof(f_577_2,plain,
! [U_1749,U_1748,U_1747,U_1746] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1746),U_1747),c_Groups_Oplus__class_Oplus(U_1746,U_1748,U_1749)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1746),U_1747),U_1749))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1746),U_1747),U_1748))
| ~ class_Rings_Ocomm__semiring__1(U_1746) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
cnf(f_577_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1746),U_1747),c_Groups_Oplus__class_Oplus(U_1746,U_1748,U_1749)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1746),U_1747),U_1749))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1746),U_1747),U_1748))
| ~ class_Rings_Ocomm__semiring__1(U_1746) ),
inference(clausify,[status(thm)],[f_577_2]) ).
fof(f_578_1,plain,
! [V_c,V_a,V_b,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) != c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq]) ).
fof(f_578_2,plain,
! [U_1753,U_1752,U_1751,U_1750] :
( U_1751 = U_1753
| c_Groups_Oplus__class_Oplus(U_1750,U_1751,U_1752) != c_Groups_Oplus__class_Oplus(U_1750,U_1753,U_1752)
| ~ class_Groups_Ocancel__semigroup__add(U_1750) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
cnf(f_578_3,plain,
( U_1751 = U_1753
| c_Groups_Oplus__class_Oplus(U_1750,U_1751,U_1752) != c_Groups_Oplus__class_Oplus(U_1750,U_1753,U_1752)
| ~ class_Groups_Ocancel__semigroup__add(U_1750) ),
inference(clausify,[status(thm)],[f_578_2]) ).
fof(f_579_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
| ~ class_Groups_Ocancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__imp__eq]) ).
fof(f_579_2,plain,
! [U_1757,U_1756,U_1755,U_1754] :
( U_1756 = U_1757
| c_Groups_Oplus__class_Oplus(U_1754,U_1755,U_1756) != c_Groups_Oplus__class_Oplus(U_1754,U_1755,U_1757)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1754) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
cnf(f_579_3,plain,
( U_1756 = U_1757
| c_Groups_Oplus__class_Oplus(U_1754,U_1755,U_1756) != c_Groups_Oplus__class_Oplus(U_1754,U_1755,U_1757)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1754) ),
inference(clausify,[status(thm)],[f_579_2]) ).
fof(f_580_1,plain,
! [V_c,V_b,V_a,T_a] :
( V_b = V_c
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).
fof(f_580_2,plain,
! [U_1761,U_1760,U_1759,U_1758] :
( U_1760 = U_1761
| c_Groups_Oplus__class_Oplus(U_1758,U_1759,U_1760) != c_Groups_Oplus__class_Oplus(U_1758,U_1759,U_1761)
| ~ class_Groups_Ocancel__semigroup__add(U_1758) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
cnf(f_580_3,plain,
( U_1760 = U_1761
| c_Groups_Oplus__class_Oplus(U_1758,U_1759,U_1760) != c_Groups_Oplus__class_Oplus(U_1758,U_1759,U_1761)
| ~ class_Groups_Ocancel__semigroup__add(U_1758) ),
inference(clausify,[status(thm)],[f_580_2]) ).
fof(f_581_1,plain,
! [V_c_2,V_aa_2,V_b_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2) != c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_581_2,plain,
! [U_1765,U_1764,U_1763,U_1762] :
( ( ( c_Groups_Oplus__class_Oplus(U_1762,U_1763,U_1764) = c_Groups_Oplus__class_Oplus(U_1762,U_1765,U_1764)
| U_1763 != U_1765 )
& ( U_1763 = U_1765
| c_Groups_Oplus__class_Oplus(U_1762,U_1763,U_1764) != c_Groups_Oplus__class_Oplus(U_1762,U_1765,U_1764) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1762) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
cnf(f_581_3,plain,
( U_1763 = U_1765
| c_Groups_Oplus__class_Oplus(U_1762,U_1763,U_1764) != c_Groups_Oplus__class_Oplus(U_1762,U_1765,U_1764)
| ~ class_Groups_Ocancel__semigroup__add(U_1762) ),
inference(clausify,[status(thm)],[f_581_2]) ).
cnf(f_581_4,plain,
( c_Groups_Oplus__class_Oplus(U_1762,U_1763,U_1764) = c_Groups_Oplus__class_Oplus(U_1762,U_1765,U_1764)
| U_1763 != U_1765
| ~ class_Groups_Ocancel__semigroup__add(U_1762) ),
inference(clausify,[status(thm)],[f_581_2]) ).
fof(f_582_1,plain,
! [V_c_2,V_b_2,V_aa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) != c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_582_2,plain,
! [U_1769,U_1768,U_1767,U_1766] :
( ( ( c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1768) = c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1769)
| U_1768 != U_1769 )
& ( U_1768 = U_1769
| c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1768) != c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1769) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1766) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
cnf(f_582_3,plain,
( U_1768 = U_1769
| c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1768) != c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1769)
| ~ class_Groups_Ocancel__semigroup__add(U_1766) ),
inference(clausify,[status(thm)],[f_582_2]) ).
cnf(f_582_4,plain,
( c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1768) = c_Groups_Oplus__class_Oplus(U_1766,U_1767,U_1769)
| U_1768 != U_1769
| ~ class_Groups_Ocancel__semigroup__add(U_1766) ),
inference(clausify,[status(thm)],[f_582_2]) ).
fof(f_583_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Groups_Oab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J]) ).
fof(f_583_2,plain,
! [U_1773,U_1772,U_1771,U_1770] :
( c_Groups_Oplus__class_Oplus(U_1770,c_Groups_Oplus__class_Oplus(U_1770,U_1771,U_1772),U_1773) = c_Groups_Oplus__class_Oplus(U_1770,U_1771,c_Groups_Oplus__class_Oplus(U_1770,U_1772,U_1773))
| ~ class_Groups_Oab__semigroup__add(U_1770) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
cnf(f_583_3,plain,
( c_Groups_Oplus__class_Oplus(U_1770,c_Groups_Oplus__class_Oplus(U_1770,U_1771,U_1772),U_1773) = c_Groups_Oplus__class_Oplus(U_1770,U_1771,c_Groups_Oplus__class_Oplus(U_1770,U_1772,U_1773))
| ~ class_Groups_Oab__semigroup__add(U_1770) ),
inference(clausify,[status(thm)],[f_583_2]) ).
fof(f_584_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).
fof(f_584_2,plain,
! [U_1778,U_1777,U_1776,U_1775,U_1774] :
( c_Groups_Oplus__class_Oplus(U_1774,c_Groups_Oplus__class_Oplus(U_1774,U_1775,U_1776),c_Groups_Oplus__class_Oplus(U_1774,U_1777,U_1778)) = c_Groups_Oplus__class_Oplus(U_1774,c_Groups_Oplus__class_Oplus(U_1774,U_1775,U_1777),c_Groups_Oplus__class_Oplus(U_1774,U_1776,U_1778))
| ~ class_Rings_Ocomm__semiring__1(U_1774) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
cnf(f_584_3,plain,
( c_Groups_Oplus__class_Oplus(U_1774,c_Groups_Oplus__class_Oplus(U_1774,U_1775,U_1776),c_Groups_Oplus__class_Oplus(U_1774,U_1777,U_1778)) = c_Groups_Oplus__class_Oplus(U_1774,c_Groups_Oplus__class_Oplus(U_1774,U_1775,U_1777),c_Groups_Oplus__class_Oplus(U_1774,U_1776,U_1778))
| ~ class_Rings_Ocomm__semiring__1(U_1774) ),
inference(clausify,[status(thm)],[f_584_2]) ).
fof(f_585_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).
fof(f_585_2,plain,
! [U_1782,U_1781,U_1780,U_1779] :
( c_Groups_Oplus__class_Oplus(U_1779,c_Groups_Oplus__class_Oplus(U_1779,U_1780,U_1781),U_1782) = c_Groups_Oplus__class_Oplus(U_1779,c_Groups_Oplus__class_Oplus(U_1779,U_1780,U_1782),U_1781)
| ~ class_Rings_Ocomm__semiring__1(U_1779) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
cnf(f_585_3,plain,
( c_Groups_Oplus__class_Oplus(U_1779,c_Groups_Oplus__class_Oplus(U_1779,U_1780,U_1781),U_1782) = c_Groups_Oplus__class_Oplus(U_1779,c_Groups_Oplus__class_Oplus(U_1779,U_1780,U_1782),U_1781)
| ~ class_Rings_Ocomm__semiring__1(U_1779) ),
inference(clausify,[status(thm)],[f_585_2]) ).
fof(f_586_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).
fof(f_586_2,plain,
! [U_1786,U_1785,U_1784,U_1783] :
( c_Groups_Oplus__class_Oplus(U_1783,c_Groups_Oplus__class_Oplus(U_1783,U_1784,U_1785),U_1786) = c_Groups_Oplus__class_Oplus(U_1783,U_1784,c_Groups_Oplus__class_Oplus(U_1783,U_1785,U_1786))
| ~ class_Rings_Ocomm__semiring__1(U_1783) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
cnf(f_586_3,plain,
( c_Groups_Oplus__class_Oplus(U_1783,c_Groups_Oplus__class_Oplus(U_1783,U_1784,U_1785),U_1786) = c_Groups_Oplus__class_Oplus(U_1783,U_1784,c_Groups_Oplus__class_Oplus(U_1783,U_1785,U_1786))
| ~ class_Rings_Ocomm__semiring__1(U_1783) ),
inference(clausify,[status(thm)],[f_586_2]) ).
fof(f_587_1,plain,
! [V_d,V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).
fof(f_587_2,plain,
! [U_1790,U_1789,U_1788,U_1787] :
( c_Groups_Oplus__class_Oplus(U_1787,U_1788,c_Groups_Oplus__class_Oplus(U_1787,U_1789,U_1790)) = c_Groups_Oplus__class_Oplus(U_1787,c_Groups_Oplus__class_Oplus(U_1787,U_1788,U_1789),U_1790)
| ~ class_Rings_Ocomm__semiring__1(U_1787) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
cnf(f_587_3,plain,
( c_Groups_Oplus__class_Oplus(U_1787,U_1788,c_Groups_Oplus__class_Oplus(U_1787,U_1789,U_1790)) = c_Groups_Oplus__class_Oplus(U_1787,c_Groups_Oplus__class_Oplus(U_1787,U_1788,U_1789),U_1790)
| ~ class_Rings_Ocomm__semiring__1(U_1787) ),
inference(clausify,[status(thm)],[f_587_2]) ).
fof(f_588_1,plain,
! [V_d,V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).
fof(f_588_2,plain,
! [U_1794,U_1793,U_1792,U_1791] :
( c_Groups_Oplus__class_Oplus(U_1791,U_1792,c_Groups_Oplus__class_Oplus(U_1791,U_1793,U_1794)) = c_Groups_Oplus__class_Oplus(U_1791,U_1793,c_Groups_Oplus__class_Oplus(U_1791,U_1792,U_1794))
| ~ class_Rings_Ocomm__semiring__1(U_1791) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
cnf(f_588_3,plain,
( c_Groups_Oplus__class_Oplus(U_1791,U_1792,c_Groups_Oplus__class_Oplus(U_1791,U_1793,U_1794)) = c_Groups_Oplus__class_Oplus(U_1791,U_1793,c_Groups_Oplus__class_Oplus(U_1791,U_1792,U_1794))
| ~ class_Rings_Ocomm__semiring__1(U_1791) ),
inference(clausify,[status(thm)],[f_588_2]) ).
fof(f_589_1,plain,
! [V_c,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
fof(f_589_2,plain,
! [U_1797,U_1796,U_1795] :
( c_Groups_Oplus__class_Oplus(U_1795,U_1796,U_1797) = c_Groups_Oplus__class_Oplus(U_1795,U_1797,U_1796)
| ~ class_Rings_Ocomm__semiring__1(U_1795) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
cnf(f_589_3,plain,
( c_Groups_Oplus__class_Oplus(U_1795,U_1796,U_1797) = c_Groups_Oplus__class_Oplus(U_1795,U_1797,U_1796)
| ~ class_Rings_Ocomm__semiring__1(U_1795) ),
inference(clausify,[status(thm)],[f_589_2]) ).
fof(f_590_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__add]) ).
fof(f_590_2,plain,
! [U_1801,U_1800,U_1799,U_1798] :
( hAPP(c_Polynomial_Opoly(U_1798,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1798),U_1799,U_1800)),U_1801) = c_Groups_Oplus__class_Oplus(U_1798,hAPP(c_Polynomial_Opoly(U_1798,U_1799),U_1801),hAPP(c_Polynomial_Opoly(U_1798,U_1800),U_1801))
| ~ class_Rings_Ocomm__semiring__0(U_1798) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
( hAPP(c_Polynomial_Opoly(U_1798,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1798),U_1799,U_1800)),U_1801) = c_Groups_Oplus__class_Oplus(U_1798,hAPP(c_Polynomial_Opoly(U_1798,U_1799),U_1801),hAPP(c_Polynomial_Opoly(U_1798,U_1800),U_1801))
| ~ class_Rings_Ocomm__semiring__0(U_1798) ),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_1,plain,
! [V_q,V_b,V_p,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pCons]) ).
fof(f_591_2,plain,
! [U_1806,U_1805,U_1804,U_1803,U_1802] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1802),c_Polynomial_OpCons(U_1802,U_1803,U_1804),c_Polynomial_OpCons(U_1802,U_1805,U_1806)) = c_Polynomial_OpCons(U_1802,c_Groups_Oplus__class_Oplus(U_1802,U_1803,U_1805),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1802),U_1804,U_1806))
| ~ class_Groups_Ocomm__monoid__add(U_1802) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
cnf(f_591_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1802),c_Polynomial_OpCons(U_1802,U_1803,U_1804),c_Polynomial_OpCons(U_1802,U_1805,U_1806)) = c_Polynomial_OpCons(U_1802,c_Groups_Oplus__class_Oplus(U_1802,U_1803,U_1805),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1802),U_1804,U_1806))
| ~ class_Groups_Ocomm__monoid__add(U_1802) ),
inference(clausify,[status(thm)],[f_591_2]) ).
fof(f_592_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))
| ~ c_Polynomial_Opos__poly(T_a,V_q)
| ~ c_Polynomial_Opos__poly(T_a,V_p)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__add]) ).
fof(f_592_2,plain,
! [U_1809,U_1808,U_1807] :
( c_Polynomial_Opos__poly(U_1807,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1807),U_1808,U_1809))
| ~ c_Polynomial_Opos__poly(U_1807,U_1809)
| ~ c_Polynomial_Opos__poly(U_1807,U_1808)
| ~ class_Rings_Olinordered__idom(U_1807) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
cnf(f_592_3,plain,
( c_Polynomial_Opos__poly(U_1807,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1807),U_1808,U_1809))
| ~ c_Polynomial_Opos__poly(U_1807,U_1809)
| ~ c_Polynomial_Opos__poly(U_1807,U_1808)
| ~ class_Rings_Olinordered__idom(U_1807) ),
inference(clausify,[status(thm)],[f_592_2]) ).
fof(f_593_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_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_593_2,plain,
! [U_1811,U_1810] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),c_Groups_Oplus__class_Oplus(U_1810,U_1811,U_1811))
| ~ c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),U_1811) )
& ( c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),U_1811)
| ~ c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),c_Groups_Oplus__class_Oplus(U_1810,U_1811,U_1811)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1810) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
cnf(f_593_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),U_1811)
| ~ c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),c_Groups_Oplus__class_Oplus(U_1810,U_1811,U_1811))
| ~ class_Groups_Olinordered__ab__group__add(U_1810) ),
inference(clausify,[status(thm)],[f_593_2]) ).
cnf(f_593_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),c_Groups_Oplus__class_Oplus(U_1810,U_1811,U_1811))
| ~ c_Orderings_Oord__class_Oless__eq(U_1810,c_Groups_Ozero__class_Ozero(U_1810),U_1811)
| ~ class_Groups_Olinordered__ab__group__add(U_1810) ),
inference(clausify,[status(thm)],[f_593_2]) ).
fof(f_594_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_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_594_2,plain,
! [U_1813,U_1812] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1812,c_Groups_Oplus__class_Oplus(U_1812,U_1813,U_1813),c_Groups_Ozero__class_Ozero(U_1812))
| ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ozero__class_Ozero(U_1812)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ozero__class_Ozero(U_1812))
| ~ c_Orderings_Oord__class_Oless__eq(U_1812,c_Groups_Oplus__class_Oplus(U_1812,U_1813,U_1813),c_Groups_Ozero__class_Ozero(U_1812)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1812) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
cnf(f_594_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ozero__class_Ozero(U_1812))
| ~ c_Orderings_Oord__class_Oless__eq(U_1812,c_Groups_Oplus__class_Oplus(U_1812,U_1813,U_1813),c_Groups_Ozero__class_Ozero(U_1812))
| ~ class_Groups_Olinordered__ab__group__add(U_1812) ),
inference(clausify,[status(thm)],[f_594_2]) ).
cnf(f_594_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1812,c_Groups_Oplus__class_Oplus(U_1812,U_1813,U_1813),c_Groups_Ozero__class_Ozero(U_1812))
| ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ozero__class_Ozero(U_1812))
| ~ class_Groups_Olinordered__ab__group__add(U_1812) ),
inference(clausify,[status(thm)],[f_594_2]) ).
fof(f_595_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg]) ).
fof(f_595_2,plain,
! [U_1816,U_1815,U_1814] :
( c_Orderings_Oord__class_Oless__eq(U_1814,c_Groups_Ozero__class_Ozero(U_1814),c_Groups_Oplus__class_Oplus(U_1814,U_1815,U_1816))
| ~ c_Orderings_Oord__class_Oless__eq(U_1814,c_Groups_Ozero__class_Ozero(U_1814),U_1816)
| ~ c_Orderings_Oord__class_Oless__eq(U_1814,c_Groups_Ozero__class_Ozero(U_1814),U_1815)
| ~ class_Groups_Oordered__comm__monoid__add(U_1814) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1814,c_Groups_Ozero__class_Ozero(U_1814),c_Groups_Oplus__class_Oplus(U_1814,U_1815,U_1816))
| ~ c_Orderings_Oord__class_Oless__eq(U_1814,c_Groups_Ozero__class_Ozero(U_1814),U_1816)
| ~ c_Orderings_Oord__class_Oless__eq(U_1814,c_Groups_Ozero__class_Ozero(U_1814),U_1815)
| ~ class_Groups_Oordered__comm__monoid__add(U_1814) ),
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_596_2,plain,
! [U_1819,U_1818,U_1817] :
( ( ( c_Groups_Oplus__class_Oplus(U_1817,U_1818,U_1819) = c_Groups_Ozero__class_Ozero(U_1817)
| U_1819 != c_Groups_Ozero__class_Ozero(U_1817)
| U_1818 != c_Groups_Ozero__class_Ozero(U_1817) )
& ( ( U_1819 = c_Groups_Ozero__class_Ozero(U_1817)
& U_1818 = c_Groups_Ozero__class_Ozero(U_1817) )
| c_Groups_Oplus__class_Oplus(U_1817,U_1818,U_1819) != c_Groups_Ozero__class_Ozero(U_1817) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1819)
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1818)
| ~ class_Groups_Oordered__comm__monoid__add(U_1817) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
cnf(f_596_3,plain,
( U_1818 = c_Groups_Ozero__class_Ozero(U_1817)
| c_Groups_Oplus__class_Oplus(U_1817,U_1818,U_1819) != c_Groups_Ozero__class_Ozero(U_1817)
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1819)
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1818)
| ~ class_Groups_Oordered__comm__monoid__add(U_1817) ),
inference(clausify,[status(thm)],[f_596_2]) ).
cnf(f_596_4,plain,
( U_1819 = c_Groups_Ozero__class_Ozero(U_1817)
| c_Groups_Oplus__class_Oplus(U_1817,U_1818,U_1819) != c_Groups_Ozero__class_Ozero(U_1817)
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1819)
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1818)
| ~ class_Groups_Oordered__comm__monoid__add(U_1817) ),
inference(clausify,[status(thm)],[f_596_2]) ).
cnf(f_596_5,plain,
( c_Groups_Oplus__class_Oplus(U_1817,U_1818,U_1819) = c_Groups_Ozero__class_Ozero(U_1817)
| U_1819 != c_Groups_Ozero__class_Ozero(U_1817)
| U_1818 != c_Groups_Ozero__class_Ozero(U_1817)
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1819)
| ~ c_Orderings_Oord__class_Oless__eq(U_1817,c_Groups_Ozero__class_Ozero(U_1817),U_1818)
| ~ class_Groups_Oordered__comm__monoid__add(U_1817) ),
inference(clausify,[status(thm)],[f_596_2]) ).
fof(f_597_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing]) ).
fof(f_597_2,plain,
! [U_1823,U_1822,U_1821,U_1820] :
( c_Orderings_Oord__class_Oless__eq(U_1820,U_1822,c_Groups_Oplus__class_Oplus(U_1820,U_1821,U_1823))
| ~ c_Orderings_Oord__class_Oless__eq(U_1820,U_1822,U_1823)
| ~ c_Orderings_Oord__class_Oless__eq(U_1820,c_Groups_Ozero__class_Ozero(U_1820),U_1821)
| ~ class_Groups_Oordered__comm__monoid__add(U_1820) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
cnf(f_597_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1820,U_1822,c_Groups_Oplus__class_Oplus(U_1820,U_1821,U_1823))
| ~ c_Orderings_Oord__class_Oless__eq(U_1820,U_1822,U_1823)
| ~ c_Orderings_Oord__class_Oless__eq(U_1820,c_Groups_Ozero__class_Ozero(U_1820),U_1821)
| ~ class_Groups_Oordered__comm__monoid__add(U_1820) ),
inference(clausify,[status(thm)],[f_597_2]) ).
fof(f_598_1,plain,
! [V_a,V_b,V_c,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__increasing2]) ).
fof(f_598_2,plain,
! [U_1827,U_1826,U_1825,U_1824] :
( c_Orderings_Oord__class_Oless__eq(U_1824,U_1826,c_Groups_Oplus__class_Oplus(U_1824,U_1827,U_1825))
| ~ c_Orderings_Oord__class_Oless__eq(U_1824,U_1826,U_1827)
| ~ c_Orderings_Oord__class_Oless__eq(U_1824,c_Groups_Ozero__class_Ozero(U_1824),U_1825)
| ~ class_Groups_Oordered__comm__monoid__add(U_1824) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1824,U_1826,c_Groups_Oplus__class_Oplus(U_1824,U_1827,U_1825))
| ~ c_Orderings_Oord__class_Oless__eq(U_1824,U_1826,U_1827)
| ~ c_Orderings_Oord__class_Oless__eq(U_1824,c_Groups_Ozero__class_Ozero(U_1824),U_1825)
| ~ class_Groups_Oordered__comm__monoid__add(U_1824) ),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos]) ).
fof(f_599_2,plain,
! [U_1830,U_1829,U_1828] :
( c_Orderings_Oord__class_Oless__eq(U_1828,c_Groups_Oplus__class_Oplus(U_1828,U_1829,U_1830),c_Groups_Ozero__class_Ozero(U_1828))
| ~ c_Orderings_Oord__class_Oless__eq(U_1828,U_1830,c_Groups_Ozero__class_Ozero(U_1828))
| ~ c_Orderings_Oord__class_Oless__eq(U_1828,U_1829,c_Groups_Ozero__class_Ozero(U_1828))
| ~ class_Groups_Oordered__comm__monoid__add(U_1828) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1828,c_Groups_Oplus__class_Oplus(U_1828,U_1829,U_1830),c_Groups_Ozero__class_Ozero(U_1828))
| ~ c_Orderings_Oord__class_Oless__eq(U_1828,U_1830,c_Groups_Ozero__class_Ozero(U_1828))
| ~ c_Orderings_Oord__class_Oless__eq(U_1828,U_1829,c_Groups_Ozero__class_Ozero(U_1828))
| ~ class_Groups_Oordered__comm__monoid__add(U_1828) ),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_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_600_2,plain,
! [U_1832,U_1831] :
( ( ( c_Orderings_Oord__class_Oless(U_1831,c_Groups_Oplus__class_Oplus(U_1831,U_1832,U_1832),c_Groups_Ozero__class_Ozero(U_1831))
| ~ c_Orderings_Oord__class_Oless(U_1831,U_1832,c_Groups_Ozero__class_Ozero(U_1831)) )
& ( c_Orderings_Oord__class_Oless(U_1831,U_1832,c_Groups_Ozero__class_Ozero(U_1831))
| ~ c_Orderings_Oord__class_Oless(U_1831,c_Groups_Oplus__class_Oplus(U_1831,U_1832,U_1832),c_Groups_Ozero__class_Ozero(U_1831)) ) )
| ~ class_Rings_Olinordered__idom(U_1831) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
cnf(f_600_3,plain,
( c_Orderings_Oord__class_Oless(U_1831,U_1832,c_Groups_Ozero__class_Ozero(U_1831))
| ~ c_Orderings_Oord__class_Oless(U_1831,c_Groups_Oplus__class_Oplus(U_1831,U_1832,U_1832),c_Groups_Ozero__class_Ozero(U_1831))
| ~ class_Rings_Olinordered__idom(U_1831) ),
inference(clausify,[status(thm)],[f_600_2]) ).
cnf(f_600_4,plain,
( c_Orderings_Oord__class_Oless(U_1831,c_Groups_Oplus__class_Oplus(U_1831,U_1832,U_1832),c_Groups_Ozero__class_Ozero(U_1831))
| ~ c_Orderings_Oord__class_Oless(U_1831,U_1832,c_Groups_Ozero__class_Ozero(U_1831))
| ~ class_Rings_Olinordered__idom(U_1831) ),
inference(clausify,[status(thm)],[f_600_2]) ).
fof(f_601_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_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_601_2,plain,
! [U_1834,U_1833] :
( ( ( c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),c_Groups_Oplus__class_Oplus(U_1833,U_1834,U_1834))
| ~ c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),U_1834) )
& ( c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),U_1834)
| ~ c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),c_Groups_Oplus__class_Oplus(U_1833,U_1834,U_1834)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1833) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
cnf(f_601_3,plain,
( c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),U_1834)
| ~ c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),c_Groups_Oplus__class_Oplus(U_1833,U_1834,U_1834))
| ~ class_Groups_Olinordered__ab__group__add(U_1833) ),
inference(clausify,[status(thm)],[f_601_2]) ).
cnf(f_601_4,plain,
( c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),c_Groups_Oplus__class_Oplus(U_1833,U_1834,U_1834))
| ~ c_Orderings_Oord__class_Oless(U_1833,c_Groups_Ozero__class_Ozero(U_1833),U_1834)
| ~ class_Groups_Olinordered__ab__group__add(U_1833) ),
inference(clausify,[status(thm)],[f_601_2]) ).
fof(f_602_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_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_602_2,plain,
! [U_1836,U_1835] :
( ( ( c_Orderings_Oord__class_Oless(U_1835,c_Groups_Oplus__class_Oplus(U_1835,U_1836,U_1836),c_Groups_Ozero__class_Ozero(U_1835))
| ~ c_Orderings_Oord__class_Oless(U_1835,U_1836,c_Groups_Ozero__class_Ozero(U_1835)) )
& ( c_Orderings_Oord__class_Oless(U_1835,U_1836,c_Groups_Ozero__class_Ozero(U_1835))
| ~ c_Orderings_Oord__class_Oless(U_1835,c_Groups_Oplus__class_Oplus(U_1835,U_1836,U_1836),c_Groups_Ozero__class_Ozero(U_1835)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1835) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
cnf(f_602_3,plain,
( c_Orderings_Oord__class_Oless(U_1835,U_1836,c_Groups_Ozero__class_Ozero(U_1835))
| ~ c_Orderings_Oord__class_Oless(U_1835,c_Groups_Oplus__class_Oplus(U_1835,U_1836,U_1836),c_Groups_Ozero__class_Ozero(U_1835))
| ~ class_Groups_Olinordered__ab__group__add(U_1835) ),
inference(clausify,[status(thm)],[f_602_2]) ).
cnf(f_602_4,plain,
( c_Orderings_Oord__class_Oless(U_1835,c_Groups_Oplus__class_Oplus(U_1835,U_1836,U_1836),c_Groups_Ozero__class_Ozero(U_1835))
| ~ c_Orderings_Oord__class_Oless(U_1835,U_1836,c_Groups_Ozero__class_Ozero(U_1835))
| ~ class_Groups_Olinordered__ab__group__add(U_1835) ),
inference(clausify,[status(thm)],[f_602_2]) ).
fof(f_603_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__pos]) ).
fof(f_603_2,plain,
! [U_1839,U_1838,U_1837] :
( c_Orderings_Oord__class_Oless(U_1837,c_Groups_Ozero__class_Ozero(U_1837),c_Groups_Oplus__class_Oplus(U_1837,U_1838,U_1839))
| ~ c_Orderings_Oord__class_Oless(U_1837,c_Groups_Ozero__class_Ozero(U_1837),U_1839)
| ~ c_Orderings_Oord__class_Oless(U_1837,c_Groups_Ozero__class_Ozero(U_1837),U_1838)
| ~ class_Groups_Oordered__comm__monoid__add(U_1837) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
cnf(f_603_3,plain,
( c_Orderings_Oord__class_Oless(U_1837,c_Groups_Ozero__class_Ozero(U_1837),c_Groups_Oplus__class_Oplus(U_1837,U_1838,U_1839))
| ~ c_Orderings_Oord__class_Oless(U_1837,c_Groups_Ozero__class_Ozero(U_1837),U_1839)
| ~ c_Orderings_Oord__class_Oless(U_1837,c_Groups_Ozero__class_Ozero(U_1837),U_1838)
| ~ class_Groups_Oordered__comm__monoid__add(U_1837) ),
inference(clausify,[status(thm)],[f_603_2]) ).
fof(f_604_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__neg]) ).
fof(f_604_2,plain,
! [U_1842,U_1841,U_1840] :
( c_Orderings_Oord__class_Oless(U_1840,c_Groups_Oplus__class_Oplus(U_1840,U_1841,U_1842),c_Groups_Ozero__class_Ozero(U_1840))
| ~ c_Orderings_Oord__class_Oless(U_1840,U_1842,c_Groups_Ozero__class_Ozero(U_1840))
| ~ c_Orderings_Oord__class_Oless(U_1840,U_1841,c_Groups_Ozero__class_Ozero(U_1840))
| ~ class_Groups_Oordered__comm__monoid__add(U_1840) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
cnf(f_604_3,plain,
( c_Orderings_Oord__class_Oless(U_1840,c_Groups_Oplus__class_Oplus(U_1840,U_1841,U_1842),c_Groups_Ozero__class_Ozero(U_1840))
| ~ c_Orderings_Oord__class_Oless(U_1840,U_1842,c_Groups_Ozero__class_Ozero(U_1840))
| ~ c_Orderings_Oord__class_Oless(U_1840,U_1841,c_Groups_Ozero__class_Ozero(U_1840))
| ~ class_Groups_Oordered__comm__monoid__add(U_1840) ),
inference(clausify,[status(thm)],[f_604_2]) ).
fof(f_605_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__add__strict]) ).
fof(f_605_2,plain,
! [U_1846,U_1845,U_1844,U_1843] :
( c_Orderings_Oord__class_Oless(U_1843,U_1845,c_Groups_Oplus__class_Oplus(U_1843,U_1844,U_1846))
| ~ c_Orderings_Oord__class_Oless(U_1843,U_1845,U_1846)
| ~ c_Orderings_Oord__class_Oless(U_1843,c_Groups_Ozero__class_Ozero(U_1843),U_1844)
| ~ class_Rings_Olinordered__semidom(U_1843) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( c_Orderings_Oord__class_Oless(U_1843,U_1845,c_Groups_Oplus__class_Oplus(U_1843,U_1844,U_1846))
| ~ c_Orderings_Oord__class_Oless(U_1843,U_1845,U_1846)
| ~ c_Orderings_Oord__class_Oless(U_1843,c_Groups_Ozero__class_Ozero(U_1843),U_1844)
| ~ class_Rings_Olinordered__semidom(U_1843) ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_1,plain,
! [V_l_2,V_P_2,T_a] :
( ( ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l_2),c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l_2),c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))) )
| ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x))) ) )
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Rings_Odvd(T_a) ),
inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex]) ).
fof(f_606_2,plain,
! [U_1853,U_1852,U_1851] :
( ( ( ? [U_1850] : hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),U_1850)))
| ! [U_1849] :
( ~ hBOOL(hAPP(U_1852,U_1849))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,U_1849,c_Groups_Ozero__class_Ozero(U_1851)))) ) )
& ( ? [U_1848] :
( hBOOL(hAPP(U_1852,U_1848))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,U_1848,c_Groups_Ozero__class_Ozero(U_1851)))) )
| ! [U_1847] : ~ hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),U_1847))) ) )
| ~ class_Rings_Osemiring__0(U_1851)
| ~ class_Rings_Odvd(U_1851) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
! [U_1853,U_1852,U_1851] :
( ( ( ? [U_1850] : hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),U_1850)))
| ! [U_1849] :
( ~ hBOOL(hAPP(U_1852,U_1849))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,U_1849,c_Groups_Ozero__class_Ozero(U_1851)))) ) )
& ( ( hBOOL(hAPP(U_1852,sK7(U_1853,U_1852,U_1851)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,sK7(U_1853,U_1852,U_1851),c_Groups_Ozero__class_Ozero(U_1851)))) )
| ! [U_1847] : ~ hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),U_1847))) ) )
| ~ class_Rings_Osemiring__0(U_1851)
| ~ class_Rings_Odvd(U_1851) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_1848,sK7(U_1853,U_1852,U_1851))],[f_606_2]) ).
fof(f_606_4,plain,
! [U_1853,U_1852,U_1851] :
( ( ( hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),sK8(U_1853,U_1852,U_1851))))
| ! [U_1849] :
( ~ hBOOL(hAPP(U_1852,U_1849))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,U_1849,c_Groups_Ozero__class_Ozero(U_1851)))) ) )
& ( ( hBOOL(hAPP(U_1852,sK7(U_1853,U_1852,U_1851)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,sK7(U_1853,U_1852,U_1851),c_Groups_Ozero__class_Ozero(U_1851)))) )
| ! [U_1847] : ~ hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),U_1847))) ) )
| ~ class_Rings_Osemiring__0(U_1851)
| ~ class_Rings_Odvd(U_1851) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_1850,sK8(U_1853,U_1852,U_1851))],[f_606_3]) ).
cnf(f_606_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,sK7(U_1853,U_1852,U_1851),c_Groups_Ozero__class_Ozero(U_1851))))
| ~ hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),U_1847)))
| ~ class_Rings_Osemiring__0(U_1851)
| ~ class_Rings_Odvd(U_1851) ),
inference(clausify,[status(thm)],[f_606_4]) ).
cnf(f_606_6,plain,
( hBOOL(hAPP(U_1852,sK7(U_1853,U_1852,U_1851)))
| ~ hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),U_1847)))
| ~ class_Rings_Osemiring__0(U_1851)
| ~ class_Rings_Odvd(U_1851) ),
inference(clausify,[status(thm)],[f_606_4]) ).
cnf(f_606_7,plain,
( hBOOL(hAPP(U_1852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1853),sK8(U_1853,U_1852,U_1851))))
| ~ hBOOL(hAPP(U_1852,U_1849))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_1851),U_1853),c_Groups_Oplus__class_Oplus(U_1851,U_1849,c_Groups_Ozero__class_Ozero(U_1851))))
| ~ class_Rings_Osemiring__0(U_1851)
| ~ class_Rings_Odvd(U_1851) ),
inference(clausify,[status(thm)],[f_606_4]) ).
fof(f_607_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__le__mono]) ).
fof(f_607_2,plain,
! [U_1858,U_1857,U_1856,U_1855,U_1854] :
( c_Orderings_Oord__class_Oless(U_1854,c_Groups_Oplus__class_Oplus(U_1854,U_1855,U_1857),c_Groups_Oplus__class_Oplus(U_1854,U_1856,U_1858))
| ~ c_Orderings_Oord__class_Oless__eq(U_1854,U_1857,U_1858)
| ~ c_Orderings_Oord__class_Oless(U_1854,U_1855,U_1856)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1854) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
cnf(f_607_3,plain,
( c_Orderings_Oord__class_Oless(U_1854,c_Groups_Oplus__class_Oplus(U_1854,U_1855,U_1857),c_Groups_Oplus__class_Oplus(U_1854,U_1856,U_1858))
| ~ c_Orderings_Oord__class_Oless__eq(U_1854,U_1857,U_1858)
| ~ c_Orderings_Oord__class_Oless(U_1854,U_1855,U_1856)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1854) ),
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__less__mono]) ).
fof(f_608_2,plain,
! [U_1863,U_1862,U_1861,U_1860,U_1859] :
( c_Orderings_Oord__class_Oless(U_1859,c_Groups_Oplus__class_Oplus(U_1859,U_1860,U_1862),c_Groups_Oplus__class_Oplus(U_1859,U_1861,U_1863))
| ~ c_Orderings_Oord__class_Oless(U_1859,U_1862,U_1863)
| ~ c_Orderings_Oord__class_Oless__eq(U_1859,U_1860,U_1861)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1859) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
cnf(f_608_3,plain,
( c_Orderings_Oord__class_Oless(U_1859,c_Groups_Oplus__class_Oplus(U_1859,U_1860,U_1862),c_Groups_Oplus__class_Oplus(U_1859,U_1861,U_1863))
| ~ c_Orderings_Oord__class_Oless(U_1859,U_1862,U_1863)
| ~ c_Orderings_Oord__class_Oless__eq(U_1859,U_1860,U_1861)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1859) ),
inference(clausify,[status(thm)],[f_608_2]) ).
fof(f_609_1,plain,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))
| V_c = V_d
| V_a != V_b
| V_r = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq]) ).
fof(f_609_2,plain,
! [U_1869,U_1868,U_1867,U_1866,U_1865,U_1864] :
( c_Groups_Oplus__class_Oplus(U_1864,U_1866,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1864),U_1865),U_1868)) != c_Groups_Oplus__class_Oplus(U_1864,U_1867,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1864),U_1865),U_1869))
| U_1868 = U_1869
| U_1866 != U_1867
| U_1865 = c_Groups_Ozero__class_Ozero(U_1864)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1864) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
cnf(f_609_3,plain,
( c_Groups_Oplus__class_Oplus(U_1864,U_1866,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1864),U_1865),U_1868)) != c_Groups_Oplus__class_Oplus(U_1864,U_1867,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1864),U_1865),U_1869))
| U_1868 = U_1869
| U_1866 != U_1867
| U_1865 = c_Groups_Ozero__class_Ozero(U_1864)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1864) ),
inference(clausify,[status(thm)],[f_609_2]) ).
fof(f_610_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).
fof(f_610_2,plain,
! [U_1872,U_1871,U_1870] :
( ( ( c_Groups_Oplus__class_Oplus(U_1870,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1871),U_1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1872),U_1872)) = c_Groups_Ozero__class_Ozero(U_1870)
| U_1872 != c_Groups_Ozero__class_Ozero(U_1870)
| U_1871 != c_Groups_Ozero__class_Ozero(U_1870) )
& ( ( U_1872 = c_Groups_Ozero__class_Ozero(U_1870)
& U_1871 = c_Groups_Ozero__class_Ozero(U_1870) )
| c_Groups_Oplus__class_Oplus(U_1870,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1871),U_1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1872),U_1872)) != c_Groups_Ozero__class_Ozero(U_1870) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1870) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
cnf(f_610_3,plain,
( U_1871 = c_Groups_Ozero__class_Ozero(U_1870)
| c_Groups_Oplus__class_Oplus(U_1870,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1871),U_1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1872),U_1872)) != c_Groups_Ozero__class_Ozero(U_1870)
| ~ class_Rings_Olinordered__ring__strict(U_1870) ),
inference(clausify,[status(thm)],[f_610_2]) ).
cnf(f_610_4,plain,
( U_1872 = c_Groups_Ozero__class_Ozero(U_1870)
| c_Groups_Oplus__class_Oplus(U_1870,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1871),U_1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1872),U_1872)) != c_Groups_Ozero__class_Ozero(U_1870)
| ~ class_Rings_Olinordered__ring__strict(U_1870) ),
inference(clausify,[status(thm)],[f_610_2]) ).
cnf(f_610_5,plain,
( c_Groups_Oplus__class_Oplus(U_1870,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1871),U_1871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1870),U_1872),U_1872)) = c_Groups_Ozero__class_Ozero(U_1870)
| U_1872 != c_Groups_Ozero__class_Ozero(U_1870)
| U_1871 != c_Groups_Ozero__class_Ozero(U_1870)
| ~ class_Rings_Olinordered__ring__strict(U_1870) ),
inference(clausify,[status(thm)],[f_610_2]) ).
fof(f_611_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__one]) ).
fof(f_611_2,plain,
! [U_1874,U_1873] :
( c_Orderings_Oord__class_Oless(U_1873,U_1874,c_Groups_Oplus__class_Oplus(U_1873,U_1874,c_Groups_Oone__class_Oone(U_1873)))
| ~ class_Rings_Olinordered__semidom(U_1873) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
cnf(f_611_3,plain,
( c_Orderings_Oord__class_Oless(U_1873,U_1874,c_Groups_Oplus__class_Oplus(U_1873,U_1874,c_Groups_Oone__class_Oone(U_1873)))
| ~ class_Rings_Olinordered__semidom(U_1873) ),
inference(clausify,[status(thm)],[f_611_2]) ).
fof(f_612_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__unique]) ).
fof(f_612_2,plain,
! [U_1877,U_1876,U_1875] :
( c_Groups_Ouminus__class_Ouminus(U_1875,U_1876) = U_1877
| c_Groups_Oplus__class_Oplus(U_1875,U_1876,U_1877) != c_Groups_Ozero__class_Ozero(U_1875)
| ~ class_Groups_Ogroup__add(U_1875) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
cnf(f_612_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1875,U_1876) = U_1877
| c_Groups_Oplus__class_Oplus(U_1875,U_1876,U_1877) != c_Groups_Ozero__class_Ozero(U_1875)
| ~ class_Groups_Ogroup__add(U_1875) ),
inference(clausify,[status(thm)],[f_612_2]) ).
fof(f_613_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__left__minus]) ).
fof(f_613_2,plain,
! [U_1879,U_1878] :
( c_Groups_Oplus__class_Oplus(U_1878,c_Groups_Ouminus__class_Ouminus(U_1878,U_1879),U_1879) = c_Groups_Ozero__class_Ozero(U_1878)
| ~ class_Groups_Oab__group__add(U_1878) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( c_Groups_Oplus__class_Oplus(U_1878,c_Groups_Ouminus__class_Ouminus(U_1878,U_1879),U_1879) = c_Groups_Ozero__class_Ozero(U_1878)
| ~ class_Groups_Oab__group__add(U_1878) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_left__minus]) ).
fof(f_614_2,plain,
! [U_1881,U_1880] :
( c_Groups_Oplus__class_Oplus(U_1880,c_Groups_Ouminus__class_Ouminus(U_1880,U_1881),U_1881) = c_Groups_Ozero__class_Ozero(U_1880)
| ~ class_Groups_Ogroup__add(U_1880) ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
cnf(f_614_3,plain,
( c_Groups_Oplus__class_Oplus(U_1880,c_Groups_Ouminus__class_Ouminus(U_1880,U_1881),U_1881) = c_Groups_Ozero__class_Ozero(U_1880)
| ~ class_Groups_Ogroup__add(U_1880) ),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( V_aa_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).
fof(f_615_2,plain,
! [U_1884,U_1883,U_1882] :
( ( ( U_1883 = c_Groups_Ouminus__class_Ouminus(U_1882,U_1884)
| c_Groups_Oplus__class_Oplus(U_1882,U_1883,U_1884) != c_Groups_Ozero__class_Ozero(U_1882) )
& ( c_Groups_Oplus__class_Oplus(U_1882,U_1883,U_1884) = c_Groups_Ozero__class_Ozero(U_1882)
| U_1883 != c_Groups_Ouminus__class_Ouminus(U_1882,U_1884) ) )
| ~ class_Groups_Ogroup__add(U_1882) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
cnf(f_615_3,plain,
( c_Groups_Oplus__class_Oplus(U_1882,U_1883,U_1884) = c_Groups_Ozero__class_Ozero(U_1882)
| U_1883 != c_Groups_Ouminus__class_Ouminus(U_1882,U_1884)
| ~ class_Groups_Ogroup__add(U_1882) ),
inference(clausify,[status(thm)],[f_615_2]) ).
cnf(f_615_4,plain,
( U_1883 = c_Groups_Ouminus__class_Ouminus(U_1882,U_1884)
| c_Groups_Oplus__class_Oplus(U_1882,U_1883,U_1884) != c_Groups_Ozero__class_Ozero(U_1882)
| ~ class_Groups_Ogroup__add(U_1882) ),
inference(clausify,[status(thm)],[f_615_2]) ).
fof(f_616_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__minus]) ).
fof(f_616_2,plain,
! [U_1886,U_1885] :
( c_Groups_Oplus__class_Oplus(U_1885,U_1886,c_Groups_Ouminus__class_Ouminus(U_1885,U_1886)) = c_Groups_Ozero__class_Ozero(U_1885)
| ~ class_Groups_Ogroup__add(U_1885) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
cnf(f_616_3,plain,
( c_Groups_Oplus__class_Oplus(U_1885,U_1886,c_Groups_Ouminus__class_Ouminus(U_1885,U_1886)) = c_Groups_Ozero__class_Ozero(U_1885)
| ~ class_Groups_Ogroup__add(U_1885) ),
inference(clausify,[status(thm)],[f_616_2]) ).
fof(f_617_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) )
& ( V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff]) ).
fof(f_617_2,plain,
! [U_1889,U_1888,U_1887] :
( ( ( c_Groups_Oplus__class_Oplus(U_1887,U_1888,U_1889) = c_Groups_Ozero__class_Ozero(U_1887)
| U_1889 != c_Groups_Ouminus__class_Ouminus(U_1887,U_1888) )
& ( U_1889 = c_Groups_Ouminus__class_Ouminus(U_1887,U_1888)
| c_Groups_Oplus__class_Oplus(U_1887,U_1888,U_1889) != c_Groups_Ozero__class_Ozero(U_1887) ) )
| ~ class_Groups_Ogroup__add(U_1887) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
cnf(f_617_3,plain,
( U_1889 = c_Groups_Ouminus__class_Ouminus(U_1887,U_1888)
| c_Groups_Oplus__class_Oplus(U_1887,U_1888,U_1889) != c_Groups_Ozero__class_Ozero(U_1887)
| ~ class_Groups_Ogroup__add(U_1887) ),
inference(clausify,[status(thm)],[f_617_2]) ).
cnf(f_617_4,plain,
( c_Groups_Oplus__class_Oplus(U_1887,U_1888,U_1889) = c_Groups_Ozero__class_Ozero(U_1887)
| U_1889 != c_Groups_Ouminus__class_Ouminus(U_1887,U_1888)
| ~ class_Groups_Ogroup__add(U_1887) ),
inference(clausify,[status(thm)],[f_617_2]) ).
fof(f_618_1,plain,
! [V_m,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_618_2,plain,
! [U_1892,U_1891,U_1890] :
( c_Groups_Oplus__class_Oplus(U_1890,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1892),U_1892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),c_Groups_Oplus__class_Oplus(U_1890,U_1891,c_Groups_Oone__class_Oone(U_1890))),U_1892)
| ~ class_Rings_Ocomm__semiring__1(U_1890) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
cnf(f_618_3,plain,
( c_Groups_Oplus__class_Oplus(U_1890,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1892),U_1892) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),c_Groups_Oplus__class_Oplus(U_1890,U_1891,c_Groups_Oone__class_Oone(U_1890))),U_1892)
| ~ class_Rings_Ocomm__semiring__1(U_1890) ),
inference(clausify,[status(thm)],[f_618_2]) ).
fof(f_619_1,plain,
! [V_a,V_m,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_619_2,plain,
! [U_1895,U_1894,U_1893] :
( c_Groups_Oplus__class_Oplus(U_1893,U_1894,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1895),U_1894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),c_Groups_Oplus__class_Oplus(U_1893,U_1895,c_Groups_Oone__class_Oone(U_1893))),U_1894)
| ~ class_Rings_Ocomm__semiring__1(U_1893) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
cnf(f_619_3,plain,
( c_Groups_Oplus__class_Oplus(U_1893,U_1894,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),U_1895),U_1894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1893),c_Groups_Oplus__class_Oplus(U_1893,U_1895,c_Groups_Oone__class_Oone(U_1893))),U_1894)
| ~ class_Rings_Ocomm__semiring__1(U_1893) ),
inference(clausify,[status(thm)],[f_619_2]) ).
fof(f_620_1,plain,
! [V_m,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_620_2,plain,
! [U_1897,U_1896] :
( c_Groups_Oplus__class_Oplus(U_1896,U_1897,U_1897) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),c_Groups_Oplus__class_Oplus(U_1896,c_Groups_Oone__class_Oone(U_1896),c_Groups_Oone__class_Oone(U_1896))),U_1897)
| ~ class_Rings_Ocomm__semiring__1(U_1896) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
cnf(f_620_3,plain,
( c_Groups_Oplus__class_Oplus(U_1896,U_1897,U_1897) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1896),c_Groups_Oplus__class_Oplus(U_1896,c_Groups_Oone__class_Oone(U_1896),c_Groups_Oone__class_Oone(U_1896))),U_1897)
| ~ class_Rings_Ocomm__semiring__1(U_1896) ),
inference(clausify,[status(thm)],[f_620_2]) ).
fof(f_621_1,plain,
! [V_q,V_n,V_p,T_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__add__less]) ).
fof(f_621_2,plain,
! [U_1901,U_1900,U_1899,U_1898] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1898,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1898),U_1899,U_1901)),U_1900)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1898,U_1901),U_1900)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1898,U_1899),U_1900)
| ~ class_Groups_Ocomm__monoid__add(U_1898) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
cnf(f_621_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1898,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1898),U_1899,U_1901)),U_1900)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1898,U_1901),U_1900)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1898,U_1899),U_1900)
| ~ class_Groups_Ocomm__monoid__add(U_1898) ),
inference(clausify,[status(thm)],[f_621_2]) ).
fof(f_622_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_q)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__add__eq__right]) ).
fof(f_622_2,plain,
! [U_1904,U_1903,U_1902] :
( c_Polynomial_Odegree(U_1902,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1902),U_1903,U_1904)) = c_Polynomial_Odegree(U_1902,U_1904)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1902,U_1903),c_Polynomial_Odegree(U_1902,U_1904))
| ~ class_Groups_Ocomm__monoid__add(U_1902) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
cnf(f_622_3,plain,
( c_Polynomial_Odegree(U_1902,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1902),U_1903,U_1904)) = c_Polynomial_Odegree(U_1902,U_1904)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1902,U_1903),c_Polynomial_Odegree(U_1902,U_1904))
| ~ class_Groups_Ocomm__monoid__add(U_1902) ),
inference(clausify,[status(thm)],[f_622_2]) ).
fof(f_623_1,plain,
! [V_p,V_q,T_a] :
( c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Polynomial_Odegree(T_a,V_p)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__add__eq__left]) ).
fof(f_623_2,plain,
! [U_1907,U_1906,U_1905] :
( c_Polynomial_Odegree(U_1905,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1905),U_1907,U_1906)) = c_Polynomial_Odegree(U_1905,U_1907)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1905,U_1906),c_Polynomial_Odegree(U_1905,U_1907))
| ~ class_Groups_Ocomm__monoid__add(U_1905) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
cnf(f_623_3,plain,
( c_Polynomial_Odegree(U_1905,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1905),U_1907,U_1906)) = c_Polynomial_Odegree(U_1905,U_1907)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1905,U_1906),c_Polynomial_Odegree(U_1905,U_1907))
| ~ class_Groups_Ocomm__monoid__add(U_1905) ),
inference(clausify,[status(thm)],[f_623_2]) ).
fof(f_624_1,plain,
! [V_q,V_n,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__add__le]) ).
fof(f_624_2,plain,
! [U_1911,U_1910,U_1909,U_1908] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1908,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1908),U_1909,U_1911)),U_1910)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1908,U_1911),U_1910)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1908,U_1909),U_1910)
| ~ class_Groups_Ocomm__monoid__add(U_1908) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
cnf(f_624_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1908,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1908),U_1909,U_1911)),U_1910)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1908,U_1911),U_1910)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1908,U_1909),U_1910)
| ~ class_Groups_Ocomm__monoid__add(U_1908) ),
inference(clausify,[status(thm)],[f_624_2]) ).
fof(f_625_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg]) ).
fof(f_625_2,plain,
! [U_1914,U_1913,U_1912] :
( c_Orderings_Oord__class_Oless(U_1912,c_Groups_Ozero__class_Ozero(U_1912),c_Groups_Oplus__class_Oplus(U_1912,U_1913,U_1914))
| ~ c_Orderings_Oord__class_Oless__eq(U_1912,c_Groups_Ozero__class_Ozero(U_1912),U_1914)
| ~ c_Orderings_Oord__class_Oless(U_1912,c_Groups_Ozero__class_Ozero(U_1912),U_1913)
| ~ class_Groups_Oordered__comm__monoid__add(U_1912) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
cnf(f_625_3,plain,
( c_Orderings_Oord__class_Oless(U_1912,c_Groups_Ozero__class_Ozero(U_1912),c_Groups_Oplus__class_Oplus(U_1912,U_1913,U_1914))
| ~ c_Orderings_Oord__class_Oless__eq(U_1912,c_Groups_Ozero__class_Ozero(U_1912),U_1914)
| ~ c_Orderings_Oord__class_Oless(U_1912,c_Groups_Ozero__class_Ozero(U_1912),U_1913)
| ~ class_Groups_Oordered__comm__monoid__add(U_1912) ),
inference(clausify,[status(thm)],[f_625_2]) ).
fof(f_626_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos]) ).
fof(f_626_2,plain,
! [U_1917,U_1916,U_1915] :
( c_Orderings_Oord__class_Oless(U_1915,c_Groups_Ozero__class_Ozero(U_1915),c_Groups_Oplus__class_Oplus(U_1915,U_1916,U_1917))
| ~ c_Orderings_Oord__class_Oless(U_1915,c_Groups_Ozero__class_Ozero(U_1915),U_1917)
| ~ c_Orderings_Oord__class_Oless__eq(U_1915,c_Groups_Ozero__class_Ozero(U_1915),U_1916)
| ~ class_Groups_Oordered__comm__monoid__add(U_1915) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
cnf(f_626_3,plain,
( c_Orderings_Oord__class_Oless(U_1915,c_Groups_Ozero__class_Ozero(U_1915),c_Groups_Oplus__class_Oplus(U_1915,U_1916,U_1917))
| ~ c_Orderings_Oord__class_Oless(U_1915,c_Groups_Ozero__class_Ozero(U_1915),U_1917)
| ~ c_Orderings_Oord__class_Oless__eq(U_1915,c_Groups_Ozero__class_Ozero(U_1915),U_1916)
| ~ class_Groups_Oordered__comm__monoid__add(U_1915) ),
inference(clausify,[status(thm)],[f_626_2]) ).
fof(f_627_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing]) ).
fof(f_627_2,plain,
! [U_1921,U_1920,U_1919,U_1918] :
( c_Orderings_Oord__class_Oless(U_1918,U_1920,c_Groups_Oplus__class_Oplus(U_1918,U_1919,U_1921))
| ~ c_Orderings_Oord__class_Oless__eq(U_1918,U_1920,U_1921)
| ~ c_Orderings_Oord__class_Oless(U_1918,c_Groups_Ozero__class_Ozero(U_1918),U_1919)
| ~ class_Groups_Oordered__comm__monoid__add(U_1918) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
cnf(f_627_3,plain,
( c_Orderings_Oord__class_Oless(U_1918,U_1920,c_Groups_Oplus__class_Oplus(U_1918,U_1919,U_1921))
| ~ c_Orderings_Oord__class_Oless__eq(U_1918,U_1920,U_1921)
| ~ c_Orderings_Oord__class_Oless(U_1918,c_Groups_Ozero__class_Ozero(U_1918),U_1919)
| ~ class_Groups_Oordered__comm__monoid__add(U_1918) ),
inference(clausify,[status(thm)],[f_627_2]) ).
fof(f_628_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2]) ).
fof(f_628_2,plain,
! [U_1925,U_1924,U_1923,U_1922] :
( c_Orderings_Oord__class_Oless(U_1922,U_1924,c_Groups_Oplus__class_Oplus(U_1922,U_1923,U_1925))
| ~ c_Orderings_Oord__class_Oless(U_1922,U_1924,U_1925)
| ~ c_Orderings_Oord__class_Oless__eq(U_1922,c_Groups_Ozero__class_Ozero(U_1922),U_1923)
| ~ class_Groups_Oordered__comm__monoid__add(U_1922) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
cnf(f_628_3,plain,
( c_Orderings_Oord__class_Oless(U_1922,U_1924,c_Groups_Oplus__class_Oplus(U_1922,U_1923,U_1925))
| ~ c_Orderings_Oord__class_Oless(U_1922,U_1924,U_1925)
| ~ c_Orderings_Oord__class_Oless__eq(U_1922,c_Groups_Ozero__class_Ozero(U_1922),U_1923)
| ~ class_Groups_Oordered__comm__monoid__add(U_1922) ),
inference(clausify,[status(thm)],[f_628_2]) ).
fof(f_629_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos]) ).
fof(f_629_2,plain,
! [U_1928,U_1927,U_1926] :
( c_Orderings_Oord__class_Oless(U_1926,c_Groups_Oplus__class_Oplus(U_1926,U_1927,U_1928),c_Groups_Ozero__class_Ozero(U_1926))
| ~ c_Orderings_Oord__class_Oless__eq(U_1926,U_1928,c_Groups_Ozero__class_Ozero(U_1926))
| ~ c_Orderings_Oord__class_Oless(U_1926,U_1927,c_Groups_Ozero__class_Ozero(U_1926))
| ~ class_Groups_Oordered__comm__monoid__add(U_1926) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
cnf(f_629_3,plain,
( c_Orderings_Oord__class_Oless(U_1926,c_Groups_Oplus__class_Oplus(U_1926,U_1927,U_1928),c_Groups_Ozero__class_Ozero(U_1926))
| ~ c_Orderings_Oord__class_Oless__eq(U_1926,U_1928,c_Groups_Ozero__class_Ozero(U_1926))
| ~ c_Orderings_Oord__class_Oless(U_1926,U_1927,c_Groups_Ozero__class_Ozero(U_1926))
| ~ class_Groups_Oordered__comm__monoid__add(U_1926) ),
inference(clausify,[status(thm)],[f_629_2]) ).
fof(f_630_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg]) ).
fof(f_630_2,plain,
! [U_1931,U_1930,U_1929] :
( c_Orderings_Oord__class_Oless(U_1929,c_Groups_Oplus__class_Oplus(U_1929,U_1930,U_1931),c_Groups_Ozero__class_Ozero(U_1929))
| ~ c_Orderings_Oord__class_Oless(U_1929,U_1931,c_Groups_Ozero__class_Ozero(U_1929))
| ~ c_Orderings_Oord__class_Oless__eq(U_1929,U_1930,c_Groups_Ozero__class_Ozero(U_1929))
| ~ class_Groups_Oordered__comm__monoid__add(U_1929) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
cnf(f_630_3,plain,
( c_Orderings_Oord__class_Oless(U_1929,c_Groups_Oplus__class_Oplus(U_1929,U_1930,U_1931),c_Groups_Ozero__class_Ozero(U_1929))
| ~ c_Orderings_Oord__class_Oless(U_1929,U_1931,c_Groups_Ozero__class_Ozero(U_1929))
| ~ c_Orderings_Oord__class_Oless__eq(U_1929,U_1930,c_Groups_Ozero__class_Ozero(U_1929))
| ~ class_Groups_Oordered__comm__monoid__add(U_1929) ),
inference(clausify,[status(thm)],[f_630_2]) ).
fof(f_631_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).
fof(f_631_2,plain,
! [U_1934,U_1933,U_1932] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1932,c_Groups_Oplus__class_Oplus(U_1932,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1934)),c_Groups_Ozero__class_Ozero(U_1932))
| U_1934 != c_Groups_Ozero__class_Ozero(U_1932)
| U_1933 != c_Groups_Ozero__class_Ozero(U_1932) )
& ( ( U_1934 = c_Groups_Ozero__class_Ozero(U_1932)
& U_1933 = c_Groups_Ozero__class_Ozero(U_1932) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1932,c_Groups_Oplus__class_Oplus(U_1932,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1934)),c_Groups_Ozero__class_Ozero(U_1932)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1932) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
cnf(f_631_3,plain,
( U_1933 = c_Groups_Ozero__class_Ozero(U_1932)
| ~ c_Orderings_Oord__class_Oless__eq(U_1932,c_Groups_Oplus__class_Oplus(U_1932,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1934)),c_Groups_Ozero__class_Ozero(U_1932))
| ~ class_Rings_Olinordered__ring__strict(U_1932) ),
inference(clausify,[status(thm)],[f_631_2]) ).
cnf(f_631_4,plain,
( U_1934 = c_Groups_Ozero__class_Ozero(U_1932)
| ~ c_Orderings_Oord__class_Oless__eq(U_1932,c_Groups_Oplus__class_Oplus(U_1932,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1934)),c_Groups_Ozero__class_Ozero(U_1932))
| ~ class_Rings_Olinordered__ring__strict(U_1932) ),
inference(clausify,[status(thm)],[f_631_2]) ).
cnf(f_631_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1932,c_Groups_Oplus__class_Oplus(U_1932,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1933),U_1933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1932),U_1934),U_1934)),c_Groups_Ozero__class_Ozero(U_1932))
| U_1934 != c_Groups_Ozero__class_Ozero(U_1932)
| U_1933 != c_Groups_Ozero__class_Ozero(U_1932)
| ~ class_Rings_Olinordered__ring__strict(U_1932) ),
inference(clausify,[status(thm)],[f_631_2]) ).
fof(f_632_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero]) ).
fof(f_632_2,plain,
! [U_1937,U_1936,U_1935] :
( c_Orderings_Oord__class_Oless__eq(U_1935,c_Groups_Ozero__class_Ozero(U_1935),c_Groups_Oplus__class_Oplus(U_1935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1936),U_1936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1937),U_1937)))
| ~ class_Rings_Olinordered__ring(U_1935) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
cnf(f_632_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1935,c_Groups_Ozero__class_Ozero(U_1935),c_Groups_Oplus__class_Oplus(U_1935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1936),U_1936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1937),U_1937)))
| ~ class_Rings_Olinordered__ring(U_1935) ),
inference(clausify,[status(thm)],[f_632_2]) ).
fof(f_633_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).
fof(f_633_2,plain,
! [U_1940,U_1939,U_1938] :
( ( ( c_Orderings_Oord__class_Oless(U_1938,c_Groups_Ozero__class_Ozero(U_1938),c_Groups_Oplus__class_Oplus(U_1938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1939),U_1939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1940),U_1940)))
| ( U_1940 = c_Groups_Ozero__class_Ozero(U_1938)
& U_1939 = c_Groups_Ozero__class_Ozero(U_1938) ) )
& ( U_1940 != c_Groups_Ozero__class_Ozero(U_1938)
| U_1939 != c_Groups_Ozero__class_Ozero(U_1938)
| ~ c_Orderings_Oord__class_Oless(U_1938,c_Groups_Ozero__class_Ozero(U_1938),c_Groups_Oplus__class_Oplus(U_1938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1939),U_1939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1940),U_1940))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1938) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
cnf(f_633_3,plain,
( U_1940 != c_Groups_Ozero__class_Ozero(U_1938)
| U_1939 != c_Groups_Ozero__class_Ozero(U_1938)
| ~ c_Orderings_Oord__class_Oless(U_1938,c_Groups_Ozero__class_Ozero(U_1938),c_Groups_Oplus__class_Oplus(U_1938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1939),U_1939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1940),U_1940)))
| ~ class_Rings_Olinordered__ring__strict(U_1938) ),
inference(clausify,[status(thm)],[f_633_2]) ).
cnf(f_633_4,plain,
( U_1939 = c_Groups_Ozero__class_Ozero(U_1938)
| c_Orderings_Oord__class_Oless(U_1938,c_Groups_Ozero__class_Ozero(U_1938),c_Groups_Oplus__class_Oplus(U_1938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1939),U_1939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1940),U_1940)))
| ~ class_Rings_Olinordered__ring__strict(U_1938) ),
inference(clausify,[status(thm)],[f_633_2]) ).
cnf(f_633_5,plain,
( U_1940 = c_Groups_Ozero__class_Ozero(U_1938)
| c_Orderings_Oord__class_Oless(U_1938,c_Groups_Ozero__class_Ozero(U_1938),c_Groups_Oplus__class_Oplus(U_1938,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1939),U_1939),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1940),U_1940)))
| ~ class_Rings_Olinordered__ring__strict(U_1938) ),
inference(clausify,[status(thm)],[f_633_2]) ).
fof(f_634_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(f_634_2,plain,
! [U_1943,U_1942,U_1941] :
( ~ c_Orderings_Oord__class_Oless(U_1941,c_Groups_Oplus__class_Oplus(U_1941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1941),U_1942),U_1942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1941),U_1943),U_1943)),c_Groups_Ozero__class_Ozero(U_1941))
| ~ class_Rings_Olinordered__ring(U_1941) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
cnf(f_634_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1941,c_Groups_Oplus__class_Oplus(U_1941,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1941),U_1942),U_1942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1941),U_1943),U_1943)),c_Groups_Ozero__class_Ozero(U_1941))
| ~ class_Rings_Olinordered__ring(U_1941) ),
inference(clausify,[status(thm)],[f_634_2]) ).
fof(f_635_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__two]) ).
fof(f_635_2,plain,
! [U_1944] :
( c_Orderings_Oord__class_Oless(U_1944,c_Groups_Ozero__class_Ozero(U_1944),c_Groups_Oplus__class_Oplus(U_1944,c_Groups_Oone__class_Oone(U_1944),c_Groups_Oone__class_Oone(U_1944)))
| ~ class_Rings_Olinordered__semidom(U_1944) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
cnf(f_635_3,plain,
( c_Orderings_Oord__class_Oless(U_1944,c_Groups_Ozero__class_Ozero(U_1944),c_Groups_Oplus__class_Oplus(U_1944,c_Groups_Oone__class_Oone(U_1944),c_Groups_Oone__class_Oone(U_1944)))
| ~ class_Rings_Olinordered__semidom(U_1944) ),
inference(clausify,[status(thm)],[f_635_2]) ).
fof(f_636_1,plain,
! [V_x,V_p,V_a,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__pCons]) ).
fof(f_636_2,plain,
! [U_1948,U_1947,U_1946,U_1945] :
( hAPP(c_Polynomial_Opoly(U_1945,c_Polynomial_OpCons(U_1945,U_1946,U_1947)),U_1948) = c_Groups_Oplus__class_Oplus(U_1945,U_1946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1945),U_1948),hAPP(c_Polynomial_Opoly(U_1945,U_1947),U_1948)))
| ~ class_Rings_Ocomm__semiring__0(U_1945) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
cnf(f_636_3,plain,
( hAPP(c_Polynomial_Opoly(U_1945,c_Polynomial_OpCons(U_1945,U_1946,U_1947)),U_1948) = c_Groups_Oplus__class_Oplus(U_1945,U_1946,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1945),U_1948),hAPP(c_Polynomial_Opoly(U_1945,U_1947),U_1948)))
| ~ class_Rings_Ocomm__semiring__0(U_1945) ),
inference(clausify,[status(thm)],[f_636_2]) ).
fof(f_637_1,plain,
! [V_t_2,V_d_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J]) ).
fof(f_637_2,plain,
! [U_1950,U_1949] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1949),U_1950))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1949),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1950))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1949),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1950)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1949),U_1950)) ) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
( ! [U_1954,U_1952] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1952),U_1954))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1952),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1954))) )
& ! [U_1953,U_1951] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1951),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1953)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1951),U_1953)) ) ),
inference(miniscope,[status(thm)],[f_637_2]) ).
cnf(f_637_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1951),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1953)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1951),U_1953)) ),
inference(clausify,[status(thm)],[f_637_3]) ).
cnf(f_637_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1952),U_1954))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1952),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1954))) ),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_1,plain,
! [V_t_2,V_d_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2)),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J]) ).
fof(f_638_2,plain,
! [U_1956,U_1955] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1955),U_1956))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1955)),U_1956)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1955)),U_1956))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1955),U_1956)) ) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
( ! [U_1960,U_1958] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1958),U_1960))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1958)),U_1960)) )
& ! [U_1959,U_1957] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1957)),U_1959))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1957),U_1959)) ) ),
inference(miniscope,[status(thm)],[f_638_2]) ).
cnf(f_638_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1957)),U_1959))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1957),U_1959)) ),
inference(clausify,[status(thm)],[f_638_3]) ).
cnf(f_638_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_1958),U_1960))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1958)),U_1960)) ),
inference(clausify,[status(thm)],[f_638_3]) ).
fof(f_639_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)
| c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
| ~ class_Rings_Olinordered__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__le]) ).
fof(f_639_2,plain,
! [U_1966,U_1965,U_1964,U_1963,U_1962,U_1961] :
( c_Orderings_Oord__class_Oless__eq(U_1961,c_Groups_Oplus__class_Oplus(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1965),U_1962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1966),U_1964)),U_1963)
| c_Groups_Oplus__class_Oplus(U_1961,U_1965,U_1966) != c_Groups_Oone__class_Oone(U_1961)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,c_Groups_Ozero__class_Ozero(U_1961),U_1966)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,c_Groups_Ozero__class_Ozero(U_1961),U_1965)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,U_1964,U_1963)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,U_1962,U_1963)
| ~ class_Rings_Olinordered__semiring__1(U_1961) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
cnf(f_639_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1961,c_Groups_Oplus__class_Oplus(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1965),U_1962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1966),U_1964)),U_1963)
| c_Groups_Oplus__class_Oplus(U_1961,U_1965,U_1966) != c_Groups_Oone__class_Oone(U_1961)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,c_Groups_Ozero__class_Ozero(U_1961),U_1966)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,c_Groups_Ozero__class_Ozero(U_1961),U_1965)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,U_1964,U_1963)
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,U_1962,U_1963)
| ~ class_Rings_Olinordered__semiring__1(U_1961) ),
inference(clausify,[status(thm)],[f_639_2]) ).
fof(f_640_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)
| c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
| ~ class_Rings_Olinordered__semiring__1__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__lt]) ).
fof(f_640_2,plain,
! [U_1972,U_1971,U_1970,U_1969,U_1968,U_1967] :
( c_Orderings_Oord__class_Oless(U_1967,c_Groups_Oplus__class_Oplus(U_1967,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1967),U_1971),U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1967),U_1972),U_1970)),U_1969)
| c_Groups_Oplus__class_Oplus(U_1967,U_1971,U_1972) != c_Groups_Oone__class_Oone(U_1967)
| ~ c_Orderings_Oord__class_Oless__eq(U_1967,c_Groups_Ozero__class_Ozero(U_1967),U_1972)
| ~ c_Orderings_Oord__class_Oless__eq(U_1967,c_Groups_Ozero__class_Ozero(U_1967),U_1971)
| ~ c_Orderings_Oord__class_Oless(U_1967,U_1970,U_1969)
| ~ c_Orderings_Oord__class_Oless(U_1967,U_1968,U_1969)
| ~ class_Rings_Olinordered__semiring__1__strict(U_1967) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
cnf(f_640_3,plain,
( c_Orderings_Oord__class_Oless(U_1967,c_Groups_Oplus__class_Oplus(U_1967,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1967),U_1971),U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1967),U_1972),U_1970)),U_1969)
| c_Groups_Oplus__class_Oplus(U_1967,U_1971,U_1972) != c_Groups_Oone__class_Oone(U_1967)
| ~ c_Orderings_Oord__class_Oless__eq(U_1967,c_Groups_Ozero__class_Ozero(U_1967),U_1972)
| ~ c_Orderings_Oord__class_Oless__eq(U_1967,c_Groups_Ozero__class_Ozero(U_1967),U_1971)
| ~ c_Orderings_Oord__class_Oless(U_1967,U_1970,U_1969)
| ~ c_Orderings_Oord__class_Oless(U_1967,U_1968,U_1969)
| ~ class_Rings_Olinordered__semiring__1__strict(U_1967) ),
inference(clausify,[status(thm)],[f_640_2]) ).
fof(f_641_1,plain,
! [V_q,V_p,V_a,T_a] :
( c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pcompose__pCons]) ).
fof(f_641_2,plain,
! [U_1976,U_1975,U_1974,U_1973] :
( c_Polynomial_Opcompose(U_1973,c_Polynomial_OpCons(U_1973,U_1974,U_1975),U_1976) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1973),c_Polynomial_OpCons(U_1973,U_1974,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1973))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1973)),U_1976),c_Polynomial_Opcompose(U_1973,U_1975,U_1976)))
| ~ class_Rings_Ocomm__semiring__0(U_1973) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
cnf(f_641_3,plain,
( c_Polynomial_Opcompose(U_1973,c_Polynomial_OpCons(U_1973,U_1974,U_1975),U_1976) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1973),c_Polynomial_OpCons(U_1973,U_1974,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1973))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1973)),U_1976),c_Polynomial_Opcompose(U_1973,U_1975,U_1976)))
| ~ class_Rings_Ocomm__semiring__0(U_1973) ),
inference(clausify,[status(thm)],[f_641_2]) ).
fof(f_642_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
cnf(f_642_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_642_1]) ).
fof(f_643_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
cnf(f_643_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_643_1]) ).
fof(f_644_1,plain,
! [V_r_2,V_qb_2,V_y_2,V_x_2,T_a] :
( ( ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_qb_2,V_r_2)
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2))
& V_r_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_y_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ( V_qb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| V_x_2 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_qb_2),V_y_2),V_r_2) )
& ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2))
| V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& V_x_2 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_qb_2),V_y_2),V_r_2) )
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_qb_2,V_r_2) ) )
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__def]) ).
fof(f_644_2,plain,
! [U_1981,U_1980,U_1979,U_1978,U_1977] :
( ( ( c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1977,U_1981),c_Polynomial_Odegree(U_1977,U_1979))
& U_1981 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
& U_1979 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977)) )
| ( U_1980 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
& U_1979 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977)) )
| U_1978 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981) )
& ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1977,U_1981),c_Polynomial_Odegree(U_1977,U_1979))
| U_1981 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1979 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977)) )
& ( U_1980 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1979 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977)) )
& U_1978 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981) )
| ~ c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981) ) )
| ~ class_Fields_Ofield(U_1977) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
cnf(f_644_3,plain,
( U_1978 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981)
| ~ c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_4,plain,
( U_1980 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1979 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| ~ c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1977,U_1981),c_Polynomial_Odegree(U_1977,U_1979))
| U_1981 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1979 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| ~ c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_6,plain,
( U_1979 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1979 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1978 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981)
| c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_7,plain,
( U_1981 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1979 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1978 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981)
| c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1977,U_1981),c_Polynomial_Odegree(U_1977,U_1979))
| U_1979 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1978 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981)
| c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_9,plain,
( U_1979 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1980 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1978 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981)
| c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_10,plain,
( U_1981 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1980 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1978 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981)
| c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
cnf(f_644_11,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_1977,U_1981),c_Polynomial_Odegree(U_1977,U_1979))
| U_1980 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1977))
| U_1978 != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1977)),U_1980),U_1979),U_1981)
| c_Polynomial_Opdivmod__rel(U_1977,U_1978,U_1979,U_1980,U_1981)
| ~ class_Fields_Ofield(U_1977) ),
inference(clausify,[status(thm)],[f_644_2]) ).
fof(f_645_1,plain,
! [V_p,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| ? [B_i] :
( hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) != c_Groups_Ozero__class_Ozero(T_a)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__le]) ).
fof(f_645_2,plain,
! [U_1985,U_1984,U_1983] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1983,U_1985),U_1984)
| ? [U_1982] :
( hAPP(c_Polynomial_Ocoeff(U_1983,U_1985),U_1982) != c_Groups_Ozero__class_Ozero(U_1983)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,U_1982) )
| ~ class_Groups_Ozero(U_1983) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
! [U_1985,U_1984,U_1983] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1983,U_1985),U_1984)
| ( hAPP(c_Polynomial_Ocoeff(U_1983,U_1985),sK9(U_1985,U_1984,U_1983)) != c_Groups_Ozero__class_Ozero(U_1983)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,sK9(U_1985,U_1984,U_1983)) )
| ~ class_Groups_Ozero(U_1983) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_1982,sK9(U_1985,U_1984,U_1983))],[f_645_2]) ).
cnf(f_645_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,sK9(U_1985,U_1984,U_1983))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1983,U_1985),U_1984)
| ~ class_Groups_Ozero(U_1983) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_5,plain,
( hAPP(c_Polynomial_Ocoeff(U_1983,U_1985),sK9(U_1985,U_1984,U_1983)) != c_Groups_Ozero__class_Ozero(U_1983)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_1983,U_1985),U_1984)
| ~ class_Groups_Ozero(U_1983) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_1,plain,
! [V_y,V_x,T_a] :
( ( ( hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Oone__class_Oone(T_a)
| ( V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
& ( hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))) = c_Groups_Ozero__class_Ozero(T_a)
| V_y != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__monic]) ).
fof(f_646_2,plain,
! [U_1988,U_1987,U_1986] :
( ( ( hAPP(c_Polynomial_Ocoeff(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988)),c_Polynomial_Odegree(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988))) = c_Groups_Oone__class_Oone(U_1986)
| ( U_1988 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986))
& U_1987 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986)) ) )
& ( hAPP(c_Polynomial_Ocoeff(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988)),c_Polynomial_Odegree(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988))) = c_Groups_Ozero__class_Ozero(U_1986)
| U_1988 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986))
| U_1987 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986)) ) )
| ~ class_Fields_Ofield(U_1986) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
cnf(f_646_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988)),c_Polynomial_Odegree(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988))) = c_Groups_Ozero__class_Ozero(U_1986)
| U_1988 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986))
| U_1987 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986))
| ~ class_Fields_Ofield(U_1986) ),
inference(clausify,[status(thm)],[f_646_2]) ).
cnf(f_646_4,plain,
( U_1987 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986))
| hAPP(c_Polynomial_Ocoeff(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988)),c_Polynomial_Odegree(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988))) = c_Groups_Oone__class_Oone(U_1986)
| ~ class_Fields_Ofield(U_1986) ),
inference(clausify,[status(thm)],[f_646_2]) ).
cnf(f_646_5,plain,
( U_1988 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1986))
| hAPP(c_Polynomial_Ocoeff(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988)),c_Polynomial_Odegree(U_1986,c_Polynomial_Opoly__gcd(U_1986,U_1987,U_1988))) = c_Groups_Oone__class_Oone(U_1986)
| ~ class_Fields_Ofield(U_1986) ),
inference(clausify,[status(thm)],[f_646_2]) ).
fof(f_647_1,plain,
! [V_p,V_n,T_a] :
( ? [B_i] :
( hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i) != c_Groups_Ozero__class_Ozero(T_a)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__degree__imp]) ).
fof(f_647_2,plain,
! [U_1992,U_1991,U_1990] :
( ? [U_1989] :
( hAPP(c_Polynomial_Ocoeff(U_1990,U_1992),U_1989) != c_Groups_Ozero__class_Ozero(U_1990)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,U_1989) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,c_Polynomial_Odegree(U_1990,U_1992))
| ~ class_Groups_Ozero(U_1990) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
! [U_1992,U_1991,U_1990] :
( ( hAPP(c_Polynomial_Ocoeff(U_1990,U_1992),sK10(U_1992,U_1991,U_1990)) != c_Groups_Ozero__class_Ozero(U_1990)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,sK10(U_1992,U_1991,U_1990)) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,c_Polynomial_Odegree(U_1990,U_1992))
| ~ class_Groups_Ozero(U_1990) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_1989,sK10(U_1992,U_1991,U_1990))],[f_647_2]) ).
cnf(f_647_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,sK10(U_1992,U_1991,U_1990))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,c_Polynomial_Odegree(U_1990,U_1992))
| ~ class_Groups_Ozero(U_1990) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_5,plain,
( hAPP(c_Polynomial_Ocoeff(U_1990,U_1992),sK10(U_1992,U_1991,U_1990)) != c_Groups_Ozero__class_Ozero(U_1990)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,c_Polynomial_Odegree(U_1990,U_1992))
| ~ class_Groups_Ozero(U_1990) ),
inference(clausify,[status(thm)],[f_647_3]) ).
fof(f_648_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_y))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__dvd2]) ).
fof(f_648_2,plain,
! [U_1995,U_1994,U_1993] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1993)),c_Polynomial_Opoly__gcd(U_1993,U_1994,U_1995)),U_1995))
| ~ class_Fields_Ofield(U_1993) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
cnf(f_648_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1993)),c_Polynomial_Opoly__gcd(U_1993,U_1994,U_1995)),U_1995))
| ~ class_Fields_Ofield(U_1993) ),
inference(clausify,[status(thm)],[f_648_2]) ).
fof(f_649_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),V_x))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__dvd1]) ).
fof(f_649_2,plain,
! [U_1998,U_1997,U_1996] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1996)),c_Polynomial_Opoly__gcd(U_1996,U_1997,U_1998)),U_1997))
| ~ class_Fields_Ofield(U_1996) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
cnf(f_649_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1996)),c_Polynomial_Opoly__gcd(U_1996,U_1997,U_1998)),U_1997))
| ~ class_Fields_Ofield(U_1996) ),
inference(clausify,[status(thm)],[f_649_2]) ).
fof(f_650_1,plain,
! [V_n,V_k,V_m] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leE]) ).
fof(f_650_2,plain,
! [U_2001,U_2000,U_1999] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2000,U_2001)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1999,U_2001) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1999,U_2000),U_2001) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
cnf(f_650_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1999,U_2001)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1999,U_2000),U_2001) ),
inference(clausify,[status(thm)],[f_650_2]) ).
cnf(f_650_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2000,U_2001)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1999,U_2000),U_2001) ),
inference(clausify,[status(thm)],[f_650_2]) ).
fof(f_651_1,plain,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).
fof(f_651_2,plain,
! [U_2004,U_2003,U_2002] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2002,U_2004)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2002,U_2003),U_2004) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
cnf(f_651_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2002,U_2004)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2002,U_2003),U_2004) ),
inference(clausify,[status(thm)],[f_651_2]) ).
fof(f_652_1,plain,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).
fof(f_652_2,plain,
! [U_2007,U_2006,U_2005] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2006,U_2007)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2005,U_2006),U_2007) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
! [U_2007,U_2006] :
( ! [U_2005] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2005,U_2006),U_2007)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2006,U_2007) ),
inference(miniscope,[status(thm)],[f_652_2]) ).
cnf(f_652_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2005,U_2006),U_2007)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2006,U_2007) ),
inference(clausify,[status(thm)],[f_652_3]) ).
fof(f_653_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).
fof(f_653_2,plain,
! [U_2011,U_2010,U_2009,U_2008] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2008,U_2010),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2009,U_2011))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2010,U_2011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2008,U_2009) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
cnf(f_653_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2008,U_2010),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2009,U_2011))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2010,U_2011)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2008,U_2009) ),
inference(clausify,[status(thm)],[f_653_2]) ).
fof(f_654_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).
fof(f_654_2,plain,
! [U_2014,U_2013,U_2012] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2012,U_2014),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2013,U_2014))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2012,U_2013) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
cnf(f_654_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2012,U_2014),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2013,U_2014))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2012,U_2013) ),
inference(clausify,[status(thm)],[f_654_2]) ).
fof(f_655_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).
fof(f_655_2,plain,
! [U_2017,U_2016,U_2015] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2015,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2017,U_2016))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2015,U_2016) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
cnf(f_655_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2015,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2017,U_2016))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2015,U_2016) ),
inference(clausify,[status(thm)],[f_655_2]) ).
fof(f_656_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).
fof(f_656_2,plain,
! [U_2020,U_2019,U_2018] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2018,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2019,U_2020))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2018,U_2019) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
cnf(f_656_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2018,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2019,U_2020))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2018,U_2019) ),
inference(clausify,[status(thm)],[f_656_2]) ).
fof(f_657_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).
fof(f_657_2,plain,
! [U_2023,U_2022,U_2021] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2021,U_2022),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2021,U_2023))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2022,U_2023) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2022,U_2023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2021,U_2022),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2021,U_2023)) ) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
( ! [U_2029,U_2027] :
( ! [U_2025] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2025,U_2027),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2025,U_2029))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2027,U_2029) )
& ! [U_2028,U_2026] :
( ! [U_2024] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2026),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2028))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2026,U_2028) ) ),
inference(miniscope,[status(thm)],[f_657_2]) ).
cnf(f_657_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2026),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2028))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2026,U_2028) ),
inference(clausify,[status(thm)],[f_657_3]) ).
cnf(f_657_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2025,U_2027),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2025,U_2029))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2027,U_2029) ),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ! [B_k] : V_nb_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) )
& ( ? [B_k] : V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).
fof(f_658_2,plain,
! [U_2033,U_2032] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2032,U_2033)
| ! [U_2031] : U_2033 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2032,U_2031) )
& ( ? [U_2030] : U_2033 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2032,U_2030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2032,U_2033) ) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
( ! [U_2037,U_2035] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2035,U_2037)
| ! [U_2031] : U_2037 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2031) )
& ! [U_2036,U_2034] :
( ? [U_2030] : U_2036 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2034,U_2030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2034,U_2036) ) ),
inference(miniscope,[status(thm)],[f_658_2]) ).
fof(f_658_4,plain,
( ! [U_2037,U_2035] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2035,U_2037)
| ! [U_2031] : U_2037 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2031) )
& ! [U_2036,U_2034] :
( U_2036 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2034,sK11(U_2036,U_2034))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2034,U_2036) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_2030,sK11(U_2036,U_2034))],[f_658_3]) ).
cnf(f_658_5,plain,
( U_2036 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2034,sK11(U_2036,U_2034))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2034,U_2036) ),
inference(clausify,[status(thm)],[f_658_4]) ).
cnf(f_658_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2035,U_2037)
| U_2037 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2035,U_2031) ),
inference(clausify,[status(thm)],[f_658_4]) ).
fof(f_659_1,plain,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
inference(fof_nnf,[status(thm)],[fact_le__add1]) ).
fof(f_659_2,plain,
! [U_2039,U_2038] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2038,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2038,U_2039)),
inference(variable_rename,[status(thm)],[f_659_1]) ).
cnf(f_659_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2038,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2038,U_2039)),
inference(clausify,[status(thm)],[f_659_2]) ).
fof(f_660_1,plain,
! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_le__add2]) ).
fof(f_660_2,plain,
! [U_2041,U_2040] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2040,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2041,U_2040)),
inference(variable_rename,[status(thm)],[f_660_1]) ).
cnf(f_660_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2040,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2041,U_2040)),
inference(clausify,[status(thm)],[f_660_2]) ).
fof(f_661_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).
fof(f_661_2,plain,
! [U_2044,U_2043,U_2042] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2044,U_2042),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2044,U_2043))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2042,U_2043) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
cnf(f_661_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2044,U_2042),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2044,U_2043))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2042,U_2043) ),
inference(clausify,[status(thm)],[f_661_2]) ).
fof(f_662_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J]) ).
fof(f_662_2,plain,
! [U_2047,U_2046,U_2045] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2045,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2047,U_2046))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2045,U_2046) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
cnf(f_662_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2045,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2047,U_2046))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2045,U_2046) ),
inference(clausify,[status(thm)],[f_662_2]) ).
fof(f_663_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J]) ).
fof(f_663_2,plain,
! [U_2050,U_2049,U_2048] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2048,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2049,U_2050))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2048,U_2049) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
cnf(f_663_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2048,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2049,U_2050))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2048,U_2049) ),
inference(clausify,[status(thm)],[f_663_2]) ).
fof(f_664_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0]) ).
fof(f_664_2,plain,
! [U_2051] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2051) = U_2051,
inference(variable_rename,[status(thm)],[f_664_1]) ).
cnf(f_664_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2051) = U_2051,
inference(clausify,[status(thm)],[f_664_2]) ).
fof(f_665_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zadd__0__right]) ).
fof(f_665_2,plain,
! [U_2052] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2052,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2052,
inference(variable_rename,[status(thm)],[f_665_1]) ).
cnf(f_665_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2052,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2052,
inference(clausify,[status(thm)],[f_665_2]) ).
fof(f_666_1,plain,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(f_666_2,plain,
! [U_2054,U_2053] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2053,U_2054)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2053),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2054)),
inference(variable_rename,[status(thm)],[f_666_1]) ).
cnf(f_666_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2053,U_2054)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2053),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2054)),
inference(clausify,[status(thm)],[f_666_2]) ).
fof(f_667_1,plain,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(f_667_2,plain,
! [U_2057,U_2056,U_2055] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2055),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2056,U_2057)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2055),U_2056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2055),U_2057)),
inference(variable_rename,[status(thm)],[f_667_1]) ).
cnf(f_667_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2055),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2056,U_2057)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2055),U_2056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2055),U_2057)),
inference(clausify,[status(thm)],[f_667_2]) ).
fof(f_668_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(f_668_2,plain,
! [U_2060,U_2059,U_2058] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2058,U_2059)),U_2060) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2058),U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2059),U_2060)),
inference(variable_rename,[status(thm)],[f_668_1]) ).
cnf(f_668_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2058,U_2059)),U_2060) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2058),U_2060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2059),U_2060)),
inference(clausify,[status(thm)],[f_668_2]) ).
fof(f_669_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J]) ).
fof(f_669_2,plain,
! [U_2063,U_2062,U_2061] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2061,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2062,U_2063))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2061,U_2062) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
cnf(f_669_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2061,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2062,U_2063))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2061,U_2062) ),
inference(clausify,[status(thm)],[f_669_2]) ).
fof(f_670_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J]) ).
fof(f_670_2,plain,
! [U_2066,U_2065,U_2064] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2064,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2066,U_2065))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2064,U_2065) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
cnf(f_670_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2064,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2066,U_2065))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2064,U_2065) ),
inference(clausify,[status(thm)],[f_670_2]) ).
fof(f_671_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).
fof(f_671_2,plain,
! [U_2069,U_2068,U_2067] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2067,U_2069),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2068,U_2069))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2067,U_2068) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
cnf(f_671_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2067,U_2069),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2068,U_2069))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2067,U_2068) ),
inference(clausify,[status(thm)],[f_671_2]) ).
fof(f_672_1,plain,
! [V_n,V_m] :
( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) != V_m ),
inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero]) ).
fof(f_672_2,plain,
! [U_2071,U_2070] :
( U_2071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2070,U_2071) != U_2070 ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
! [U_2071] :
( ! [U_2070] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2070,U_2071) != U_2070
| U_2071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_672_2]) ).
cnf(f_672_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2070,U_2071) != U_2070
| U_2071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).
fof(f_673_2,plain,
! [U_2073,U_2072] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2072,U_2073) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2073 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2072 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_2073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2072,U_2073) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
( ! [U_2077,U_2075] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2075,U_2077) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2075 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2076,U_2074] :
( ( U_2076 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2074,U_2076) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_673_2]) ).
cnf(f_673_4,plain,
( U_2074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2074,U_2076) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_673_3]) ).
cnf(f_673_5,plain,
( U_2076 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2074,U_2076) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_673_3]) ).
cnf(f_673_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2075,U_2077) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2075 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_673_3]) ).
fof(f_674_1,plain,
! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
inference(fof_nnf,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(f_674_2,plain,
! [U_2078] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2078,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2078,
inference(variable_rename,[status(thm)],[f_674_1]) ).
cnf(f_674_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2078,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2078,
inference(clausify,[status(thm)],[f_674_2]) ).
fof(f_675_1,plain,
! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(f_675_2,plain,
! [U_2079] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2079) = U_2079,
inference(variable_rename,[status(thm)],[f_675_1]) ).
cnf(f_675_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2079) = U_2079,
inference(clausify,[status(thm)],[f_675_2]) ).
fof(f_676_1,plain,
! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k),
inference(fof_nnf,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(f_676_2,plain,
! [U_2083,U_2082,U_2081,U_2080] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2080),U_2081),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2082),U_2081),U_2083)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2080,U_2082)),U_2081),U_2083),
inference(variable_rename,[status(thm)],[f_676_1]) ).
cnf(f_676_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2080),U_2081),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2082),U_2081),U_2083)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2080,U_2082)),U_2081),U_2083),
inference(clausify,[status(thm)],[f_676_2]) ).
fof(f_677_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).
fof(f_677_2,plain,
! [U_2086,U_2085,U_2084] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2084,U_2085)),U_2086) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2084),U_2086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2085),U_2086)),
inference(variable_rename,[status(thm)],[f_677_1]) ).
cnf(f_677_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2084,U_2085)),U_2086) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2084),U_2086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2085),U_2086)),
inference(clausify,[status(thm)],[f_677_2]) ).
fof(f_678_1,plain,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).
fof(f_678_2,plain,
! [U_2089,U_2088,U_2087] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2087),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2087),U_2088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2087),U_2089)),
inference(variable_rename,[status(thm)],[f_678_1]) ).
cnf(f_678_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2087),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2087),U_2088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2087),U_2089)),
inference(clausify,[status(thm)],[f_678_2]) ).
fof(f_679_1,plain,
! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i),
inference(fof_nnf,[status(thm)],[fact_not__add__less1]) ).
fof(f_679_2,plain,
! [U_2091,U_2090] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2090,U_2091),U_2090),
inference(variable_rename,[status(thm)],[f_679_1]) ).
cnf(f_679_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2090,U_2091),U_2090),
inference(clausify,[status(thm)],[f_679_2]) ).
fof(f_680_1,plain,
! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i),
inference(fof_nnf,[status(thm)],[fact_not__add__less2]) ).
fof(f_680_2,plain,
! [U_2093,U_2092] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2092,U_2093),U_2093),
inference(variable_rename,[status(thm)],[f_680_1]) ).
cnf(f_680_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2092,U_2093),U_2093),
inference(clausify,[status(thm)],[f_680_2]) ).
fof(f_681_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).
fof(f_681_2,plain,
! [U_2096,U_2095,U_2094] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2094,U_2095),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2094,U_2096))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2095,U_2096) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2095,U_2096)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2094,U_2095),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2094,U_2096)) ) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
( ! [U_2102,U_2100] :
( ! [U_2098] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2100),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2102))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2100,U_2102) )
& ! [U_2101,U_2099] :
( ! [U_2097] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2097,U_2099),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2097,U_2101))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2099,U_2101) ) ),
inference(miniscope,[status(thm)],[f_681_2]) ).
cnf(f_681_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2097,U_2099),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2097,U_2101))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2099,U_2101) ),
inference(clausify,[status(thm)],[f_681_3]) ).
cnf(f_681_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2100),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2098,U_2102))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2100,U_2102) ),
inference(clausify,[status(thm)],[f_681_3]) ).
fof(f_682_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).
fof(f_682_2,plain,
! [U_2105,U_2104,U_2103] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2103,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2104,U_2105))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2103,U_2104) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
cnf(f_682_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2103,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2104,U_2105))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2103,U_2104) ),
inference(clausify,[status(thm)],[f_682_2]) ).
fof(f_683_1,plain,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).
fof(f_683_2,plain,
! [U_2108,U_2107,U_2106] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2106,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2108,U_2107))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2106,U_2107) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
cnf(f_683_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2106,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2108,U_2107))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2106,U_2107) ),
inference(clausify,[status(thm)],[f_683_2]) ).
fof(f_684_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).
fof(f_684_2,plain,
! [U_2111,U_2110,U_2109] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2109,U_2111),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2110,U_2111))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2109,U_2110) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
cnf(f_684_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2109,U_2111),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2110,U_2111))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2109,U_2110) ),
inference(clausify,[status(thm)],[f_684_2]) ).
fof(f_685_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).
fof(f_685_2,plain,
! [U_2115,U_2114,U_2113,U_2112] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2112,U_2114),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2113,U_2115))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2114,U_2115)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2112,U_2113) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
cnf(f_685_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2112,U_2114),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2113,U_2115))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2114,U_2115)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2112,U_2113) ),
inference(clausify,[status(thm)],[f_685_2]) ).
fof(f_686_1,plain,
! [V_n,V_m,V_l,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) ),
inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).
fof(f_686_2,plain,
! [U_2119,U_2118,U_2117,U_2116] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2118,U_2119)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2118,U_2117) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2116,U_2119)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2116,U_2117) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
cnf(f_686_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2118,U_2119)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2118,U_2117) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2116,U_2119)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2116,U_2117) ),
inference(clausify,[status(thm)],[f_686_2]) ).
fof(f_687_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).
fof(f_687_2,plain,
! [U_2122,U_2121,U_2120] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2120,U_2122)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2120,U_2121),U_2122) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
cnf(f_687_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2120,U_2122)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2120,U_2121),U_2122) ),
inference(clausify,[status(thm)],[f_687_2]) ).
fof(f_688_1,plain,
! [V_nb_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_nb_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_nb_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd__reduce]) ).
fof(f_688_2,plain,
! [U_2124,U_2123] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2123),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2124,U_2123)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2123),U_2124)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2123),U_2124))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2123),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2124,U_2123))) ) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
fof(f_688_3,plain,
( ! [U_2128,U_2126] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2126),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2128,U_2126)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2126),U_2128)) )
& ! [U_2127,U_2125] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2125),U_2127))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2125),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2127,U_2125))) ) ),
inference(miniscope,[status(thm)],[f_688_2]) ).
cnf(f_688_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2125),U_2127))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2125),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2127,U_2125))) ),
inference(clausify,[status(thm)],[f_688_3]) ).
cnf(f_688_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2126),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2128,U_2126)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2126),U_2128)) ),
inference(clausify,[status(thm)],[f_688_3]) ).
fof(f_689_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__shift]) ).
fof(f_689_2,plain,
! [U_2130,U_2129] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2129),U_2130) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2129,c_Nat_OSuc(U_2130)),
inference(variable_rename,[status(thm)],[f_689_1]) ).
cnf(f_689_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2129),U_2130) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2129,c_Nat_OSuc(U_2130)),
inference(clausify,[status(thm)],[f_689_2]) ).
fof(f_690_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).
fof(f_690_2,plain,
! [U_2132,U_2131] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2131),U_2132) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2131,U_2132)),
inference(variable_rename,[status(thm)],[f_690_1]) ).
cnf(f_690_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2131),U_2132) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2131,U_2132)),
inference(clausify,[status(thm)],[f_690_2]) ).
fof(f_691_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).
fof(f_691_2,plain,
! [U_2134,U_2133] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2133,c_Nat_OSuc(U_2134)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2133,U_2134)),
inference(variable_rename,[status(thm)],[f_691_1]) ).
cnf(f_691_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2133,c_Nat_OSuc(U_2134)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2133,U_2134)),
inference(clausify,[status(thm)],[f_691_2]) ).
fof(f_692_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__zero__iff]) ).
fof(f_692_2,plain,
! [U_2137,U_2136,U_2135] :
( ( ( c_Polynomial_Opoly__gcd(U_2135,U_2136,U_2137) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| U_2137 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| U_2136 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135)) )
& ( ( U_2137 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
& U_2136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135)) )
| c_Polynomial_Opoly__gcd(U_2135,U_2136,U_2137) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135)) ) )
| ~ class_Fields_Ofield(U_2135) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
cnf(f_692_3,plain,
( U_2136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| c_Polynomial_Opoly__gcd(U_2135,U_2136,U_2137) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| ~ class_Fields_Ofield(U_2135) ),
inference(clausify,[status(thm)],[f_692_2]) ).
cnf(f_692_4,plain,
( U_2137 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| c_Polynomial_Opoly__gcd(U_2135,U_2136,U_2137) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| ~ class_Fields_Ofield(U_2135) ),
inference(clausify,[status(thm)],[f_692_2]) ).
cnf(f_692_5,plain,
( c_Polynomial_Opoly__gcd(U_2135,U_2136,U_2137) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| U_2137 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| U_2136 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2135))
| ~ class_Fields_Ofield(U_2135) ),
inference(clausify,[status(thm)],[f_692_2]) ).
fof(f_693_1,plain,
! [T_a] :
( c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__0__0]) ).
fof(f_693_2,plain,
! [U_2138] :
( c_Polynomial_Opoly__gcd(U_2138,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2138)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2138))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2138))
| ~ class_Fields_Ofield(U_2138) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
cnf(f_693_3,plain,
( c_Polynomial_Opoly__gcd(U_2138,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2138)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2138))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2138))
| ~ class_Fields_Ofield(U_2138) ),
inference(clausify,[status(thm)],[f_693_2]) ).
fof(f_694_1,plain,
! [V_b,V_a,T_a] :
( c_Polynomial_Opoly__gcd(T_a,V_a,V_b) = c_Polynomial_Opoly__gcd(T_a,V_b,V_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd_Ocommute]) ).
fof(f_694_2,plain,
! [U_2141,U_2140,U_2139] :
( c_Polynomial_Opoly__gcd(U_2139,U_2140,U_2141) = c_Polynomial_Opoly__gcd(U_2139,U_2141,U_2140)
| ~ class_Fields_Ofield(U_2139) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
cnf(f_694_3,plain,
( c_Polynomial_Opoly__gcd(U_2139,U_2140,U_2141) = c_Polynomial_Opoly__gcd(U_2139,U_2141,U_2140)
| ~ class_Fields_Ofield(U_2139) ),
inference(clausify,[status(thm)],[f_694_2]) ).
fof(f_695_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c)) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd_Oleft__commute]) ).
fof(f_695_2,plain,
! [U_2145,U_2144,U_2143,U_2142] :
( c_Polynomial_Opoly__gcd(U_2142,U_2143,c_Polynomial_Opoly__gcd(U_2142,U_2144,U_2145)) = c_Polynomial_Opoly__gcd(U_2142,U_2144,c_Polynomial_Opoly__gcd(U_2142,U_2143,U_2145))
| ~ class_Fields_Ofield(U_2142) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
cnf(f_695_3,plain,
( c_Polynomial_Opoly__gcd(U_2142,U_2143,c_Polynomial_Opoly__gcd(U_2142,U_2144,U_2145)) = c_Polynomial_Opoly__gcd(U_2142,U_2144,c_Polynomial_Opoly__gcd(U_2142,U_2143,U_2145))
| ~ class_Fields_Ofield(U_2142) ),
inference(clausify,[status(thm)],[f_695_2]) ).
fof(f_696_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c) = c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd_Oassoc]) ).
fof(f_696_2,plain,
! [U_2149,U_2148,U_2147,U_2146] :
( c_Polynomial_Opoly__gcd(U_2146,c_Polynomial_Opoly__gcd(U_2146,U_2147,U_2148),U_2149) = c_Polynomial_Opoly__gcd(U_2146,U_2147,c_Polynomial_Opoly__gcd(U_2146,U_2148,U_2149))
| ~ class_Fields_Ofield(U_2146) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
cnf(f_696_3,plain,
( c_Polynomial_Opoly__gcd(U_2146,c_Polynomial_Opoly__gcd(U_2146,U_2147,U_2148),U_2149) = c_Polynomial_Opoly__gcd(U_2146,U_2147,c_Polynomial_Opoly__gcd(U_2146,U_2148,U_2149))
| ~ class_Fields_Ofield(U_2146) ),
inference(clausify,[status(thm)],[f_696_2]) ).
fof(f_697_1,plain,
! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
( V_q1 = V_q2
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__unique__div]) ).
fof(f_697_2,plain,
! [U_2156,U_2155,U_2154,U_2153,U_2152,U_2151,U_2150] :
( U_2153 = U_2155
| ~ c_Polynomial_Opdivmod__rel(U_2150,U_2151,U_2152,U_2155,U_2156)
| ~ c_Polynomial_Opdivmod__rel(U_2150,U_2151,U_2152,U_2153,U_2154)
| ~ class_Fields_Ofield(U_2150) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
cnf(f_697_3,plain,
( U_2153 = U_2155
| ~ c_Polynomial_Opdivmod__rel(U_2150,U_2151,U_2152,U_2155,U_2156)
| ~ c_Polynomial_Opdivmod__rel(U_2150,U_2151,U_2152,U_2153,U_2154)
| ~ class_Fields_Ofield(U_2150) ),
inference(clausify,[status(thm)],[f_697_2]) ).
fof(f_698_1,plain,
! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
( V_r1 = V_r2
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__unique__mod]) ).
fof(f_698_2,plain,
! [U_2163,U_2162,U_2161,U_2160,U_2159,U_2158,U_2157] :
( U_2161 = U_2163
| ~ c_Polynomial_Opdivmod__rel(U_2157,U_2158,U_2159,U_2162,U_2163)
| ~ c_Polynomial_Opdivmod__rel(U_2157,U_2158,U_2159,U_2160,U_2161)
| ~ class_Fields_Ofield(U_2157) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
cnf(f_698_3,plain,
( U_2161 = U_2163
| ~ c_Polynomial_Opdivmod__rel(U_2157,U_2158,U_2159,U_2162,U_2163)
| ~ c_Polynomial_Opdivmod__rel(U_2157,U_2158,U_2159,U_2160,U_2161)
| ~ class_Fields_Ofield(U_2157) ),
inference(clausify,[status(thm)],[f_698_2]) ).
fof(f_699_1,plain,
! [V_r2,V_q2,V_r1,V_q1,V_y,V_x,T_a] :
( ( V_r1 = V_r2
& V_q1 = V_q2 )
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__unique]) ).
fof(f_699_2,plain,
! [U_2170,U_2169,U_2168,U_2167,U_2166,U_2165,U_2164] :
( ( U_2168 = U_2170
& U_2167 = U_2169 )
| ~ c_Polynomial_Opdivmod__rel(U_2164,U_2165,U_2166,U_2169,U_2170)
| ~ c_Polynomial_Opdivmod__rel(U_2164,U_2165,U_2166,U_2167,U_2168)
| ~ class_Fields_Ofield(U_2164) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
cnf(f_699_3,plain,
( U_2167 = U_2169
| ~ c_Polynomial_Opdivmod__rel(U_2164,U_2165,U_2166,U_2169,U_2170)
| ~ c_Polynomial_Opdivmod__rel(U_2164,U_2165,U_2166,U_2167,U_2168)
| ~ class_Fields_Ofield(U_2164) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_4,plain,
( U_2168 = U_2170
| ~ c_Polynomial_Opdivmod__rel(U_2164,U_2165,U_2166,U_2169,U_2170)
| ~ c_Polynomial_Opdivmod__rel(U_2164,U_2165,U_2166,U_2167,U_2168)
| ~ class_Fields_Ofield(U_2164) ),
inference(clausify,[status(thm)],[f_699_2]) ).
fof(f_700_1,plain,
! [V_r_2,V_qb_2,V_y_2,T_a] :
( ( ( c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_qb_2,V_r_2)
| V_r_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_qb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( ( V_r_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_qb_2,V_r_2) ) )
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__0__iff]) ).
fof(f_700_2,plain,
! [U_2174,U_2173,U_2172,U_2171] :
( ( ( c_Polynomial_Opdivmod__rel(U_2171,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171)),U_2172,U_2173,U_2174)
| U_2174 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171))
| U_2173 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171)) )
& ( ( U_2174 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171))
& U_2173 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171)) )
| ~ c_Polynomial_Opdivmod__rel(U_2171,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171)),U_2172,U_2173,U_2174) ) )
| ~ class_Fields_Ofield(U_2171) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
cnf(f_700_3,plain,
( U_2173 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171))
| ~ c_Polynomial_Opdivmod__rel(U_2171,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171)),U_2172,U_2173,U_2174)
| ~ class_Fields_Ofield(U_2171) ),
inference(clausify,[status(thm)],[f_700_2]) ).
cnf(f_700_4,plain,
( U_2174 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171))
| ~ c_Polynomial_Opdivmod__rel(U_2171,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171)),U_2172,U_2173,U_2174)
| ~ class_Fields_Ofield(U_2171) ),
inference(clausify,[status(thm)],[f_700_2]) ).
cnf(f_700_5,plain,
( c_Polynomial_Opdivmod__rel(U_2171,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171)),U_2172,U_2173,U_2174)
| U_2174 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171))
| U_2173 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2171))
| ~ class_Fields_Ofield(U_2171) ),
inference(clausify,[status(thm)],[f_700_2]) ).
fof(f_701_1,plain,
! [V_r_2,V_qb_2,V_x_2,T_a] :
( ( ( c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_qb_2,V_r_2)
| V_r_2 != V_x_2
| V_qb_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( ( V_r_2 = V_x_2
& V_qb_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_qb_2,V_r_2) ) )
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__by__0__iff]) ).
fof(f_701_2,plain,
! [U_2178,U_2177,U_2176,U_2175] :
( ( ( c_Polynomial_Opdivmod__rel(U_2175,U_2176,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175)),U_2177,U_2178)
| U_2178 != U_2176
| U_2177 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175)) )
& ( ( U_2178 = U_2176
& U_2177 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175)) )
| ~ c_Polynomial_Opdivmod__rel(U_2175,U_2176,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175)),U_2177,U_2178) ) )
| ~ class_Fields_Ofield(U_2175) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
cnf(f_701_3,plain,
( U_2177 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175))
| ~ c_Polynomial_Opdivmod__rel(U_2175,U_2176,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175)),U_2177,U_2178)
| ~ class_Fields_Ofield(U_2175) ),
inference(clausify,[status(thm)],[f_701_2]) ).
cnf(f_701_4,plain,
( U_2178 = U_2176
| ~ c_Polynomial_Opdivmod__rel(U_2175,U_2176,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175)),U_2177,U_2178)
| ~ class_Fields_Ofield(U_2175) ),
inference(clausify,[status(thm)],[f_701_2]) ).
cnf(f_701_5,plain,
( c_Polynomial_Opdivmod__rel(U_2175,U_2176,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175)),U_2177,U_2178)
| U_2178 != U_2176
| U_2177 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2175))
| ~ class_Fields_Ofield(U_2175) ),
inference(clausify,[status(thm)],[f_701_2]) ).
fof(f_702_1,plain,
! [V_y,T_a] :
( c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__0]) ).
fof(f_702_2,plain,
! [U_2180,U_2179] :
( c_Polynomial_Opdivmod__rel(U_2179,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2179)),U_2180,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2179)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2179)))
| ~ class_Fields_Ofield(U_2179) ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
cnf(f_702_3,plain,
( c_Polynomial_Opdivmod__rel(U_2179,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2179)),U_2180,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2179)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2179)))
| ~ class_Fields_Ofield(U_2179) ),
inference(clausify,[status(thm)],[f_702_2]) ).
fof(f_703_1,plain,
! [V_x,T_a] :
( c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__by__0]) ).
fof(f_703_2,plain,
! [U_2182,U_2181] :
( c_Polynomial_Opdivmod__rel(U_2181,U_2182,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2181)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2181)),U_2182)
| ~ class_Fields_Ofield(U_2181) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
cnf(f_703_3,plain,
( c_Polynomial_Opdivmod__rel(U_2181,U_2182,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2181)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2181)),U_2182)
| ~ class_Fields_Ofield(U_2181) ),
inference(clausify,[status(thm)],[f_703_2]) ).
fof(f_704_1,plain,
! [V_y,V_x,V_k,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k),V_x))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__greatest]) ).
fof(f_704_2,plain,
! [U_2186,U_2185,U_2184,U_2183] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2183)),U_2184),c_Polynomial_Opoly__gcd(U_2183,U_2185,U_2186)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2183)),U_2184),U_2186))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2183)),U_2184),U_2185))
| ~ class_Fields_Ofield(U_2183) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
cnf(f_704_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2183)),U_2184),c_Polynomial_Opoly__gcd(U_2183,U_2185,U_2186)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2183)),U_2184),U_2186))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2183)),U_2184),U_2185))
| ~ class_Fields_Ofield(U_2183) ),
inference(clausify,[status(thm)],[f_704_2]) ).
fof(f_705_1,plain,
! [V_y_2,V_x_2,V_k_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_x_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),V_x_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_k_2),c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2))) ) )
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__poly__gcd__iff]) ).
fof(f_705_2,plain,
! [U_2190,U_2189,U_2188,U_2187] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),c_Polynomial_Opoly__gcd(U_2187,U_2189,U_2190)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2190))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2189)) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2190))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2189)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),c_Polynomial_Opoly__gcd(U_2187,U_2189,U_2190))) ) )
| ~ class_Fields_Ofield(U_2187) ),
inference(variable_rename,[status(thm)],[f_705_1]) ).
cnf(f_705_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2189))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),c_Polynomial_Opoly__gcd(U_2187,U_2189,U_2190)))
| ~ class_Fields_Ofield(U_2187) ),
inference(clausify,[status(thm)],[f_705_2]) ).
cnf(f_705_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2190))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),c_Polynomial_Opoly__gcd(U_2187,U_2189,U_2190)))
| ~ class_Fields_Ofield(U_2187) ),
inference(clausify,[status(thm)],[f_705_2]) ).
cnf(f_705_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),c_Polynomial_Opoly__gcd(U_2187,U_2189,U_2190)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2190))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2187)),U_2188),U_2189))
| ~ class_Fields_Ofield(U_2187) ),
inference(clausify,[status(thm)],[f_705_2]) ).
fof(f_706_1,plain,
! [V_y,V_x,T_a] :
( c_Polynomial_Opoly__gcd(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__minus__left]) ).
fof(f_706_2,plain,
! [U_2193,U_2192,U_2191] :
( c_Polynomial_Opoly__gcd(U_2191,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2191),U_2192),U_2193) = c_Polynomial_Opoly__gcd(U_2191,U_2192,U_2193)
| ~ class_Fields_Ofield(U_2191) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
cnf(f_706_3,plain,
( c_Polynomial_Opoly__gcd(U_2191,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2191),U_2192),U_2193) = c_Polynomial_Opoly__gcd(U_2191,U_2192,U_2193)
| ~ class_Fields_Ofield(U_2191) ),
inference(clausify,[status(thm)],[f_706_2]) ).
fof(f_707_1,plain,
! [V_y,V_x,T_a] :
( c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Polynomial_Opoly__gcd(T_a,V_x,V_y)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__minus__right]) ).
fof(f_707_2,plain,
! [U_2196,U_2195,U_2194] :
( c_Polynomial_Opoly__gcd(U_2194,U_2195,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2194),U_2196)) = c_Polynomial_Opoly__gcd(U_2194,U_2195,U_2196)
| ~ class_Fields_Ofield(U_2194) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
cnf(f_707_3,plain,
( c_Polynomial_Opoly__gcd(U_2194,U_2195,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2194),U_2196)) = c_Polynomial_Opoly__gcd(U_2194,U_2195,U_2196)
| ~ class_Fields_Ofield(U_2194) ),
inference(clausify,[status(thm)],[f_707_2]) ).
fof(f_708_1,plain,
! [V_x,T_a] :
( c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__1__right]) ).
fof(f_708_2,plain,
! [U_2198,U_2197] :
( c_Polynomial_Opoly__gcd(U_2197,U_2198,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2197))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2197))
| ~ class_Fields_Ofield(U_2197) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
cnf(f_708_3,plain,
( c_Polynomial_Opoly__gcd(U_2197,U_2198,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2197))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2197))
| ~ class_Fields_Ofield(U_2197) ),
inference(clausify,[status(thm)],[f_708_2]) ).
fof(f_709_1,plain,
! [V_y,T_a] :
( c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__1__left]) ).
fof(f_709_2,plain,
! [U_2200,U_2199] :
( c_Polynomial_Opoly__gcd(U_2199,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2199)),U_2200) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2199))
| ~ class_Fields_Ofield(U_2199) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
cnf(f_709_3,plain,
( c_Polynomial_Opoly__gcd(U_2199,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2199)),U_2200) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_2199))
| ~ class_Fields_Ofield(U_2199) ),
inference(clausify,[status(thm)],[f_709_2]) ).
fof(f_710_1,plain,
! [V_q,V_p,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_710_2,plain,
! [U_2204,U_2203,U_2202,U_2201] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),hAPP(hAPP(c_Power_Opower__class_Opower(U_2201),U_2202),U_2203)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2201),U_2202),U_2204)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2201),U_2202),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2203,U_2204))
| ~ class_Rings_Ocomm__semiring__1(U_2201) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
cnf(f_710_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2201),hAPP(hAPP(c_Power_Opower__class_Opower(U_2201),U_2202),U_2203)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2201),U_2202),U_2204)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2201),U_2202),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2203,U_2204))
| ~ class_Rings_Ocomm__semiring__1(U_2201) ),
inference(clausify,[status(thm)],[f_710_2]) ).
fof(f_711_1,plain,
! [V_n,V_m,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__add]) ).
fof(f_711_2,plain,
! [U_2208,U_2207,U_2206,U_2205] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2205),U_2206),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2207,U_2208)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),hAPP(hAPP(c_Power_Opower__class_Opower(U_2205),U_2206),U_2207)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2205),U_2206),U_2208))
| ~ class_Groups_Omonoid__mult(U_2205) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
cnf(f_711_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2205),U_2206),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2207,U_2208)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2205),hAPP(hAPP(c_Power_Opower__class_Opower(U_2205),U_2206),U_2207)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2205),U_2206),U_2208))
| ~ class_Groups_Omonoid__mult(U_2205) ),
inference(clausify,[status(thm)],[f_711_2]) ).
fof(f_712_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( V_nb_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_nb_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).
fof(f_712_2,plain,
! [U_2210,U_2209] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2209,U_2210) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2210 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2209 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2210 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2209 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2210 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2209 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2209,U_2210) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
( ! [U_2214,U_2212] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2212,U_2214) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2214 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2214 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2212 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2213,U_2211] :
( ( U_2213 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2211 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2213) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_712_2]) ).
cnf(f_712_4,plain,
( U_2211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2211 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2213) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_5,plain,
( U_2213 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2211 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2213) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_6,plain,
( U_2211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2213) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_7,plain,
( U_2213 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2213) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_8,plain,
( U_2214 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2212 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2212,U_2214) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_9,plain,
( U_2214 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2212,U_2214) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2)
| ( ( V_nb_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( V_nb_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_nb_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)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).
fof(f_713_2,plain,
! [U_2216,U_2215] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2215,U_2216)
| ( ( U_2216 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2215 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2216 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2215 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2216 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2216 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2215 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2215,U_2216) ) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
( ! [U_2220,U_2218] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2218,U_2220)
| ( ( U_2220 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2218 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2220 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2218 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2219,U_2217] :
( ( U_2219 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2217 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2219) ) ),
inference(miniscope,[status(thm)],[f_713_2]) ).
cnf(f_713_4,plain,
( U_2217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2217 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2219) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_5,plain,
( U_2219 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2217 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2219) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_6,plain,
( U_2217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2219) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_7,plain,
( U_2219 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2217,U_2219) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_8,plain,
( U_2220 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2218 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2218,U_2220) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_9,plain,
( U_2220 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2218 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2218,U_2220) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_nb_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).
fof(f_714_2,plain,
! [U_2222,U_2221] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2221,U_2222))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2222)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2221) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2222)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2221)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2221,U_2222)) ) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
fof(f_714_3,plain,
( ! [U_2226,U_2224] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2224,U_2226))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2226)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2224) ) )
& ! [U_2225,U_2223] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2225)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2223)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2223,U_2225)) ) ),
inference(miniscope,[status(thm)],[f_714_2]) ).
cnf(f_714_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2225)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2223)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2223,U_2225)) ),
inference(clausify,[status(thm)],[f_714_3]) ).
cnf(f_714_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2224)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2224,U_2226)) ),
inference(clausify,[status(thm)],[f_714_3]) ).
cnf(f_714_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2226)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2224,U_2226)) ),
inference(clausify,[status(thm)],[f_714_3]) ).
fof(f_715_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_715_2,plain,
! [U_2228,U_2227] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2227,U_2228))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2228)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2227) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
cnf(f_715_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2227,U_2228))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2228)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2227) ),
inference(clausify,[status(thm)],[f_715_2]) ).
fof(f_716_1,plain,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).
fof(f_716_2,plain,
! [U_2230,U_2229] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2229,U_2230))),
inference(variable_rename,[status(thm)],[f_716_1]) ).
cnf(f_716_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2229,U_2230))),
inference(clausify,[status(thm)],[f_716_2]) ).
fof(f_717_1,plain,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).
fof(f_717_2,plain,
! [U_2232,U_2231] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2232,U_2231))),
inference(variable_rename,[status(thm)],[f_717_1]) ).
cnf(f_717_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2232,U_2231))),
inference(clausify,[status(thm)],[f_717_2]) ).
fof(f_718_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ! [B_k] : V_nb_2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) )
& ( ? [B_k] : V_nb_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).
fof(f_718_2,plain,
! [U_2236,U_2235] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2235,U_2236)
| ! [U_2234] : U_2236 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2235,U_2234)) )
& ( ? [U_2233] : U_2236 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2235,U_2233))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2235,U_2236) ) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
fof(f_718_3,plain,
( ! [U_2240,U_2238] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2238,U_2240)
| ! [U_2234] : U_2240 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2238,U_2234)) )
& ! [U_2239,U_2237] :
( ? [U_2233] : U_2239 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2237,U_2233))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2237,U_2239) ) ),
inference(miniscope,[status(thm)],[f_718_2]) ).
fof(f_718_4,plain,
( ! [U_2240,U_2238] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2238,U_2240)
| ! [U_2234] : U_2240 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2238,U_2234)) )
& ! [U_2239,U_2237] :
( U_2239 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2237,sK12(U_2239,U_2237)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2237,U_2239) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_2233,sK12(U_2239,U_2237))],[f_718_3]) ).
cnf(f_718_5,plain,
( U_2239 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2237,sK12(U_2239,U_2237)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2237,U_2239) ),
inference(clausify,[status(thm)],[f_718_4]) ).
cnf(f_718_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2238,U_2240)
| U_2240 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2238,U_2234)) ),
inference(clausify,[status(thm)],[f_718_4]) ).
fof(f_719_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_odd__nonzero]) ).
fof(f_719_2,plain,
! [U_2241] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2241),U_2241) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_719_1]) ).
cnf(f_719_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2241),U_2241) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_719_2]) ).
fof(f_720_1,plain,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).
fof(f_720_2,plain,
! [U_2245,U_2244,U_2243,U_2242] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2242,U_2244),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2243,U_2245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2244,U_2245)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2242,U_2243) ),
inference(variable_rename,[status(thm)],[f_720_1]) ).
cnf(f_720_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2242,U_2244),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2243,U_2245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2244,U_2245)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2242,U_2243) ),
inference(clausify,[status(thm)],[f_720_2]) ).
fof(f_721_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc__right]) ).
fof(f_721_2,plain,
! [U_2247,U_2246] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),c_Nat_OSuc(U_2247)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2246,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2247)),
inference(variable_rename,[status(thm)],[f_721_1]) ).
cnf(f_721_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),c_Nat_OSuc(U_2247)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2246,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2246),U_2247)),
inference(clausify,[status(thm)],[f_721_2]) ).
fof(f_722_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc]) ).
fof(f_722_2,plain,
! [U_2249,U_2248] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2248)),U_2249) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2248),U_2249)),
inference(variable_rename,[status(thm)],[f_722_1]) ).
cnf(f_722_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2248)),U_2249) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2248),U_2249)),
inference(clausify,[status(thm)],[f_722_2]) ).
fof(f_723_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( V_w_2 != V_z_2
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) )
& ( V_w_2 = V_z_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).
fof(f_723_2,plain,
! [U_2251,U_2250] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2250,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2251,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_2250 != U_2251
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2250,U_2251) ) )
& ( U_2250 = U_2251
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2250,U_2251)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2250,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2251,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
( ! [U_2255,U_2253] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2253,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2255,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_2253 != U_2255
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2253,U_2255) ) )
& ! [U_2254,U_2252] :
( U_2252 = U_2254
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2252,U_2254)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2252,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2254,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_723_2]) ).
cnf(f_723_4,plain,
( U_2252 = U_2254
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2252,U_2254)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2252,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2254,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_723_3]) ).
cnf(f_723_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2253,U_2255)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2253,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2255,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_723_3]) ).
cnf(f_723_6,plain,
( U_2253 != U_2255
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2253,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2255,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(f_724_2,plain,
! [U_2256] : c_Nat_OSuc(U_2256) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2256),
inference(variable_rename,[status(thm)],[f_724_1]) ).
cnf(f_724_3,plain,
c_Nat_OSuc(U_2256) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2256),
inference(clausify,[status(thm)],[f_724_2]) ).
fof(f_725_1,plain,
! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(f_725_2,plain,
! [U_2257] : c_Nat_OSuc(U_2257) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2257,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_725_1]) ).
cnf(f_725_3,plain,
c_Nat_OSuc(U_2257) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2257,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_725_2]) ).
fof(f_726_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(f_726_2,plain,
! [U_2258] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2258),U_2258) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_726_1]) ).
cnf(f_726_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2258),U_2258) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_726_2]) ).
fof(f_727_1,plain,
! [V_c_2,V_t_2,V_x_2,V_d_2,V_aa_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2)),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2)),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_aa_2),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__period]) ).
fof(f_727_2,plain,
! [U_2263,U_2262,U_2261,U_2260,U_2259] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2263),U_2260)),U_2262))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2263),U_2260)),U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,U_2262))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),U_2260)) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
cnf(f_727_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2263),U_2260)),U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),U_2260)) ),
inference(clausify,[status(thm)],[f_727_2]) ).
cnf(f_727_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2263),U_2260)),U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2259),U_2260)) ),
inference(clausify,[status(thm)],[f_727_2]) ).
fof(f_728_1,plain,
! [V_m_2,V_nb_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_nb_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_nb_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_nb_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_nb_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__reduce]) ).
fof(f_728_2,plain,
! [U_2266,U_2265,U_2264] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2264),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2265,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2264),U_2266))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2264),U_2265)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2264),U_2265))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2264),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2265,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2264),U_2266)))) ) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
( ! [U_2272,U_2270,U_2268] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2268),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2270,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2268),U_2272))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2268),U_2270)) )
& ! [U_2271,U_2269,U_2267] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2267),U_2269))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2267),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2267),U_2271)))) ) ),
inference(miniscope,[status(thm)],[f_728_2]) ).
cnf(f_728_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2267),U_2269))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2267),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2267),U_2271)))) ),
inference(clausify,[status(thm)],[f_728_3]) ).
cnf(f_728_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2268),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2270,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2268),U_2272))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2268),U_2270)) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_1,plain,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(f_729_2,plain,
! [U_2275,U_2274,U_2273] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2273),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2274,U_2275)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2273),U_2274)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2273),U_2275)),
inference(variable_rename,[status(thm)],[f_729_1]) ).
cnf(f_729_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2273),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2274,U_2275)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2273),U_2274)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2273),U_2275)),
inference(clausify,[status(thm)],[f_729_2]) ).
fof(f_730_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).
fof(f_730_2,plain,
! [U_2276] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2276),U_2276),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2276,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2276,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2276),U_2276),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
( ! [U_2278] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2278),U_2278),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2278,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2277] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2277,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2277),U_2277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_730_2]) ).
cnf(f_730_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2277,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2277),U_2277),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_730_3]) ).
cnf(f_730_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2278),U_2278),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2278,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).
fof(f_731_2,plain,
! [U_2280,U_2279] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2279,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2280,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2279,U_2280) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2279,U_2280)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2279,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2280,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
fof(f_731_3,plain,
( ! [U_2284,U_2282] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2282,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2284,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2282,U_2284) )
& ! [U_2283,U_2281] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2281,U_2283)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2281,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2283,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_731_2]) ).
cnf(f_731_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2281,U_2283)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2281,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2283,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_731_3]) ).
cnf(f_731_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2282,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2284,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2282,U_2284) ),
inference(clausify,[status(thm)],[f_731_3]) ).
fof(f_732_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2) ) ),
inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).
fof(f_732_2,plain,
! [U_2286,U_2285] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2285,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2286)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2285,U_2286) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2285,U_2286)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2285,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2286) ) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
fof(f_732_3,plain,
( ! [U_2290,U_2288] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2288,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2290)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2288,U_2290) )
& ! [U_2289,U_2287] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2287,U_2289)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2287,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2289) ) ),
inference(miniscope,[status(thm)],[f_732_2]) ).
cnf(f_732_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2287,U_2289)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2287,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2289) ),
inference(clausify,[status(thm)],[f_732_3]) ).
cnf(f_732_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2288,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2290)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2288,U_2290) ),
inference(clausify,[status(thm)],[f_732_3]) ).
fof(f_733_1,plain,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) ),
inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).
fof(f_733_2,plain,
! [U_2292,U_2291] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2291,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2292)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2291,U_2292) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
cnf(f_733_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2291,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2292)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2291,U_2292) ),
inference(clausify,[status(thm)],[f_733_2]) ).
fof(f_734_1,plain,
! [V_r_H,V_q_H,V_z,V_r,V_q,V_y,V_x,T_a] :
( c_Polynomial_Opdivmod__rel(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z),V_q_H,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_r_H),V_r))
| ~ c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pdivmod__rel__mult]) ).
fof(f_734_2,plain,
! [U_2300,U_2299,U_2298,U_2297,U_2296,U_2295,U_2294,U_2293] :
( c_Polynomial_Opdivmod__rel(U_2293,U_2294,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2293)),U_2295),U_2298),U_2299,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2293)),U_2295),U_2300),U_2297))
| ~ c_Polynomial_Opdivmod__rel(U_2293,U_2296,U_2298,U_2299,U_2300)
| ~ c_Polynomial_Opdivmod__rel(U_2293,U_2294,U_2295,U_2296,U_2297)
| ~ class_Fields_Ofield(U_2293) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
cnf(f_734_3,plain,
( c_Polynomial_Opdivmod__rel(U_2293,U_2294,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2293)),U_2295),U_2298),U_2299,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2293)),U_2295),U_2300),U_2297))
| ~ c_Polynomial_Opdivmod__rel(U_2293,U_2296,U_2298,U_2299,U_2300)
| ~ c_Polynomial_Opdivmod__rel(U_2293,U_2294,U_2295,U_2296,U_2297)
| ~ class_Fields_Ofield(U_2293) ),
inference(clausify,[status(thm)],[f_734_2]) ).
fof(f_735_1,plain,
! [V_q,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__mult__le]) ).
fof(f_735_2,plain,
! [U_2303,U_2302,U_2301] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2301,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2301)),U_2302),U_2303)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(U_2301,U_2302),c_Polynomial_Odegree(U_2301,U_2303)))
| ~ class_Rings_Ocomm__semiring__0(U_2301) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
cnf(f_735_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2301,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2301)),U_2302),U_2303)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(U_2301,U_2302),c_Polynomial_Odegree(U_2301,U_2303)))
| ~ class_Rings_Ocomm__semiring__0(U_2301) ),
inference(clausify,[status(thm)],[f_735_2]) ).
fof(f_736_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Odegree(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))
| V_q = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__mult__eq]) ).
fof(f_736_2,plain,
! [U_2306,U_2305,U_2304] :
( c_Polynomial_Odegree(U_2304,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2304)),U_2305),U_2306)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(U_2304,U_2305),c_Polynomial_Odegree(U_2304,U_2306))
| U_2306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2304))
| U_2305 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2304))
| ~ class_Rings_Oidom(U_2304) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
cnf(f_736_3,plain,
( c_Polynomial_Odegree(U_2304,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2304)),U_2305),U_2306)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(U_2304,U_2305),c_Polynomial_Odegree(U_2304,U_2306))
| U_2306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2304))
| U_2305 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2304))
| ~ class_Rings_Oidom(U_2304) ),
inference(clausify,[status(thm)],[f_736_2]) ).
fof(f_737_1,plain,
! [V_n,V_b,V_m,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__monom]) ).
fof(f_737_2,plain,
! [U_2311,U_2310,U_2309,U_2308,U_2307] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2307)),c_Polynomial_Omonom(U_2307,U_2308,U_2309)),c_Polynomial_Omonom(U_2307,U_2310,U_2311)) = c_Polynomial_Omonom(U_2307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2307),U_2308),U_2310),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2309,U_2311))
| ~ class_Rings_Ocomm__semiring__0(U_2307) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
cnf(f_737_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2307)),c_Polynomial_Omonom(U_2307,U_2308,U_2309)),c_Polynomial_Omonom(U_2307,U_2310,U_2311)) = c_Polynomial_Omonom(U_2307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2307),U_2308),U_2310),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2309,U_2311))
| ~ class_Rings_Ocomm__semiring__0(U_2307) ),
inference(clausify,[status(thm)],[f_737_2]) ).
fof(f_738_1,plain,
! [V_z] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__0__less]) ).
fof(f_738_2,plain,
! [U_2312] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2312))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2312) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
cnf(f_738_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2312))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2312) ),
inference(clausify,[status(thm)],[f_738_2]) ).
fof(f_739_1,plain,
! [V_q,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__mult__degree__sum]) ).
fof(f_739_2,plain,
! [U_2315,U_2314,U_2313] :
( hAPP(c_Polynomial_Ocoeff(U_2313,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2313)),U_2314),U_2315)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(U_2313,U_2314),c_Polynomial_Odegree(U_2313,U_2315))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2313),hAPP(c_Polynomial_Ocoeff(U_2313,U_2314),c_Polynomial_Odegree(U_2313,U_2314))),hAPP(c_Polynomial_Ocoeff(U_2313,U_2315),c_Polynomial_Odegree(U_2313,U_2315)))
| ~ class_Rings_Ocomm__semiring__0(U_2313) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
cnf(f_739_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_2313,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2313)),U_2314),U_2315)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(U_2313,U_2314),c_Polynomial_Odegree(U_2313,U_2315))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2313),hAPP(c_Polynomial_Ocoeff(U_2313,U_2314),c_Polynomial_Odegree(U_2313,U_2314))),hAPP(c_Polynomial_Ocoeff(U_2313,U_2315),c_Polynomial_Odegree(U_2313,U_2315)))
| ~ class_Rings_Ocomm__semiring__0(U_2313) ),
inference(clausify,[status(thm)],[f_739_2]) ).
fof(f_740_1,plain,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
| V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1]) ).
fof(f_740_2,plain,
! [U_2318,U_2317,U_2316] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2318)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2317,U_2316)
| U_2316 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2317,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2318))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2316) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
cnf(f_740_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2318)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2317,U_2316)
| U_2316 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2317,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2318))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2316) ),
inference(clausify,[status(thm)],[f_740_2]) ).
fof(f_741_1,plain,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
| V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2]) ).
fof(f_741_2,plain,
! [U_2321,U_2320,U_2319] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2321,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2320)
| U_2319 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2320,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2319),U_2321))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2319) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
cnf(f_741_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2321,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2320)
| U_2319 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2320,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2319),U_2321))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2319) ),
inference(clausify,[status(thm)],[f_741_2]) ).
fof(f_742_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma]) ).
fof(f_742_2,plain,
! [U_2327,U_2326,U_2325,U_2324,U_2323,U_2322] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2326,U_2323)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2325,U_2322)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2325)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2327)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2324,U_2322)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2325),U_2326),U_2327),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2322),U_2323),U_2324) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2325),U_2326),U_2327) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
cnf(f_742_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2326,U_2323)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2325,U_2322)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2325)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2327)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2324,U_2322)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2325),U_2326),U_2327),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2322),U_2323),U_2324) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2325),U_2326),U_2327) ),
inference(clausify,[status(thm)],[f_742_2]) ).
fof(f_743_1,plain,
! [V_nb_2,V_k_2,V_m_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2)
| V_m_2 != V_nb_2 )
& ( V_m_2 = V_nb_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_nb_2,V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).
fof(f_743_2,plain,
! [U_2330,U_2329,U_2328] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2328,U_2329) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2330,U_2329)
| U_2328 != U_2330 )
& ( U_2328 = U_2330
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2328,U_2329) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2330,U_2329) ) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
fof(f_743_3,plain,
( ! [U_2336,U_2334,U_2332] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2332,U_2334) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2336,U_2334)
| U_2332 != U_2336 )
& ! [U_2335,U_2333,U_2331] :
( U_2331 = U_2335
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2331,U_2333) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2335,U_2333) ) ),
inference(miniscope,[status(thm)],[f_743_2]) ).
cnf(f_743_4,plain,
( U_2331 = U_2335
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2331,U_2333) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2335,U_2333) ),
inference(clausify,[status(thm)],[f_743_3]) ).
cnf(f_743_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2332,U_2334) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2336,U_2334)
| U_2332 != U_2336 ),
inference(clausify,[status(thm)],[f_743_3]) ).
fof(f_744_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2)
| V_m_2 != V_nb_2 )
& ( V_m_2 = V_nb_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_nb_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).
fof(f_744_2,plain,
! [U_2339,U_2338,U_2337] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2337,U_2338) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2337,U_2339)
| U_2338 != U_2339 )
& ( U_2338 = U_2339
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2337,U_2338) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2337,U_2339) ) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
fof(f_744_3,plain,
( ! [U_2345,U_2343] :
( ! [U_2341] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2341,U_2343) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2341,U_2345)
| U_2343 != U_2345 )
& ! [U_2344,U_2342] :
( ! [U_2340] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2340,U_2342) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2340,U_2344)
| U_2342 = U_2344 ) ),
inference(miniscope,[status(thm)],[f_744_2]) ).
cnf(f_744_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2340,U_2342) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2340,U_2344)
| U_2342 = U_2344 ),
inference(clausify,[status(thm)],[f_744_3]) ).
cnf(f_744_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2341,U_2343) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2341,U_2345)
| U_2343 != U_2345 ),
inference(clausify,[status(thm)],[f_744_3]) ).
fof(f_745_1,plain,
! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).
fof(f_745_2,plain,
! [U_2348,U_2347,U_2346] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2346,U_2347),U_2348) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2346,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2347,U_2348)),
inference(variable_rename,[status(thm)],[f_745_1]) ).
cnf(f_745_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2346,U_2347),U_2348) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2346,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2347,U_2348)),
inference(clausify,[status(thm)],[f_745_2]) ).
fof(f_746_1,plain,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).
fof(f_746_2,plain,
! [U_2351,U_2350,U_2349] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2349,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2350,U_2351)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2350,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2349,U_2351)),
inference(variable_rename,[status(thm)],[f_746_1]) ).
cnf(f_746_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2349,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2350,U_2351)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2350,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2349,U_2351)),
inference(clausify,[status(thm)],[f_746_2]) ).
fof(f_747_1,plain,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).
fof(f_747_2,plain,
! [U_2353,U_2352] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2352,U_2353) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2353,U_2352),
inference(variable_rename,[status(thm)],[f_747_1]) ).
cnf(f_747_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2352,U_2353) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2353,U_2352),
inference(clausify,[status(thm)],[f_747_2]) ).
fof(f_748_1,plain,
! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).
fof(f_748_2,plain,
! [U_2356,U_2355,U_2354] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2354,U_2355),U_2356) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2354,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2355,U_2356)),
inference(variable_rename,[status(thm)],[f_748_1]) ).
cnf(f_748_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2354,U_2355),U_2356) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2354,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2355,U_2356)),
inference(clausify,[status(thm)],[f_748_2]) ).
fof(f_749_1,plain,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).
fof(f_749_2,plain,
! [U_2359,U_2358,U_2357] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2357,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2358,U_2359)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2358,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2357,U_2359)),
inference(variable_rename,[status(thm)],[f_749_1]) ).
cnf(f_749_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2357,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2358,U_2359)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2358,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2357,U_2359)),
inference(clausify,[status(thm)],[f_749_2]) ).
fof(f_750_1,plain,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).
fof(f_750_2,plain,
! [U_2361,U_2360] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2360,U_2361) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2361,U_2360),
inference(variable_rename,[status(thm)],[f_750_1]) ).
cnf(f_750_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2360,U_2361) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2361,U_2360),
inference(clausify,[status(thm)],[f_750_2]) ).
fof(f_751_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)) ),
inference(fof_nnf,[status(thm)],[fact_q__pos__lemma]) ).
fof(f_751_2,plain,
! [U_2364,U_2363,U_2362] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2363)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2362)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2364,U_2362)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2362),U_2363),U_2364)) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
cnf(f_751_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2363)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2362)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2364,U_2362)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2362),U_2363),U_2364)) ),
inference(clausify,[status(thm)],[f_751_2]) ).
fof(f_752_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_q__neg__lemma]) ).
fof(f_752_2,plain,
! [U_2367,U_2366,U_2365] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2366,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2365)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2367)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2365),U_2366),U_2367),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
cnf(f_752_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2366,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2365)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2367)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2365),U_2366),U_2367),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_752_2]) ).
fof(f_753_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma]) ).
fof(f_753_2,plain,
! [U_2372,U_2371,U_2370,U_2369,U_2368] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2369,U_2371)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2372,U_2368)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2370,U_2368)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2370)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2368),U_2369),U_2370),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2368),U_2371),U_2372)) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
cnf(f_753_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2369,U_2371)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2372,U_2368)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2370,U_2368)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2370)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2368),U_2369),U_2370),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2368),U_2371),U_2372)) ),
inference(clausify,[status(thm)],[f_753_2]) ).
fof(f_754_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma]) ).
fof(f_754_2,plain,
! [U_2378,U_2377,U_2376,U_2375,U_2374,U_2373] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2374,U_2377)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2376,U_2373)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2376)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2375)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2378,U_2376)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2376),U_2377),U_2378))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2373),U_2374),U_2375) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2376),U_2377),U_2378) ),
inference(variable_rename,[status(thm)],[f_754_1]) ).
cnf(f_754_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2374,U_2377)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2376,U_2373)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2376)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2375)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2378,U_2376)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2376),U_2377),U_2378))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2373),U_2374),U_2375) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2376),U_2377),U_2378) ),
inference(clausify,[status(thm)],[f_754_2]) ).
fof(f_755_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg]) ).
fof(f_755_2,plain,
! [U_2383,U_2382,U_2381,U_2380,U_2379] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2382,U_2380)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2379,U_2381)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2379,U_2383)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2383,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2379),U_2380),U_2381),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2379),U_2382),U_2383)) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
cnf(f_755_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2382,U_2380)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2379,U_2381)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2379,U_2383)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2383,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2379),U_2380),U_2381),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2379),U_2382),U_2383)) ),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_1,plain,
! [V_y,V_x,V_d,T_a] :
( c_Polynomial_Opoly__gcd(T_a,V_x,V_y) = V_d
| ( hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) != c_Groups_Oone__class_Oone(T_a)
& ( V_y != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ( hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d)) != c_Groups_Ozero__class_Ozero(T_a)
& V_y = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| ? [B_k] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_d))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_y))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),B_k),V_x)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a)),V_d),V_x))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__gcd__unique]) ).
fof(f_756_2,plain,
! [U_2388,U_2387,U_2386,U_2385] :
( c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ( hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
& ( U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385)) ) )
| ( hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
& U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
& U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385)) )
| ? [U_2384] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2384),U_2386))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2384),U_2388))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2384),U_2387)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
! [U_2388,U_2387,U_2386,U_2385] :
( c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ( hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
& ( U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385)) ) )
| ( hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
& U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
& U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2386))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2388))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2387)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_2384,sK13(U_2388,U_2387,U_2386,U_2385))],[f_756_2]) ).
cnf(f_756_4,plain,
( U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_5,plain,
( U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_6,plain,
( U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_7,plain,
( U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_8,plain,
( U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_9,plain,
( hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_10,plain,
( U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_11,plain,
( U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_12,plain,
( U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_13,plain,
( U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_14,plain,
( U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_15,plain,
( hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_16,plain,
( U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2386))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_17,plain,
( U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2386))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_18,plain,
( U_2387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2386))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_19,plain,
( U_2388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2386))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_20,plain,
( U_2388 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| U_2387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2385))
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2386))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_21,plain,
( hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Oone__class_Oone(U_2385)
| hAPP(c_Polynomial_Ocoeff(U_2385,U_2386),c_Polynomial_Odegree(U_2385,U_2386)) != c_Groups_Ozero__class_Ozero(U_2385)
| c_Polynomial_Opoly__gcd(U_2385,U_2387,U_2388) = U_2386
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),sK13(U_2388,U_2387,U_2386,U_2385)),U_2386))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2388))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2385)),U_2386),U_2387))
| ~ class_Fields_Ofield(U_2385) ),
inference(clausify,[status(thm)],[f_756_3]) ).
fof(f_757_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
| ! [B_n] : V_l_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) )
& ( ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__ex__iff]) ).
fof(f_757_2,plain,
! [U_2392,U_2391] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2391,U_2392)
| ! [U_2390] : U_2392 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2391,U_2390) )
& ( ? [U_2389] : U_2392 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2391,U_2389)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2391,U_2392) ) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
fof(f_757_3,plain,
( ! [U_2396,U_2394] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2394,U_2396)
| ! [U_2390] : U_2396 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2394,U_2390) )
& ! [U_2395,U_2393] :
( ? [U_2389] : U_2395 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2393,U_2389)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2393,U_2395) ) ),
inference(miniscope,[status(thm)],[f_757_2]) ).
fof(f_757_4,plain,
( ! [U_2396,U_2394] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2394,U_2396)
| ! [U_2390] : U_2396 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2394,U_2390) )
& ! [U_2395,U_2393] :
( U_2395 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2393,sK14(U_2395,U_2393))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2393,U_2395) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_2389,sK14(U_2395,U_2393))],[f_757_3]) ).
cnf(f_757_5,plain,
( U_2395 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2393,sK14(U_2395,U_2393))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2393,U_2395) ),
inference(clausify,[status(thm)],[f_757_4]) ).
cnf(f_757_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2394,U_2396)
| U_2396 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2394,U_2390) ),
inference(clausify,[status(thm)],[f_757_4]) ).
fof(f_758_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
| ~ hBOOL(hAPP(V_P_2,B_x)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2)))
& hBOOL(hAPP(V_P_2,B_x)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).
fof(f_758_2,plain,
! [U_2401,U_2400,U_2399] :
( ! [U_2398] :
( hBOOL(hAPP(U_2400,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2401),U_2399))))
| ~ hBOOL(hAPP(U_2400,U_2398)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2401)
| ? [U_2397] :
( ~ hBOOL(hAPP(U_2400,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2397,U_2399)))
& hBOOL(hAPP(U_2400,U_2397)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2399) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
fof(f_758_3,plain,
! [U_2401,U_2400,U_2399] :
( ! [U_2398] :
( hBOOL(hAPP(U_2400,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2401),U_2399))))
| ~ hBOOL(hAPP(U_2400,U_2398)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2401)
| ( ~ hBOOL(hAPP(U_2400,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK15(U_2401,U_2400,U_2399),U_2399)))
& hBOOL(hAPP(U_2400,sK15(U_2401,U_2400,U_2399))) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2399) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_2397,sK15(U_2401,U_2400,U_2399))],[f_758_2]) ).
cnf(f_758_4,plain,
( hBOOL(hAPP(U_2400,sK15(U_2401,U_2400,U_2399)))
| hBOOL(hAPP(U_2400,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2401),U_2399))))
| ~ hBOOL(hAPP(U_2400,U_2398))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2401)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2399) ),
inference(clausify,[status(thm)],[f_758_3]) ).
cnf(f_758_5,plain,
( ~ hBOOL(hAPP(U_2400,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK15(U_2401,U_2400,U_2399),U_2399)))
| hBOOL(hAPP(U_2400,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2398,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2401),U_2399))))
| ~ hBOOL(hAPP(U_2400,U_2398))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2401)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2399) ),
inference(clausify,[status(thm)],[f_758_3]) ).
fof(f_759_1,plain,
! [V_nb_2,V_P_2] :
( ? [B_k] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_nb_2) )
| ~ hBOOL(hAPP(V_P_2,V_nb_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_759_2,plain,
! [U_2405,U_2404] :
( ? [U_2403] :
( hBOOL(hAPP(U_2404,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2403,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_2402] :
( ~ hBOOL(hAPP(U_2404,U_2402))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2402,U_2403) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2403,U_2405) )
| ~ hBOOL(hAPP(U_2404,U_2405))
| hBOOL(hAPP(U_2404,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
fof(f_759_3,plain,
! [U_2405,U_2404] :
( ( hBOOL(hAPP(U_2404,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK16(U_2405,U_2404),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_2402] :
( ~ hBOOL(hAPP(U_2404,U_2402))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2402,sK16(U_2405,U_2404)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK16(U_2405,U_2404),U_2405) )
| ~ hBOOL(hAPP(U_2404,U_2405))
| hBOOL(hAPP(U_2404,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_2403,sK16(U_2405,U_2404))],[f_759_2]) ).
cnf(f_759_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK16(U_2405,U_2404),U_2405)
| ~ hBOOL(hAPP(U_2404,U_2405))
| hBOOL(hAPP(U_2404,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_759_3]) ).
cnf(f_759_5,plain,
( ~ hBOOL(hAPP(U_2404,U_2402))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2402,sK16(U_2405,U_2404))
| ~ hBOOL(hAPP(U_2404,U_2405))
| hBOOL(hAPP(U_2404,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_759_3]) ).
cnf(f_759_6,plain,
( hBOOL(hAPP(U_2404,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK16(U_2405,U_2404),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(U_2404,U_2405))
| hBOOL(hAPP(U_2404,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_759_3]) ).
fof(f_760_1,plain,
! [V_x,V_n,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult]) ).
fof(f_760_2,plain,
! [U_2408,U_2407,U_2406] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2408),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2407,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2408) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2408),U_2407)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2407)
| ~ class_Groups_Omonoid__mult(U_2406) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
cnf(f_760_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2408),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2407,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_2408) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2408),U_2407)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2407)
| ~ class_Groups_Omonoid__mult(U_2406) ),
inference(clausify,[status(thm)],[f_760_2]) ).
fof(f_761_1,plain,
! [V_y_2,V_x_2,V_f_2,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_f_2,V_x_2),hAPP(V_f_2,V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,T_a,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OmonoD]) ).
fof(f_761_2,plain,
! [U_2412,U_2411,U_2410,U_2409] :
( c_Orderings_Oord__class_Oless__eq(U_2409,hAPP(U_2410,U_2411),hAPP(U_2410,U_2412))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2411),U_2412))
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_2409,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2410)
| ~ class_Orderings_Oorder(U_2409) ),
inference(variable_rename,[status(thm)],[f_761_1]) ).
cnf(f_761_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2409,hAPP(U_2410,U_2411),hAPP(U_2410,U_2412))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2411),U_2412))
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_2409,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2410)
| ~ class_Orderings_Oorder(U_2409) ),
inference(clausify,[status(thm)],[f_761_2]) ).
fof(f_762_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).
fof(f_762_2,plain,
! [U_2415,U_2414,U_2413] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2415,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2414,U_2413)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2415,U_2413),U_2414)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413,U_2414) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
cnf(f_762_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2415,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2414,U_2413)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2415,U_2413),U_2414)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413,U_2414) ),
inference(clausify,[status(thm)],[f_762_2]) ).
fof(f_763_1,plain,
! [V_i_2,V_k_2,V_j_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__conv]) ).
fof(f_763_2,plain,
! [U_2418,U_2417,U_2416] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2416,U_2417),U_2418)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2416,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2418,U_2417)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2416,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2418,U_2417))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2416,U_2417),U_2418) ) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
fof(f_763_3,plain,
( ! [U_2424,U_2422,U_2420] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2420,U_2422),U_2424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2420,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2424,U_2422)) )
& ! [U_2423,U_2421,U_2419] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2419,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2423,U_2421))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2419,U_2421),U_2423) ) ),
inference(miniscope,[status(thm)],[f_763_2]) ).
cnf(f_763_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2419,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2423,U_2421))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2419,U_2421),U_2423) ),
inference(clausify,[status(thm)],[f_763_3]) ).
cnf(f_763_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2420,U_2422),U_2424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2420,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2424,U_2422)) ),
inference(clausify,[status(thm)],[f_763_3]) ).
fof(f_764_1,plain,
! [V_m,V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).
fof(f_764_2,plain,
! [U_2427,U_2426,U_2425] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2427,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2426,U_2427),U_2425))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2425,U_2426) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
cnf(f_764_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2427,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2426,U_2427),U_2425))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2425,U_2426) ),
inference(clausify,[status(thm)],[f_764_2]) ).
fof(f_765_1,plain,
! [V_m,V_n] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse]) ).
fof(f_765_2,plain,
! [U_2429,U_2428] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2428,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2429,U_2428)) = U_2429
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2428,U_2429) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
cnf(f_765_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2428,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2429,U_2428)) = U_2429
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2428,U_2429) ),
inference(clausify,[status(thm)],[f_765_2]) ).
fof(f_766_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).
fof(f_766_2,plain,
! [U_2432,U_2431,U_2430] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2432,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2431,U_2430)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2432,U_2431),U_2430)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2430,U_2431) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
cnf(f_766_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2432,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2431,U_2430)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2432,U_2431),U_2430)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2430,U_2431) ),
inference(clausify,[status(thm)],[f_766_2]) ).
fof(f_767_1,plain,
! [V_i_2,V_j_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__conv2]) ).
fof(f_767_2,plain,
! [U_2435,U_2434,U_2433] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2435,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2434,U_2433))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2435,U_2433),U_2434) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2435,U_2433),U_2434)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2435,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2434,U_2433)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2433,U_2434) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
cnf(f_767_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2435,U_2433),U_2434)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2435,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2434,U_2433))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2433,U_2434) ),
inference(clausify,[status(thm)],[f_767_2]) ).
cnf(f_767_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2435,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2434,U_2433))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2435,U_2433),U_2434)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2433,U_2434) ),
inference(clausify,[status(thm)],[f_767_2]) ).
fof(f_768_1,plain,
! [V_m,V_n] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2]) ).
fof(f_768_2,plain,
! [U_2437,U_2436] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2437,U_2436),U_2436) = U_2437
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2436,U_2437) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
cnf(f_768_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2437,U_2436),U_2436) = U_2437
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2436,U_2437) ),
inference(clausify,[status(thm)],[f_768_2]) ).
fof(f_769_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
| V_j_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) )
& ( V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) != V_k_2 ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add]) ).
fof(f_769_2,plain,
! [U_2440,U_2439,U_2438] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2439,U_2438) = U_2440
| U_2439 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2440,U_2438) )
& ( U_2439 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2440,U_2438)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2439,U_2438) != U_2440 ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2439) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
cnf(f_769_3,plain,
( U_2439 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2440,U_2438)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2439,U_2438) != U_2440
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2439) ),
inference(clausify,[status(thm)],[f_769_2]) ).
cnf(f_769_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2439,U_2438) = U_2440
| U_2439 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2440,U_2438)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2438,U_2439) ),
inference(clausify,[status(thm)],[f_769_2]) ).
fof(f_770_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).
fof(f_770_2,plain,
! [U_2443,U_2442,U_2441] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2443,U_2442),U_2441) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2443,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2442,U_2441))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2441,U_2442) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
cnf(f_770_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2443,U_2442),U_2441) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2443,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2442,U_2441))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2441,U_2442) ),
inference(clausify,[status(thm)],[f_770_2]) ).
fof(f_771_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).
fof(f_771_2,plain,
! [U_2446,U_2445,U_2444] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2445,U_2444),U_2446) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2445,U_2446),U_2444)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2444,U_2445) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
cnf(f_771_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2445,U_2444),U_2446) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2445,U_2446),U_2444)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2444,U_2445) ),
inference(clausify,[status(thm)],[f_771_2]) ).
fof(f_772_1,plain,
! [V_i,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).
fof(f_772_2,plain,
! [U_2449,U_2448,U_2447] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2448,U_2449),U_2447) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2448,U_2447),U_2449)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2447,U_2448) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
cnf(f_772_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2448,U_2449),U_2447) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2448,U_2447),U_2449)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2447,U_2448) ),
inference(clausify,[status(thm)],[f_772_2]) ).
fof(f_773_1,plain,
! [V_n,V_m] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).
fof(f_773_2,plain,
! [U_2451,U_2450] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2451,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2450,U_2451)) = U_2450
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2450,U_2451) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
cnf(f_773_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2451,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2450,U_2451)) = U_2450
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2450,U_2451) ),
inference(clausify,[status(thm)],[f_773_2]) ).
fof(f_774_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__conv]) ).
fof(f_774_2,plain,
! [U_2454,U_2453,U_2452] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2452,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2453,U_2454))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2452,U_2454),U_2453) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2452,U_2454),U_2453)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2452,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2453,U_2454)) ) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
fof(f_774_3,plain,
( ! [U_2460,U_2458,U_2456] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2456,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2458,U_2460))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2456,U_2460),U_2458) )
& ! [U_2459,U_2457,U_2455] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2455,U_2459),U_2457)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2455,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2457,U_2459)) ) ),
inference(miniscope,[status(thm)],[f_774_2]) ).
cnf(f_774_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2455,U_2459),U_2457)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2455,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2457,U_2459)) ),
inference(clausify,[status(thm)],[f_774_3]) ).
cnf(f_774_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2456,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2458,U_2460))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2456,U_2460),U_2458) ),
inference(clausify,[status(thm)],[f_774_3]) ).
fof(f_775_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_diff__add__0]) ).
fof(f_775_2,plain,
! [U_2462,U_2461] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2461,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2461,U_2462)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_775_1]) ).
cnf(f_775_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2461,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2461,U_2462)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_775_2]) ).
fof(f_776_1,plain,
! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).
fof(f_776_2,plain,
! [U_2465,U_2464,U_2463] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2463,U_2464),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2465,U_2464)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2463,U_2465),
inference(variable_rename,[status(thm)],[f_776_1]) ).
cnf(f_776_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2463,U_2464),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2465,U_2464)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2463,U_2465),
inference(clausify,[status(thm)],[f_776_2]) ).
fof(f_777_1,plain,
! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).
fof(f_777_2,plain,
! [U_2468,U_2467,U_2466] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2466,U_2467),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2466,U_2468)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2467,U_2468),
inference(variable_rename,[status(thm)],[f_777_1]) ).
cnf(f_777_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2466,U_2467),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2466,U_2468)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2467,U_2468),
inference(clausify,[status(thm)],[f_777_2]) ).
fof(f_778_1,plain,
! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).
fof(f_778_2,plain,
! [U_2471,U_2470,U_2469] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2469,U_2470),U_2471) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2469,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2470,U_2471)),
inference(variable_rename,[status(thm)],[f_778_1]) ).
cnf(f_778_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2469,U_2470),U_2471) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2469,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2470,U_2471)),
inference(clausify,[status(thm)],[f_778_2]) ).
fof(f_779_1,plain,
! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse]) ).
fof(f_779_2,plain,
! [U_2473,U_2472] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2472,U_2473),U_2472) = U_2473,
inference(variable_rename,[status(thm)],[f_779_1]) ).
cnf(f_779_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2472,U_2473),U_2472) = U_2473,
inference(clausify,[status(thm)],[f_779_2]) ).
fof(f_780_1,plain,
! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m,
inference(fof_nnf,[status(thm)],[fact_diff__add__inverse2]) ).
fof(f_780_2,plain,
! [U_2475,U_2474] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2474,U_2475),U_2475) = U_2474,
inference(variable_rename,[status(thm)],[f_780_1]) ).
cnf(f_780_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2474,U_2475),U_2475) = U_2474,
inference(clausify,[status(thm)],[f_780_2]) ).
fof(f_781_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__cancel]) ).
fof(f_781_2,plain,
! [U_2478,U_2477,U_2476] :
( c_Groups_Ominus__class_Ominus(U_2476,c_Groups_Oplus__class_Oplus(U_2476,U_2477,U_2478),U_2478) = U_2477
| ~ class_Groups_Ogroup__add(U_2476) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
cnf(f_781_3,plain,
( c_Groups_Ominus__class_Ominus(U_2476,c_Groups_Oplus__class_Oplus(U_2476,U_2477,U_2478),U_2478) = U_2477
| ~ class_Groups_Ogroup__add(U_2476) ),
inference(clausify,[status(thm)],[f_781_2]) ).
fof(f_782_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__add__cancel]) ).
fof(f_782_2,plain,
! [U_2481,U_2480,U_2479] :
( c_Groups_Oplus__class_Oplus(U_2479,c_Groups_Ominus__class_Ominus(U_2479,U_2480,U_2481),U_2481) = U_2480
| ~ class_Groups_Ogroup__add(U_2479) ),
inference(variable_rename,[status(thm)],[f_782_1]) ).
cnf(f_782_3,plain,
( c_Groups_Oplus__class_Oplus(U_2479,c_Groups_Ominus__class_Ominus(U_2479,U_2480,U_2481),U_2481) = U_2480
| ~ class_Groups_Ogroup__add(U_2479) ),
inference(clausify,[status(thm)],[f_782_2]) ).
fof(f_783_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__diff__mult]) ).
fof(f_783_2,plain,
! [U_2486,U_2485,U_2484,U_2483,U_2482] :
( c_Groups_Ominus__class_Ominus(U_2482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2483),U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2486)) = c_Groups_Oplus__class_Oplus(U_2482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2483),c_Groups_Ominus__class_Ominus(U_2482,U_2484,U_2486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),c_Groups_Ominus__class_Ominus(U_2482,U_2483,U_2485)),U_2486))
| ~ class_Rings_Oring(U_2482) ),
inference(variable_rename,[status(thm)],[f_783_1]) ).
cnf(f_783_3,plain,
( c_Groups_Ominus__class_Ominus(U_2482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2483),U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2485),U_2486)) = c_Groups_Oplus__class_Oplus(U_2482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),U_2483),c_Groups_Ominus__class_Ominus(U_2482,U_2484,U_2486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2482),c_Groups_Ominus__class_Ominus(U_2482,U_2483,U_2485)),U_2486))
| ~ class_Rings_Oring(U_2482) ),
inference(clausify,[status(thm)],[f_783_2]) ).
fof(f_784_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
| V_c_2 != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2) )
& ( V_c_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2) ) )
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).
fof(f_784_2,plain,
! [U_2492,U_2491,U_2490,U_2489,U_2488,U_2487] :
( ( ( c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2489),U_2490) = c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2491),U_2489),U_2492)
| U_2490 != c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),c_Groups_Ominus__class_Ominus(U_2487,U_2491,U_2488)),U_2489),U_2492) )
& ( U_2490 = c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),c_Groups_Ominus__class_Ominus(U_2487,U_2491,U_2488)),U_2489),U_2492)
| c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2489),U_2490) != c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2491),U_2489),U_2492) ) )
| ~ class_Rings_Oring(U_2487) ),
inference(variable_rename,[status(thm)],[f_784_1]) ).
cnf(f_784_3,plain,
( U_2490 = c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),c_Groups_Ominus__class_Ominus(U_2487,U_2491,U_2488)),U_2489),U_2492)
| c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2489),U_2490) != c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2491),U_2489),U_2492)
| ~ class_Rings_Oring(U_2487) ),
inference(clausify,[status(thm)],[f_784_2]) ).
cnf(f_784_4,plain,
( c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2489),U_2490) = c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2491),U_2489),U_2492)
| U_2490 != c_Groups_Oplus__class_Oplus(U_2487,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),c_Groups_Ominus__class_Ominus(U_2487,U_2491,U_2488)),U_2489),U_2492)
| ~ class_Rings_Oring(U_2487) ),
inference(clausify,[status(thm)],[f_784_2]) ).
fof(f_785_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2) != V_d_2 )
& ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2) = V_d_2
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2) ) )
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).
fof(f_785_2,plain,
! [U_2498,U_2497,U_2496,U_2495,U_2494,U_2493] :
( ( ( c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495),U_2496) = c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2497),U_2495),U_2498)
| c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),c_Groups_Ominus__class_Ominus(U_2493,U_2494,U_2497)),U_2495),U_2496) != U_2498 )
& ( c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),c_Groups_Ominus__class_Ominus(U_2493,U_2494,U_2497)),U_2495),U_2496) = U_2498
| c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495),U_2496) != c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2497),U_2495),U_2498) ) )
| ~ class_Rings_Oring(U_2493) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
cnf(f_785_3,plain,
( c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),c_Groups_Ominus__class_Ominus(U_2493,U_2494,U_2497)),U_2495),U_2496) = U_2498
| c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495),U_2496) != c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2497),U_2495),U_2498)
| ~ class_Rings_Oring(U_2493) ),
inference(clausify,[status(thm)],[f_785_2]) ).
cnf(f_785_4,plain,
( c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2494),U_2495),U_2496) = c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),U_2497),U_2495),U_2498)
| c_Groups_Oplus__class_Oplus(U_2493,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2493),c_Groups_Ominus__class_Ominus(U_2493,U_2494,U_2497)),U_2495),U_2496) != U_2498
| ~ class_Rings_Oring(U_2493) ),
inference(clausify,[status(thm)],[f_785_2]) ).
fof(f_786_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod]) ).
fof(f_786_2,plain,
! [U_2503,U_2502,U_2501,U_2500,U_2499] :
( c_Groups_Ominus__class_Ominus(U_2499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),U_2501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2502),U_2503)) = c_Groups_Oplus__class_Oplus(U_2499,c_Groups_Oplus__class_Oplus(U_2499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),c_Groups_Ominus__class_Ominus(U_2499,U_2500,U_2502)),c_Groups_Ominus__class_Ominus(U_2499,U_2501,U_2503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),c_Groups_Ominus__class_Ominus(U_2499,U_2500,U_2502)),U_2503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2502),c_Groups_Ominus__class_Ominus(U_2499,U_2501,U_2503)))
| ~ class_RealVector_Oreal__normed__algebra(U_2499) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
cnf(f_786_3,plain,
( c_Groups_Ominus__class_Ominus(U_2499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),U_2501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2502),U_2503)) = c_Groups_Oplus__class_Oplus(U_2499,c_Groups_Oplus__class_Oplus(U_2499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),c_Groups_Ominus__class_Ominus(U_2499,U_2500,U_2502)),c_Groups_Ominus__class_Ominus(U_2499,U_2501,U_2503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),c_Groups_Ominus__class_Ominus(U_2499,U_2500,U_2502)),U_2503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2502),c_Groups_Ominus__class_Ominus(U_2499,U_2501,U_2503)))
| ~ class_RealVector_Oreal__normed__algebra(U_2499) ),
inference(clausify,[status(thm)],[f_786_2]) ).
fof(f_787_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J]) ).
fof(f_787_2,plain,
! [U_2506,U_2505,U_2504] :
( c_Groups_Ominus__class_Ominus(U_2504,U_2505,U_2506) = c_Groups_Oplus__class_Oplus(U_2504,U_2505,c_Groups_Ouminus__class_Ouminus(U_2504,U_2506))
| ~ class_Rings_Ocomm__ring__1(U_2504) ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
cnf(f_787_3,plain,
( c_Groups_Ominus__class_Ominus(U_2504,U_2505,U_2506) = c_Groups_Oplus__class_Oplus(U_2504,U_2505,c_Groups_Ouminus__class_Ouminus(U_2504,U_2506))
| ~ class_Rings_Ocomm__ring__1(U_2504) ),
inference(clausify,[status(thm)],[f_787_2]) ).
fof(f_788_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add]) ).
fof(f_788_2,plain,
! [U_2509,U_2508,U_2507] :
( c_Groups_Ominus__class_Ominus(U_2507,U_2508,c_Groups_Ouminus__class_Ouminus(U_2507,U_2509)) = c_Groups_Oplus__class_Oplus(U_2507,U_2508,U_2509)
| ~ class_Groups_Ogroup__add(U_2507) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
cnf(f_788_3,plain,
( c_Groups_Ominus__class_Ominus(U_2507,U_2508,c_Groups_Ouminus__class_Ouminus(U_2507,U_2509)) = c_Groups_Oplus__class_Oplus(U_2507,U_2508,U_2509)
| ~ class_Groups_Ogroup__add(U_2507) ),
inference(clausify,[status(thm)],[f_788_2]) ).
fof(f_789_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__diff__minus]) ).
fof(f_789_2,plain,
! [U_2512,U_2511,U_2510] :
( c_Groups_Ominus__class_Ominus(U_2510,U_2511,U_2512) = c_Groups_Oplus__class_Oplus(U_2510,U_2511,c_Groups_Ouminus__class_Ouminus(U_2510,U_2512))
| ~ class_Groups_Oab__group__add(U_2510) ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
cnf(f_789_3,plain,
( c_Groups_Ominus__class_Ominus(U_2510,U_2511,U_2512) = c_Groups_Oplus__class_Oplus(U_2510,U_2511,c_Groups_Ouminus__class_Ouminus(U_2510,U_2512))
| ~ class_Groups_Oab__group__add(U_2510) ),
inference(clausify,[status(thm)],[f_789_2]) ).
fof(f_790_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__def]) ).
fof(f_790_2,plain,
! [U_2515,U_2514,U_2513] :
( c_Groups_Ominus__class_Ominus(U_2513,U_2514,U_2515) = c_Groups_Oplus__class_Oplus(U_2513,U_2514,c_Groups_Ouminus__class_Ouminus(U_2513,U_2515))
| ~ class_Groups_Ogroup__add(U_2513) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
cnf(f_790_3,plain,
( c_Groups_Ominus__class_Ominus(U_2513,U_2514,U_2515) = c_Groups_Oplus__class_Oplus(U_2513,U_2514,c_Groups_Ouminus__class_Ouminus(U_2513,U_2515))
| ~ class_Groups_Ogroup__add(U_2513) ),
inference(clausify,[status(thm)],[f_790_2]) ).
fof(f_791_1,plain,
! [V_m_2,V_nb_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_m_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).
fof(f_791_2,plain,
! [U_2517,U_2516] :
( ( 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_2516,U_2517))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2517,U_2516) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2517,U_2516)
| ~ 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_2516,U_2517)) ) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
fof(f_791_3,plain,
( ! [U_2521,U_2519] :
( 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_2519,U_2521))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2521,U_2519) )
& ! [U_2520,U_2518] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2520,U_2518)
| ~ 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_2518,U_2520)) ) ),
inference(miniscope,[status(thm)],[f_791_2]) ).
cnf(f_791_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2520,U_2518)
| ~ 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_2518,U_2520)) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2519,U_2521))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2521,U_2519) ),
inference(clausify,[status(thm)],[f_791_3]) ).
fof(f_792_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__less]) ).
fof(f_792_2,plain,
! [U_2523,U_2522] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2523,U_2522),U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2522) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
cnf(f_792_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2523,U_2522),U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2522) ),
inference(clausify,[status(thm)],[f_792_2]) ).
fof(f_793_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).
fof(f_793_2,plain,
! [U_2525,U_2524] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2524,U_2525),c_Nat_OSuc(U_2524)),
inference(variable_rename,[status(thm)],[f_793_1]) ).
cnf(f_793_3,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2524,U_2525),c_Nat_OSuc(U_2524)),
inference(clausify,[status(thm)],[f_793_2]) ).
fof(f_794_1,plain,
! [V_nb_2,V_m_2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_nb_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_nb_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).
fof(f_794_2,plain,
! [U_2527,U_2526] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2526,U_2527) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2526,U_2527) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2526,U_2527)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2526,U_2527) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
fof(f_794_3,plain,
( ! [U_2531,U_2529] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2529,U_2531) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2529,U_2531) )
& ! [U_2530,U_2528] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2528,U_2530)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2528,U_2530) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_794_2]) ).
cnf(f_794_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2528,U_2530)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2528,U_2530) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_794_3]) ).
cnf(f_794_5,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2529,U_2531) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2529,U_2531) ),
inference(clausify,[status(thm)],[f_794_3]) ).
fof(f_795_1,plain,
! [V_n,V_m] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H]) ).
fof(f_795_2,plain,
! [U_2533,U_2532] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2532,U_2533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2532,U_2533) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
cnf(f_795_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2532,U_2533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2532,U_2533) ),
inference(clausify,[status(thm)],[f_795_2]) ).
fof(f_796_1,plain,
! [V_m,V_n] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).
fof(f_796_2,plain,
! [U_2535,U_2534] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2535),U_2534) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2535,U_2534))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2534,U_2535) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
cnf(f_796_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2535),U_2534) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2535,U_2534))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2534,U_2535) ),
inference(clausify,[status(thm)],[f_796_2]) ).
fof(f_797_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( ( 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_nb_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ 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_nb_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
| ~ 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_797_2,plain,
! [U_2538,U_2537,U_2536] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2537,U_2536),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2538,U_2536))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2537,U_2538) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2537,U_2538)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2537,U_2536),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2538,U_2536)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2536,U_2538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2536,U_2537) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
cnf(f_797_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2537,U_2538)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2537,U_2536),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2538,U_2536))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2536,U_2538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2536,U_2537) ),
inference(clausify,[status(thm)],[f_797_2]) ).
cnf(f_797_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2537,U_2536),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2538,U_2536))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2537,U_2538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2536,U_2538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2536,U_2537) ),
inference(clausify,[status(thm)],[f_797_2]) ).
fof(f_798_1,plain,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).
fof(f_798_2,plain,
! [U_2541,U_2540,U_2539] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2539,U_2541),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2540,U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2541,U_2539)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2539,U_2540) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
cnf(f_798_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2539,U_2541),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2540,U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2541,U_2539)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2539,U_2540) ),
inference(clausify,[status(thm)],[f_798_2]) ).
fof(f_799_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diffD1]) ).
fof(f_799_2,plain,
! [U_2544,U_2543,U_2542] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2542),U_2544))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2544,U_2543)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2542),U_2543))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2543,U_2544))) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
cnf(f_799_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2542),U_2544))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2544,U_2543)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2542),U_2543))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2543,U_2544))) ),
inference(clausify,[status(thm)],[f_799_2]) ).
fof(f_800_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diffD]) ).
fof(f_800_2,plain,
! [U_2547,U_2546,U_2545] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2545),U_2546))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2547,U_2546)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2545),U_2547))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2545),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2546,U_2547))) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
cnf(f_800_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2545),U_2546))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2547,U_2546)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2545),U_2547))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2545),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2546,U_2547))) ),
inference(clausify,[status(thm)],[f_800_2]) ).
fof(f_801_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_801_2,plain,
! [U_2548] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2548),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2548,
inference(variable_rename,[status(thm)],[f_801_1]) ).
cnf(f_801_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2548),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2548,
inference(clausify,[status(thm)],[f_801_2]) ).
fof(f_802_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_802_2,plain,
! [U_2550,U_2549] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,c_Nat_OSuc(U_2550)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2550),
inference(variable_rename,[status(thm)],[f_802_1]) ).
cnf(f_802_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,c_Nat_OSuc(U_2550)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2549,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2550),
inference(clausify,[status(thm)],[f_802_2]) ).
fof(f_803_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__diff__eq]) ).
fof(f_803_2,plain,
! [U_2553,U_2552,U_2551] :
( c_Groups_Ouminus__class_Ouminus(U_2551,c_Groups_Ominus__class_Ominus(U_2551,U_2552,U_2553)) = c_Groups_Ominus__class_Ominus(U_2551,U_2553,U_2552)
| ~ class_Groups_Oab__group__add(U_2551) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
cnf(f_803_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_2551,c_Groups_Ominus__class_Ominus(U_2551,U_2552,U_2553)) = c_Groups_Ominus__class_Ominus(U_2551,U_2553,U_2552)
| ~ class_Groups_Oab__group__add(U_2551) ),
inference(clausify,[status(thm)],[f_803_2]) ).
fof(f_804_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).
fof(f_804_2,plain,
! [U_2558,U_2557,U_2556,U_2555,U_2554] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2555,U_2554),U_2556,U_2557),U_2558) = c_Groups_Ominus__class_Ominus(U_2554,hAPP(U_2556,U_2558),hAPP(U_2557,U_2558))
| ~ class_Groups_Ominus(U_2554) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
cnf(f_804_3,plain,
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2555,U_2554),U_2556,U_2557),U_2558) = c_Groups_Ominus__class_Ominus(U_2554,hAPP(U_2556,U_2558),hAPP(U_2557,U_2558))
| ~ class_Groups_Ominus(U_2554) ),
inference(clausify,[status(thm)],[f_804_2]) ).
fof(f_805_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_805_2,plain,
! [U_2560,U_2559] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2559),c_Nat_OSuc(U_2560)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2559,U_2560),
inference(variable_rename,[status(thm)],[f_805_1]) ).
cnf(f_805_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2559),c_Nat_OSuc(U_2560)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2559,U_2560),
inference(clausify,[status(thm)],[f_805_2]) ).
fof(f_806_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_806_2,plain,
! [U_2563,U_2562,U_2561] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2561),U_2562),c_Nat_OSuc(U_2563)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2561,U_2562),U_2563),
inference(variable_rename,[status(thm)],[f_806_1]) ).
cnf(f_806_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2561),U_2562),c_Nat_OSuc(U_2563)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2561,U_2562),U_2563),
inference(clausify,[status(thm)],[f_806_2]) ).
fof(f_807_1,plain,
! [V_q,V_b,V_p,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__pCons]) ).
fof(f_807_2,plain,
! [U_2568,U_2567,U_2566,U_2565,U_2564] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2564),c_Polynomial_OpCons(U_2564,U_2565,U_2566),c_Polynomial_OpCons(U_2564,U_2567,U_2568)) = c_Polynomial_OpCons(U_2564,c_Groups_Ominus__class_Ominus(U_2564,U_2565,U_2567),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2564),U_2566,U_2568))
| ~ class_Groups_Oab__group__add(U_2564) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
cnf(f_807_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2564),c_Polynomial_OpCons(U_2564,U_2565,U_2566),c_Polynomial_OpCons(U_2564,U_2567,U_2568)) = c_Polynomial_OpCons(U_2564,c_Groups_Ominus__class_Ominus(U_2564,U_2565,U_2567),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2564),U_2566,U_2568))
| ~ class_Groups_Oab__group__add(U_2564) ),
inference(clausify,[status(thm)],[f_807_2]) ).
fof(f_808_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__diff]) ).
fof(f_808_2,plain,
! [U_2572,U_2571,U_2570,U_2569] :
( hAPP(c_Polynomial_Opoly(U_2569,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2569),U_2570,U_2571)),U_2572) = c_Groups_Ominus__class_Ominus(U_2569,hAPP(c_Polynomial_Opoly(U_2569,U_2570),U_2572),hAPP(c_Polynomial_Opoly(U_2569,U_2571),U_2572))
| ~ class_Rings_Ocomm__ring(U_2569) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
cnf(f_808_3,plain,
( hAPP(c_Polynomial_Opoly(U_2569,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2569),U_2570,U_2571)),U_2572) = c_Groups_Ominus__class_Ominus(U_2569,hAPP(c_Polynomial_Opoly(U_2569,U_2570),U_2572),hAPP(c_Polynomial_Opoly(U_2569,U_2571),U_2572))
| ~ class_Rings_Ocomm__ring(U_2569) ),
inference(clausify,[status(thm)],[f_808_2]) ).
fof(f_809_1,plain,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( ( ( V_aa_2 = V_b_2
| V_c_2 != V_d_2 )
& ( V_c_2 = V_d_2
| V_aa_2 != V_b_2 ) )
| c_Groups_Ominus__class_Ominus(T_a,V_aa_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_809_2,plain,
! [U_2577,U_2576,U_2575,U_2574,U_2573] :
( ( ( U_2574 = U_2575
| U_2576 != U_2577 )
& ( U_2576 = U_2577
| U_2574 != U_2575 ) )
| c_Groups_Ominus__class_Ominus(U_2573,U_2574,U_2575) != c_Groups_Ominus__class_Ominus(U_2573,U_2576,U_2577)
| ~ class_Groups_Oab__group__add(U_2573) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
cnf(f_809_3,plain,
( U_2576 = U_2577
| U_2574 != U_2575
| c_Groups_Ominus__class_Ominus(U_2573,U_2574,U_2575) != c_Groups_Ominus__class_Ominus(U_2573,U_2576,U_2577)
| ~ class_Groups_Oab__group__add(U_2573) ),
inference(clausify,[status(thm)],[f_809_2]) ).
cnf(f_809_4,plain,
( U_2574 = U_2575
| U_2576 != U_2577
| c_Groups_Ominus__class_Ominus(U_2573,U_2574,U_2575) != c_Groups_Ominus__class_Ominus(U_2573,U_2576,U_2577)
| ~ class_Groups_Oab__group__add(U_2573) ),
inference(clausify,[status(thm)],[f_809_2]) ).
fof(f_810_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_810_2,plain,
! [U_2580,U_2579,U_2578] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2578,U_2579),U_2580) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2578,U_2580),U_2579),
inference(variable_rename,[status(thm)],[f_810_1]) ).
cnf(f_810_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2578,U_2579),U_2580) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2578,U_2580),U_2579),
inference(clausify,[status(thm)],[f_810_2]) ).
fof(f_811_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat]) ).
fof(f_811_2,plain,
! [U_2583,U_2582,U_2581] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2581),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2582,U_2583)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2581),U_2583))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2581),U_2582)) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
cnf(f_811_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2581),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2582,U_2583)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2581),U_2583))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_2581),U_2582)) ),
inference(clausify,[status(thm)],[f_811_2]) ).
fof(f_812_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diff]) ).
fof(f_812_2,plain,
! [U_2587,U_2586,U_2585,U_2584] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2584),U_2585),c_Groups_Ominus__class_Ominus(U_2584,U_2586,U_2587)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2584),U_2585),U_2587))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2584),U_2585),U_2586))
| ~ class_Rings_Ocomm__ring__1(U_2584) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
cnf(f_812_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2584),U_2585),c_Groups_Ominus__class_Ominus(U_2584,U_2586,U_2587)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2584),U_2585),U_2587))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2584),U_2585),U_2586))
| ~ class_Rings_Ocomm__ring__1(U_2584) ),
inference(clausify,[status(thm)],[f_812_2]) ).
fof(f_813_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__monom]) ).
fof(f_813_2,plain,
! [U_2591,U_2590,U_2589,U_2588] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2588),c_Polynomial_Omonom(U_2588,U_2589,U_2590),c_Polynomial_Omonom(U_2588,U_2591,U_2590)) = c_Polynomial_Omonom(U_2588,c_Groups_Ominus__class_Ominus(U_2588,U_2589,U_2591),U_2590)
| ~ class_Groups_Oab__group__add(U_2588) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
cnf(f_813_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2588),c_Polynomial_Omonom(U_2588,U_2589,U_2590),c_Polynomial_Omonom(U_2588,U_2591,U_2590)) = c_Polynomial_Omonom(U_2588,c_Groups_Ominus__class_Ominus(U_2588,U_2589,U_2591),U_2590)
| ~ class_Groups_Oab__group__add(U_2588) ),
inference(clausify,[status(thm)],[f_813_2]) ).
fof(f_814_1,plain,
! [V_n,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_coeff__diff]) ).
fof(f_814_2,plain,
! [U_2595,U_2594,U_2593,U_2592] :
( hAPP(c_Polynomial_Ocoeff(U_2592,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2592),U_2593,U_2594)),U_2595) = c_Groups_Ominus__class_Ominus(U_2592,hAPP(c_Polynomial_Ocoeff(U_2592,U_2593),U_2595),hAPP(c_Polynomial_Ocoeff(U_2592,U_2594),U_2595))
| ~ class_Groups_Oab__group__add(U_2592) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
cnf(f_814_3,plain,
( hAPP(c_Polynomial_Ocoeff(U_2592,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2592),U_2593,U_2594)),U_2595) = c_Groups_Ominus__class_Ominus(U_2592,hAPP(c_Polynomial_Ocoeff(U_2592,U_2593),U_2595),hAPP(c_Polynomial_Ocoeff(U_2592,U_2594),U_2595))
| ~ class_Groups_Oab__group__add(U_2592) ),
inference(clausify,[status(thm)],[f_814_2]) ).
fof(f_815_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_815_2,plain,
! [U_2598,U_2597,U_2596] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2596),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2597,U_2598)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2596),U_2597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2596),U_2598)),
inference(variable_rename,[status(thm)],[f_815_1]) ).
cnf(f_815_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2596),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2597,U_2598)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2596),U_2597),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2596),U_2598)),
inference(clausify,[status(thm)],[f_815_2]) ).
fof(f_816_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_816_2,plain,
! [U_2601,U_2600,U_2599] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2599,U_2600)),U_2601) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2599),U_2601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2600),U_2601)),
inference(variable_rename,[status(thm)],[f_816_1]) ).
cnf(f_816_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2599,U_2600)),U_2601) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2599),U_2601),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2600),U_2601)),
inference(clausify,[status(thm)],[f_816_2]) ).
fof(f_817_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).
fof(f_817_2,plain,
! [U_2604,U_2603,U_2602] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2604,U_2603),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2604,U_2602))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2602,U_2604)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2602,U_2603) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
cnf(f_817_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2604,U_2603),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2604,U_2602))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2602,U_2604)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2602,U_2603) ),
inference(clausify,[status(thm)],[f_817_2]) ).
fof(f_818_1,plain,
! [V_n,V_k,V_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).
fof(f_818_2,plain,
! [U_2607,U_2606,U_2605] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2605,U_2607),U_2606)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2605,U_2606) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
cnf(f_818_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2605,U_2607),U_2606)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2605,U_2606) ),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_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_819_2,plain,
! [U_2609,U_2608] :
( U_2608 = U_2609
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2609,U_2608) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2608,U_2609) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
cnf(f_819_3,plain,
( U_2608 = U_2609
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2609,U_2608) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2608,U_2609) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_819_2]) ).
fof(f_820_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_820_2,plain,
! [U_2610] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2610,U_2610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_820_1]) ).
cnf(f_820_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2610,U_2610) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_820_2]) ).
fof(f_821_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_821_2,plain,
! [U_2611] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2611,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2611,
inference(variable_rename,[status(thm)],[f_821_1]) ).
cnf(f_821_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2611,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2611,
inference(clausify,[status(thm)],[f_821_2]) ).
fof(f_822_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_822_2,plain,
! [U_2612] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2612) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_822_1]) ).
cnf(f_822_3,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2612) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_822_2]) ).
fof(f_823_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_823_2,plain,
! [U_2616,U_2615,U_2614,U_2613] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2613),U_2614),c_Groups_Ominus__class_Ominus(U_2613,U_2615,U_2616)) = c_Groups_Ominus__class_Ominus(U_2613,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2613),U_2614),U_2615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2613),U_2614),U_2616))
| ~ class_RealVector_Oreal__normed__algebra(U_2613) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
cnf(f_823_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2613),U_2614),c_Groups_Ominus__class_Ominus(U_2613,U_2615,U_2616)) = c_Groups_Ominus__class_Ominus(U_2613,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2613),U_2614),U_2615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2613),U_2614),U_2616))
| ~ class_RealVector_Oreal__normed__algebra(U_2613) ),
inference(clausify,[status(thm)],[f_823_2]) ).
fof(f_824_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_824_2,plain,
! [U_2620,U_2619,U_2618,U_2617] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2617),U_2618),c_Groups_Ominus__class_Ominus(U_2617,U_2619,U_2620)) = c_Groups_Ominus__class_Ominus(U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2617),U_2618),U_2619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2617),U_2618),U_2620))
| ~ class_RealVector_Oreal__normed__algebra(U_2617) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
cnf(f_824_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2617),U_2618),c_Groups_Ominus__class_Ominus(U_2617,U_2619,U_2620)) = c_Groups_Ominus__class_Ominus(U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2617),U_2618),U_2619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2617),U_2618),U_2620))
| ~ class_RealVector_Oreal__normed__algebra(U_2617) ),
inference(clausify,[status(thm)],[f_824_2]) ).
fof(f_825_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_825_2,plain,
! [U_2624,U_2623,U_2622,U_2621] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2621),c_Groups_Ominus__class_Ominus(U_2621,U_2622,U_2623)),U_2624) = c_Groups_Ominus__class_Ominus(U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2621),U_2622),U_2624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2621),U_2623),U_2624))
| ~ class_RealVector_Oreal__normed__algebra(U_2621) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
cnf(f_825_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2621),c_Groups_Ominus__class_Ominus(U_2621,U_2622,U_2623)),U_2624) = c_Groups_Ominus__class_Ominus(U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2621),U_2622),U_2624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2621),U_2623),U_2624))
| ~ class_RealVector_Oreal__normed__algebra(U_2621) ),
inference(clausify,[status(thm)],[f_825_2]) ).
fof(f_826_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_826_2,plain,
! [U_2628,U_2627,U_2626,U_2625] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2625),c_Groups_Ominus__class_Ominus(U_2625,U_2626,U_2627)),U_2628) = c_Groups_Ominus__class_Ominus(U_2625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2625),U_2626),U_2628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2625),U_2627),U_2628))
| ~ class_RealVector_Oreal__normed__algebra(U_2625) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
cnf(f_826_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2625),c_Groups_Ominus__class_Ominus(U_2625,U_2626,U_2627)),U_2628) = c_Groups_Ominus__class_Ominus(U_2625,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2625),U_2626),U_2628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2625),U_2627),U_2628))
| ~ class_RealVector_Oreal__normed__algebra(U_2625) ),
inference(clausify,[status(thm)],[f_826_2]) ).
fof(f_827_1,plain,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2) ) )
| c_Groups_Ominus__class_Ominus(T_a,V_aa_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_827_2,plain,
! [U_2633,U_2632,U_2631,U_2630,U_2629] :
( ( ( c_Orderings_Oord__class_Oless(U_2629,U_2630,U_2631)
| ~ c_Orderings_Oord__class_Oless(U_2629,U_2632,U_2633) )
& ( c_Orderings_Oord__class_Oless(U_2629,U_2632,U_2633)
| ~ c_Orderings_Oord__class_Oless(U_2629,U_2630,U_2631) ) )
| c_Groups_Ominus__class_Ominus(U_2629,U_2630,U_2631) != c_Groups_Ominus__class_Ominus(U_2629,U_2632,U_2633)
| ~ class_Groups_Oordered__ab__group__add(U_2629) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
cnf(f_827_3,plain,
( c_Orderings_Oord__class_Oless(U_2629,U_2632,U_2633)
| ~ c_Orderings_Oord__class_Oless(U_2629,U_2630,U_2631)
| c_Groups_Ominus__class_Ominus(U_2629,U_2630,U_2631) != c_Groups_Ominus__class_Ominus(U_2629,U_2632,U_2633)
| ~ class_Groups_Oordered__ab__group__add(U_2629) ),
inference(clausify,[status(thm)],[f_827_2]) ).
cnf(f_827_4,plain,
( c_Orderings_Oord__class_Oless(U_2629,U_2630,U_2631)
| ~ c_Orderings_Oord__class_Oless(U_2629,U_2632,U_2633)
| c_Groups_Ominus__class_Ominus(U_2629,U_2630,U_2631) != c_Groups_Ominus__class_Ominus(U_2629,U_2632,U_2633)
| ~ class_Groups_Oordered__ab__group__add(U_2629) ),
inference(clausify,[status(thm)],[f_827_2]) ).
fof(f_828_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_828_2,plain,
! [U_2635,U_2634] :
( c_Groups_Ominus__class_Ominus(U_2634,U_2635,c_Groups_Ozero__class_Ozero(U_2634)) = U_2635
| ~ class_Groups_Ogroup__add(U_2634) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
cnf(f_828_3,plain,
( c_Groups_Ominus__class_Ominus(U_2634,U_2635,c_Groups_Ozero__class_Ozero(U_2634)) = U_2635
| ~ class_Groups_Ogroup__add(U_2634) ),
inference(clausify,[status(thm)],[f_828_2]) ).
fof(f_829_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_829_2,plain,
! [U_2637,U_2636] :
( c_Groups_Ominus__class_Ominus(U_2636,U_2637,U_2637) = c_Groups_Ozero__class_Ozero(U_2636)
| ~ class_Groups_Ogroup__add(U_2636) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
cnf(f_829_3,plain,
( c_Groups_Ominus__class_Ominus(U_2636,U_2637,U_2637) = c_Groups_Ozero__class_Ozero(U_2636)
| ~ class_Groups_Ogroup__add(U_2636) ),
inference(clausify,[status(thm)],[f_829_2]) ).
fof(f_830_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( V_aa_2 = V_b_2
| c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 != V_b_2 ) )
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).
fof(f_830_2,plain,
! [U_2640,U_2639,U_2638] :
( ( ( U_2639 = U_2640
| c_Groups_Ominus__class_Ominus(U_2638,U_2639,U_2640) != c_Groups_Ozero__class_Ozero(U_2638) )
& ( c_Groups_Ominus__class_Ominus(U_2638,U_2639,U_2640) = c_Groups_Ozero__class_Ozero(U_2638)
| U_2639 != U_2640 ) )
| ~ class_Groups_Oab__group__add(U_2638) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
cnf(f_830_3,plain,
( c_Groups_Ominus__class_Ominus(U_2638,U_2639,U_2640) = c_Groups_Ozero__class_Ozero(U_2638)
| U_2639 != U_2640
| ~ class_Groups_Oab__group__add(U_2638) ),
inference(clausify,[status(thm)],[f_830_2]) ).
cnf(f_830_4,plain,
( U_2639 = U_2640
| c_Groups_Ominus__class_Ominus(U_2638,U_2639,U_2640) != c_Groups_Ozero__class_Ozero(U_2638)
| ~ class_Groups_Oab__group__add(U_2638) ),
inference(clausify,[status(thm)],[f_830_2]) ).
fof(f_831_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 != V_b_2 )
& ( V_aa_2 = V_b_2
| c_Groups_Ominus__class_Ominus(T_a,V_aa_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_831_2,plain,
! [U_2643,U_2642,U_2641] :
( ( ( c_Groups_Ominus__class_Ominus(U_2641,U_2642,U_2643) = c_Groups_Ozero__class_Ozero(U_2641)
| U_2642 != U_2643 )
& ( U_2642 = U_2643
| c_Groups_Ominus__class_Ominus(U_2641,U_2642,U_2643) != c_Groups_Ozero__class_Ozero(U_2641) ) )
| ~ class_Groups_Ogroup__add(U_2641) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
cnf(f_831_3,plain,
( U_2642 = U_2643
| c_Groups_Ominus__class_Ominus(U_2641,U_2642,U_2643) != c_Groups_Ozero__class_Ozero(U_2641)
| ~ class_Groups_Ogroup__add(U_2641) ),
inference(clausify,[status(thm)],[f_831_2]) ).
cnf(f_831_4,plain,
( c_Groups_Ominus__class_Ominus(U_2641,U_2642,U_2643) = c_Groups_Ozero__class_Ozero(U_2641)
| U_2642 != U_2643
| ~ class_Groups_Ogroup__add(U_2641) ),
inference(clausify,[status(thm)],[f_831_2]) ).
fof(f_832_1,plain,
! [V_d_2,V_c_2,V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2) ) )
| c_Groups_Ominus__class_Ominus(T_a,V_aa_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_832_2,plain,
! [U_2648,U_2647,U_2646,U_2645,U_2644] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2644,U_2645,U_2646)
| ~ c_Orderings_Oord__class_Oless__eq(U_2644,U_2647,U_2648) )
& ( c_Orderings_Oord__class_Oless__eq(U_2644,U_2647,U_2648)
| ~ c_Orderings_Oord__class_Oless__eq(U_2644,U_2645,U_2646) ) )
| c_Groups_Ominus__class_Ominus(U_2644,U_2645,U_2646) != c_Groups_Ominus__class_Ominus(U_2644,U_2647,U_2648)
| ~ class_Groups_Oordered__ab__group__add(U_2644) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
cnf(f_832_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2644,U_2647,U_2648)
| ~ c_Orderings_Oord__class_Oless__eq(U_2644,U_2645,U_2646)
| c_Groups_Ominus__class_Ominus(U_2644,U_2645,U_2646) != c_Groups_Ominus__class_Ominus(U_2644,U_2647,U_2648)
| ~ class_Groups_Oordered__ab__group__add(U_2644) ),
inference(clausify,[status(thm)],[f_832_2]) ).
cnf(f_832_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2644,U_2645,U_2646)
| ~ c_Orderings_Oord__class_Oless__eq(U_2644,U_2647,U_2648)
| c_Groups_Ominus__class_Ominus(U_2644,U_2645,U_2646) != c_Groups_Ominus__class_Ominus(U_2644,U_2647,U_2648)
| ~ class_Groups_Oordered__ab__group__add(U_2644) ),
inference(clausify,[status(thm)],[f_832_2]) ).
fof(f_833_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m),
inference(fof_nnf,[status(thm)],[fact_diff__le__self]) ).
fof(f_833_2,plain,
! [U_2650,U_2649] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2649,U_2650),U_2649),
inference(variable_rename,[status(thm)],[f_833_1]) ).
cnf(f_833_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2649,U_2650),U_2649),
inference(clausify,[status(thm)],[f_833_2]) ).
fof(f_834_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).
fof(f_834_2,plain,
! [U_2653,U_2652,U_2651] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2653,U_2652),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2653,U_2651))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2651,U_2652) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
cnf(f_834_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2653,U_2652),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2653,U_2651))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2651,U_2652) ),
inference(clausify,[status(thm)],[f_834_2]) ).
fof(f_835_1,plain,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).
fof(f_835_2,plain,
! [U_2656,U_2655,U_2654] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2654,U_2656),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2655,U_2656))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2654,U_2655) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
cnf(f_835_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2654,U_2656),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2655,U_2656))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2654,U_2655) ),
inference(clausify,[status(thm)],[f_835_2]) ).
fof(f_836_1,plain,
! [V_n,V_i] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).
fof(f_836_2,plain,
! [U_2658,U_2657] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2658,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2658,U_2657)) = U_2657
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2657,U_2658) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
cnf(f_836_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2658,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2658,U_2657)) = U_2657
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2657,U_2658) ),
inference(clausify,[status(thm)],[f_836_2]) ).
fof(f_837_1,plain,
! [V_nb_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_nb_2,V_k_2)
| V_m_2 != V_nb_2 )
& ( V_m_2 = V_nb_2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_nb_2,V_k_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
| ~ 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_837_2,plain,
! [U_2661,U_2660,U_2659] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2660,U_2659) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2661,U_2659)
| U_2660 != U_2661 )
& ( U_2660 = U_2661
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2660,U_2659) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2661,U_2659) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2659,U_2661)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2659,U_2660) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
cnf(f_837_3,plain,
( U_2660 = U_2661
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2660,U_2659) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2661,U_2659)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2659,U_2661)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2659,U_2660) ),
inference(clausify,[status(thm)],[f_837_2]) ).
cnf(f_837_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2660,U_2659) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2661,U_2659)
| U_2660 != U_2661
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2659,U_2661)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2659,U_2660) ),
inference(clausify,[status(thm)],[f_837_2]) ).
fof(f_838_1,plain,
! [V_n,V_m,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m) ),
inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq]) ).
fof(f_838_2,plain,
! [U_2664,U_2663,U_2662] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2663,U_2662),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2664,U_2662)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2663,U_2664)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2662,U_2664)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2662,U_2663) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
cnf(f_838_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2663,U_2662),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2664,U_2662)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2663,U_2664)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2662,U_2664)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2662,U_2663) ),
inference(clausify,[status(thm)],[f_838_2]) ).
fof(f_839_1,plain,
! [V_nb_2,V_m_2,V_k_2] :
( ( ( 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_nb_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ 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_nb_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_nb_2)
| ~ 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_839_2,plain,
! [U_2667,U_2666,U_2665] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2666,U_2665),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2667,U_2665))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2666,U_2667) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2666,U_2667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2666,U_2665),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2667,U_2665)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2666) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
cnf(f_839_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2666,U_2667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2666,U_2665),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2667,U_2665))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2666) ),
inference(clausify,[status(thm)],[f_839_2]) ).
cnf(f_839_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2666,U_2665),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2667,U_2665))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2666,U_2667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2665,U_2666) ),
inference(clausify,[status(thm)],[f_839_2]) ).
fof(f_840_1,plain,
! [V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__0]) ).
fof(f_840_2,plain,
! [U_2669,U_2668] :
( c_Groups_Ominus__class_Ominus(U_2668,c_Groups_Ozero__class_Ozero(U_2668),U_2669) = c_Groups_Ouminus__class_Ouminus(U_2668,U_2669)
| ~ class_Groups_Ogroup__add(U_2668) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
cnf(f_840_3,plain,
( c_Groups_Ominus__class_Ominus(U_2668,c_Groups_Ozero__class_Ozero(U_2668),U_2669) = c_Groups_Ouminus__class_Ouminus(U_2668,U_2669)
| ~ class_Groups_Ogroup__add(U_2668) ),
inference(clausify,[status(thm)],[f_840_2]) ).
fof(f_841_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_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_841_2,plain,
! [U_2672,U_2671,U_2670] :
( ( ( c_Orderings_Oord__class_Oless(U_2670,U_2671,U_2672)
| ~ c_Orderings_Oord__class_Oless(U_2670,c_Groups_Ominus__class_Ominus(U_2670,U_2671,U_2672),c_Groups_Ozero__class_Ozero(U_2670)) )
& ( c_Orderings_Oord__class_Oless(U_2670,c_Groups_Ominus__class_Ominus(U_2670,U_2671,U_2672),c_Groups_Ozero__class_Ozero(U_2670))
| ~ c_Orderings_Oord__class_Oless(U_2670,U_2671,U_2672) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2670) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
cnf(f_841_3,plain,
( c_Orderings_Oord__class_Oless(U_2670,c_Groups_Ominus__class_Ominus(U_2670,U_2671,U_2672),c_Groups_Ozero__class_Ozero(U_2670))
| ~ c_Orderings_Oord__class_Oless(U_2670,U_2671,U_2672)
| ~ class_Groups_Oordered__ab__group__add(U_2670) ),
inference(clausify,[status(thm)],[f_841_2]) ).
cnf(f_841_4,plain,
( c_Orderings_Oord__class_Oless(U_2670,U_2671,U_2672)
| ~ c_Orderings_Oord__class_Oless(U_2670,c_Groups_Ominus__class_Ominus(U_2670,U_2671,U_2672),c_Groups_Ozero__class_Ozero(U_2670))
| ~ class_Groups_Oordered__ab__group__add(U_2670) ),
inference(clausify,[status(thm)],[f_841_2]) ).
fof(f_842_1,plain,
! [V_b_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_aa_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_842_2,plain,
! [U_2675,U_2674,U_2673] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2673,U_2674,U_2675)
| ~ c_Orderings_Oord__class_Oless__eq(U_2673,c_Groups_Ominus__class_Ominus(U_2673,U_2674,U_2675),c_Groups_Ozero__class_Ozero(U_2673)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2673,c_Groups_Ominus__class_Ominus(U_2673,U_2674,U_2675),c_Groups_Ozero__class_Ozero(U_2673))
| ~ c_Orderings_Oord__class_Oless__eq(U_2673,U_2674,U_2675) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2673) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
cnf(f_842_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2673,c_Groups_Ominus__class_Ominus(U_2673,U_2674,U_2675),c_Groups_Ozero__class_Ozero(U_2673))
| ~ c_Orderings_Oord__class_Oless__eq(U_2673,U_2674,U_2675)
| ~ class_Groups_Oordered__ab__group__add(U_2673) ),
inference(clausify,[status(thm)],[f_842_2]) ).
cnf(f_842_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2673,U_2674,U_2675)
| ~ c_Orderings_Oord__class_Oless__eq(U_2673,c_Groups_Ominus__class_Ominus(U_2673,U_2674,U_2675),c_Groups_Ozero__class_Ozero(U_2673))
| ~ class_Groups_Oordered__ab__group__add(U_2673) ),
inference(clausify,[status(thm)],[f_842_2]) ).
fof(f_843_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).
fof(f_843_2,plain,
! [U_2681,U_2680,U_2679,U_2678,U_2677,U_2676] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2677),U_2678),U_2679),c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2680),U_2678),U_2681))
| ~ c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),c_Groups_Ominus__class_Ominus(U_2676,U_2677,U_2680)),U_2678),U_2679),U_2681) )
& ( c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),c_Groups_Ominus__class_Ominus(U_2676,U_2677,U_2680)),U_2678),U_2679),U_2681)
| ~ c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2677),U_2678),U_2679),c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2680),U_2678),U_2681)) ) )
| ~ class_Rings_Oordered__ring(U_2676) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
cnf(f_843_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),c_Groups_Ominus__class_Ominus(U_2676,U_2677,U_2680)),U_2678),U_2679),U_2681)
| ~ c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2677),U_2678),U_2679),c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2680),U_2678),U_2681))
| ~ class_Rings_Oordered__ring(U_2676) ),
inference(clausify,[status(thm)],[f_843_2]) ).
cnf(f_843_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2677),U_2678),U_2679),c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),U_2680),U_2678),U_2681))
| ~ c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Oplus__class_Oplus(U_2676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2676),c_Groups_Ominus__class_Ominus(U_2676,U_2677,U_2680)),U_2678),U_2679),U_2681)
| ~ class_Rings_Oordered__ring(U_2676) ),
inference(clausify,[status(thm)],[f_843_2]) ).
fof(f_844_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).
fof(f_844_2,plain,
! [U_2687,U_2686,U_2685,U_2684,U_2683,U_2682] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2682,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684),U_2685),c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2686),U_2684),U_2687))
| ~ c_Orderings_Oord__class_Oless__eq(U_2682,U_2685,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),c_Groups_Ominus__class_Ominus(U_2682,U_2686,U_2683)),U_2684),U_2687)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2682,U_2685,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),c_Groups_Ominus__class_Ominus(U_2682,U_2686,U_2683)),U_2684),U_2687))
| ~ c_Orderings_Oord__class_Oless__eq(U_2682,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684),U_2685),c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2686),U_2684),U_2687)) ) )
| ~ class_Rings_Oordered__ring(U_2682) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
cnf(f_844_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2682,U_2685,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),c_Groups_Ominus__class_Ominus(U_2682,U_2686,U_2683)),U_2684),U_2687))
| ~ c_Orderings_Oord__class_Oless__eq(U_2682,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684),U_2685),c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2686),U_2684),U_2687))
| ~ class_Rings_Oordered__ring(U_2682) ),
inference(clausify,[status(thm)],[f_844_2]) ).
cnf(f_844_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2682,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2683),U_2684),U_2685),c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),U_2686),U_2684),U_2687))
| ~ c_Orderings_Oord__class_Oless__eq(U_2682,U_2685,c_Groups_Oplus__class_Oplus(U_2682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2682),c_Groups_Ominus__class_Ominus(U_2682,U_2686,U_2683)),U_2684),U_2687))
| ~ class_Rings_Oordered__ring(U_2682) ),
inference(clausify,[status(thm)],[f_844_2]) ).
fof(f_845_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)),V_e_2),V_c_2),V_d_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).
fof(f_845_2,plain,
! [U_2693,U_2692,U_2691,U_2690,U_2689,U_2688] :
( ( ( c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2689),U_2690),U_2691),c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2692),U_2690),U_2693))
| ~ c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),c_Groups_Ominus__class_Ominus(U_2688,U_2689,U_2692)),U_2690),U_2691),U_2693) )
& ( c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),c_Groups_Ominus__class_Ominus(U_2688,U_2689,U_2692)),U_2690),U_2691),U_2693)
| ~ c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2689),U_2690),U_2691),c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2692),U_2690),U_2693)) ) )
| ~ class_Rings_Oordered__ring(U_2688) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
cnf(f_845_3,plain,
( c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),c_Groups_Ominus__class_Ominus(U_2688,U_2689,U_2692)),U_2690),U_2691),U_2693)
| ~ c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2689),U_2690),U_2691),c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2692),U_2690),U_2693))
| ~ class_Rings_Oordered__ring(U_2688) ),
inference(clausify,[status(thm)],[f_845_2]) ).
cnf(f_845_4,plain,
( c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2689),U_2690),U_2691),c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),U_2692),U_2690),U_2693))
| ~ c_Orderings_Oord__class_Oless(U_2688,c_Groups_Oplus__class_Oplus(U_2688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2688),c_Groups_Ominus__class_Ominus(U_2688,U_2689,U_2692)),U_2690),U_2691),U_2693)
| ~ class_Rings_Oordered__ring(U_2688) ),
inference(clausify,[status(thm)],[f_845_2]) ).
fof(f_846_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2)),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).
fof(f_846_2,plain,
! [U_2699,U_2698,U_2697,U_2696,U_2695,U_2694] :
( ( ( c_Orderings_Oord__class_Oless(U_2694,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2695),U_2696),U_2697),c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2698),U_2696),U_2699))
| ~ c_Orderings_Oord__class_Oless(U_2694,U_2697,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),c_Groups_Ominus__class_Ominus(U_2694,U_2698,U_2695)),U_2696),U_2699)) )
& ( c_Orderings_Oord__class_Oless(U_2694,U_2697,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),c_Groups_Ominus__class_Ominus(U_2694,U_2698,U_2695)),U_2696),U_2699))
| ~ c_Orderings_Oord__class_Oless(U_2694,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2695),U_2696),U_2697),c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2698),U_2696),U_2699)) ) )
| ~ class_Rings_Oordered__ring(U_2694) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
cnf(f_846_3,plain,
( c_Orderings_Oord__class_Oless(U_2694,U_2697,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),c_Groups_Ominus__class_Ominus(U_2694,U_2698,U_2695)),U_2696),U_2699))
| ~ c_Orderings_Oord__class_Oless(U_2694,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2695),U_2696),U_2697),c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2698),U_2696),U_2699))
| ~ class_Rings_Oordered__ring(U_2694) ),
inference(clausify,[status(thm)],[f_846_2]) ).
cnf(f_846_4,plain,
( c_Orderings_Oord__class_Oless(U_2694,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2695),U_2696),U_2697),c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),U_2698),U_2696),U_2699))
| ~ c_Orderings_Oord__class_Oless(U_2694,U_2697,c_Groups_Oplus__class_Oplus(U_2694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2694),c_Groups_Ominus__class_Ominus(U_2694,U_2698,U_2695)),U_2696),U_2699))
| ~ class_Rings_Oordered__ring(U_2694) ),
inference(clausify,[status(thm)],[f_846_2]) ).
fof(f_847_1,plain,
! [V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored]) ).
fof(f_847_2,plain,
! [U_2701,U_2700] :
( c_Groups_Ominus__class_Ominus(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2701),c_Groups_Oone__class_Oone(U_2700)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),c_Groups_Oplus__class_Oplus(U_2700,U_2701,c_Groups_Oone__class_Oone(U_2700))),c_Groups_Ominus__class_Ominus(U_2700,U_2701,c_Groups_Oone__class_Oone(U_2700)))
| ~ class_Rings_Oring__1(U_2700) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
cnf(f_847_3,plain,
( c_Groups_Ominus__class_Ominus(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2701),c_Groups_Oone__class_Oone(U_2700)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),c_Groups_Oplus__class_Oplus(U_2700,U_2701,c_Groups_Oone__class_Oone(U_2700))),c_Groups_Ominus__class_Ominus(U_2700,U_2701,c_Groups_Oone__class_Oone(U_2700)))
| ~ class_Rings_Oring__1(U_2700) ),
inference(clausify,[status(thm)],[f_847_2]) ).
fof(f_848_1,plain,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ! [B_x,B_k] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),V_D_2))
| ~ class_Rings_Odvd(T_a)
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J]) ).
fof(f_848_2,plain,
! [U_2707,U_2706,U_2705,U_2704] :
( ! [U_2703,U_2702] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,U_2703,U_2707)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,c_Groups_Ominus__class_Ominus(U_2704,U_2703,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2702),U_2706)),U_2707))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,c_Groups_Ominus__class_Ominus(U_2704,U_2703,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2702),U_2706)),U_2707)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,U_2703,U_2707))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),U_2706))
| ~ class_Rings_Odvd(U_2704)
| ~ class_Rings_Ocomm__ring(U_2704) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
! [U_2707,U_2706,U_2705,U_2704] :
( ( ! [U_2711] :
( ! [U_2709] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,c_Groups_Ominus__class_Ominus(U_2704,U_2711,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2709),U_2706)),U_2707)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,U_2711,U_2707))) )
& ! [U_2710] :
( ! [U_2708] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,c_Groups_Ominus__class_Ominus(U_2704,U_2710,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2708),U_2706)),U_2707)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,U_2710,U_2707))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),U_2706))
| ~ class_Rings_Odvd(U_2704)
| ~ class_Rings_Ocomm__ring(U_2704) ),
inference(miniscope,[status(thm)],[f_848_2]) ).
cnf(f_848_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,c_Groups_Ominus__class_Ominus(U_2704,U_2710,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2708),U_2706)),U_2707)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,U_2710,U_2707)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),U_2706))
| ~ class_Rings_Odvd(U_2704)
| ~ class_Rings_Ocomm__ring(U_2704) ),
inference(clausify,[status(thm)],[f_848_3]) ).
cnf(f_848_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,c_Groups_Ominus__class_Ominus(U_2704,U_2711,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2709),U_2706)),U_2707)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2704,U_2711,U_2707)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2704),U_2705),U_2706))
| ~ class_Rings_Odvd(U_2704)
| ~ class_Rings_Ocomm__ring(U_2704) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_1,plain,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ! [B_x,B_k] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_d_2),V_D_2))
| ~ class_Rings_Odvd(T_a)
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J]) ).
fof(f_849_2,plain,
! [U_2717,U_2716,U_2715,U_2714] :
( ! [U_2713,U_2712] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,U_2713,U_2717)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,c_Groups_Ominus__class_Ominus(U_2714,U_2713,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2712),U_2716)),U_2717))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,c_Groups_Ominus__class_Ominus(U_2714,U_2713,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2712),U_2716)),U_2717)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,U_2713,U_2717))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),U_2716))
| ~ class_Rings_Odvd(U_2714)
| ~ class_Rings_Ocomm__ring(U_2714) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
! [U_2717,U_2716,U_2715,U_2714] :
( ( ! [U_2721] :
( ! [U_2719] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,c_Groups_Ominus__class_Ominus(U_2714,U_2721,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2719),U_2716)),U_2717)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,U_2721,U_2717))) )
& ! [U_2720] :
( ! [U_2718] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,c_Groups_Ominus__class_Ominus(U_2714,U_2720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716)),U_2717)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,U_2720,U_2717))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),U_2716))
| ~ class_Rings_Odvd(U_2714)
| ~ class_Rings_Ocomm__ring(U_2714) ),
inference(miniscope,[status(thm)],[f_849_2]) ).
cnf(f_849_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,c_Groups_Ominus__class_Ominus(U_2714,U_2720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716)),U_2717)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,U_2720,U_2717)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),U_2716))
| ~ class_Rings_Odvd(U_2714)
| ~ class_Rings_Ocomm__ring(U_2714) ),
inference(clausify,[status(thm)],[f_849_3]) ).
cnf(f_849_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,c_Groups_Ominus__class_Ominus(U_2714,U_2721,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2719),U_2716)),U_2717)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),c_Groups_Oplus__class_Oplus(U_2714,U_2721,U_2717)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2714),U_2715),U_2716))
| ~ class_Rings_Odvd(U_2714)
| ~ class_Rings_Ocomm__ring(U_2714) ),
inference(clausify,[status(thm)],[f_849_3]) ).
fof(f_850_1,plain,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).
fof(f_850_2,plain,
! [U_2723,U_2722] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2722,c_Nat_OSuc(U_2723)),U_2722)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2722) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
cnf(f_850_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2722,c_Nat_OSuc(U_2723)),U_2722)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2722) ),
inference(clausify,[status(thm)],[f_850_2]) ).
fof(f_851_1,plain,
! [V_n] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).
fof(f_851_2,plain,
! [U_2724] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2724,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2724
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2724) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
cnf(f_851_3,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2724,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2724
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2724) ),
inference(clausify,[status(thm)],[f_851_2]) ).
fof(f_852_1,plain,
! [V_b_2,V_aa_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_aa_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(f_852_2,plain,
! [U_2729,U_2728,U_2727] :
( ( hBOOL(hAPP(U_2727,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2728,U_2729)))
| ? [U_2726] :
( ~ hBOOL(hAPP(U_2727,U_2726))
& U_2728 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2729,U_2726) )
| ( ~ hBOOL(hAPP(U_2727,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2728,U_2729) ) )
& ( ( ! [U_2725] :
( hBOOL(hAPP(U_2727,U_2725))
| U_2728 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2729,U_2725) )
& ( hBOOL(hAPP(U_2727,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2728,U_2729) ) )
| ~ hBOOL(hAPP(U_2727,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2728,U_2729))) ) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
fof(f_852_3,plain,
( ! [U_2735,U_2733,U_2731] :
( hBOOL(hAPP(U_2731,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2733,U_2735)))
| ? [U_2726] :
( ~ hBOOL(hAPP(U_2731,U_2726))
& U_2733 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2735,U_2726) )
| ( ~ hBOOL(hAPP(U_2731,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2733,U_2735) ) )
& ! [U_2734,U_2732,U_2730] :
( ( ! [U_2725] :
( hBOOL(hAPP(U_2730,U_2725))
| U_2732 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2734,U_2725) )
& ( hBOOL(hAPP(U_2730,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2732,U_2734) ) )
| ~ hBOOL(hAPP(U_2730,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2732,U_2734))) ) ),
inference(miniscope,[status(thm)],[f_852_2]) ).
fof(f_852_4,plain,
( ! [U_2735,U_2733,U_2731] :
( hBOOL(hAPP(U_2731,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2733,U_2735)))
| ( ~ hBOOL(hAPP(U_2731,sK17(U_2735,U_2733,U_2731)))
& U_2733 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2735,sK17(U_2735,U_2733,U_2731)) )
| ( ~ hBOOL(hAPP(U_2731,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2733,U_2735) ) )
& ! [U_2734,U_2732,U_2730] :
( ( ! [U_2725] :
( hBOOL(hAPP(U_2730,U_2725))
| U_2732 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2734,U_2725) )
& ( hBOOL(hAPP(U_2730,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2732,U_2734) ) )
| ~ hBOOL(hAPP(U_2730,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2732,U_2734))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_2726,sK17(U_2735,U_2733,U_2731))],[f_852_3]) ).
cnf(f_852_5,plain,
( hBOOL(hAPP(U_2730,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2732,U_2734)
| ~ hBOOL(hAPP(U_2730,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2732,U_2734))) ),
inference(clausify,[status(thm)],[f_852_4]) ).
cnf(f_852_6,plain,
( hBOOL(hAPP(U_2730,U_2725))
| U_2732 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2734,U_2725)
| ~ hBOOL(hAPP(U_2730,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2732,U_2734))) ),
inference(clausify,[status(thm)],[f_852_4]) ).
cnf(f_852_7,plain,
( U_2733 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2735,sK17(U_2735,U_2733,U_2731))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2733,U_2735)
| hBOOL(hAPP(U_2731,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2733,U_2735))) ),
inference(clausify,[status(thm)],[f_852_4]) ).
cnf(f_852_8,plain,
( ~ hBOOL(hAPP(U_2731,sK17(U_2735,U_2733,U_2731)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2733,U_2735)
| hBOOL(hAPP(U_2731,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2733,U_2735))) ),
inference(clausify,[status(thm)],[f_852_4]) ).
cnf(f_852_9,plain,
( U_2733 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2735,sK17(U_2735,U_2733,U_2731))
| ~ hBOOL(hAPP(U_2731,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2731,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2733,U_2735))) ),
inference(clausify,[status(thm)],[f_852_4]) ).
cnf(f_852_10,plain,
( ~ hBOOL(hAPP(U_2731,sK17(U_2735,U_2733,U_2731)))
| ~ hBOOL(hAPP(U_2731,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2731,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2733,U_2735))) ),
inference(clausify,[status(thm)],[f_852_4]) ).
fof(f_853_1,plain,
! [V_b_2,V_aa_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_aa_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_aa_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).
fof(f_853_2,plain,
! [U_2740,U_2739,U_2738] :
( ( hBOOL(hAPP(U_2738,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2739,U_2740)))
| ? [U_2737] :
( ~ hBOOL(hAPP(U_2738,U_2737))
& U_2739 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2740,U_2737) )
| ( ~ hBOOL(hAPP(U_2738,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2739,U_2740) ) )
& ( ( ! [U_2736] :
( hBOOL(hAPP(U_2738,U_2736))
| U_2739 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2740,U_2736) )
& ( hBOOL(hAPP(U_2738,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2739,U_2740) ) )
| ~ hBOOL(hAPP(U_2738,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2739,U_2740))) ) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
fof(f_853_3,plain,
( ! [U_2746,U_2744,U_2742] :
( hBOOL(hAPP(U_2742,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2744,U_2746)))
| ? [U_2737] :
( ~ hBOOL(hAPP(U_2742,U_2737))
& U_2744 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2746,U_2737) )
| ( ~ hBOOL(hAPP(U_2742,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2744,U_2746) ) )
& ! [U_2745,U_2743,U_2741] :
( ( ! [U_2736] :
( hBOOL(hAPP(U_2741,U_2736))
| U_2743 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2745,U_2736) )
& ( hBOOL(hAPP(U_2741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2743,U_2745) ) )
| ~ hBOOL(hAPP(U_2741,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2743,U_2745))) ) ),
inference(miniscope,[status(thm)],[f_853_2]) ).
fof(f_853_4,plain,
( ! [U_2746,U_2744,U_2742] :
( hBOOL(hAPP(U_2742,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2744,U_2746)))
| ( ~ hBOOL(hAPP(U_2742,sK18(U_2746,U_2744,U_2742)))
& U_2744 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2746,sK18(U_2746,U_2744,U_2742)) )
| ( ~ hBOOL(hAPP(U_2742,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2744,U_2746) ) )
& ! [U_2745,U_2743,U_2741] :
( ( ! [U_2736] :
( hBOOL(hAPP(U_2741,U_2736))
| U_2743 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2745,U_2736) )
& ( hBOOL(hAPP(U_2741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2743,U_2745) ) )
| ~ hBOOL(hAPP(U_2741,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2743,U_2745))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_2737,sK18(U_2746,U_2744,U_2742))],[f_853_3]) ).
cnf(f_853_5,plain,
( hBOOL(hAPP(U_2741,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2743,U_2745)
| ~ hBOOL(hAPP(U_2741,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2743,U_2745))) ),
inference(clausify,[status(thm)],[f_853_4]) ).
cnf(f_853_6,plain,
( hBOOL(hAPP(U_2741,U_2736))
| U_2743 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2745,U_2736)
| ~ hBOOL(hAPP(U_2741,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2743,U_2745))) ),
inference(clausify,[status(thm)],[f_853_4]) ).
cnf(f_853_7,plain,
( U_2744 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2746,sK18(U_2746,U_2744,U_2742))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2744,U_2746)
| hBOOL(hAPP(U_2742,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2744,U_2746))) ),
inference(clausify,[status(thm)],[f_853_4]) ).
cnf(f_853_8,plain,
( ~ hBOOL(hAPP(U_2742,sK18(U_2746,U_2744,U_2742)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2744,U_2746)
| hBOOL(hAPP(U_2742,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2744,U_2746))) ),
inference(clausify,[status(thm)],[f_853_4]) ).
cnf(f_853_9,plain,
( U_2744 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2746,sK18(U_2746,U_2744,U_2742))
| ~ hBOOL(hAPP(U_2742,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2742,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2744,U_2746))) ),
inference(clausify,[status(thm)],[f_853_4]) ).
cnf(f_853_10,plain,
( ~ hBOOL(hAPP(U_2742,sK18(U_2746,U_2744,U_2742)))
| ~ hBOOL(hAPP(U_2742,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_2742,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2744,U_2746))) ),
inference(clausify,[status(thm)],[f_853_4]) ).
fof(f_854_1,plain,
! [V_m,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2]) ).
fof(f_854_2,plain,
! [U_2749,U_2748,U_2747] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2748,U_2747)),U_2749) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2748),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2747,U_2749))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2747,U_2748) ),
inference(variable_rename,[status(thm)],[f_854_1]) ).
cnf(f_854_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2748,U_2747)),U_2749) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2748),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2747,U_2749))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2747,U_2748) ),
inference(clausify,[status(thm)],[f_854_2]) ).
fof(f_855_1,plain,
! [V_m,V_j,V_k] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1]) ).
fof(f_855_2,plain,
! [U_2752,U_2751,U_2750] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2752,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2751,U_2750))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2752,U_2750),c_Nat_OSuc(U_2751))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2750,U_2751) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
cnf(f_855_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2752,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2751,U_2750))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2752,U_2750),c_Nat_OSuc(U_2751))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_855_2]) ).
fof(f_856_1,plain,
! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_nb_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_nb_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1]) ).
fof(f_856_2,plain,
! [U_2757,U_2756,U_2755,U_2754,U_2753] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2754),U_2755),U_2756),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2753),U_2755),U_2757))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2754,U_2753)),U_2755),U_2756),U_2757) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2754,U_2753)),U_2755),U_2756),U_2757)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2754),U_2755),U_2756),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2753),U_2755),U_2757)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2753,U_2754) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
cnf(f_856_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2754,U_2753)),U_2755),U_2756),U_2757)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2754),U_2755),U_2756),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2753),U_2755),U_2757))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2753,U_2754) ),
inference(clausify,[status(thm)],[f_856_2]) ).
cnf(f_856_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2754),U_2755),U_2756),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2753),U_2755),U_2757))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2754,U_2753)),U_2755),U_2756),U_2757)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2753,U_2754) ),
inference(clausify,[status(thm)],[f_856_2]) ).
fof(f_857_1,plain,
! [V_n,V_m,V_u,V_i,V_j] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1]) ).
fof(f_857_2,plain,
! [U_2762,U_2761,U_2760,U_2759,U_2758] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2759),U_2760),U_2761),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2758),U_2760),U_2762)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2759,U_2758)),U_2760),U_2761),U_2762)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2758,U_2759) ),
inference(variable_rename,[status(thm)],[f_857_1]) ).
cnf(f_857_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2759),U_2760),U_2761),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2758),U_2760),U_2762)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2759,U_2758)),U_2760),U_2761),U_2762)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2758,U_2759) ),
inference(clausify,[status(thm)],[f_857_2]) ).
fof(f_858_1,plain,
! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) != V_nb_2 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_nb_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1]) ).
fof(f_858_2,plain,
! [U_2767,U_2766,U_2765,U_2764,U_2763] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2764),U_2765),U_2766) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2763),U_2765),U_2767)
| 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_2764,U_2763)),U_2765),U_2766) != U_2767 )
& ( 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_2764,U_2763)),U_2765),U_2766) = U_2767
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2764),U_2765),U_2766) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2763),U_2765),U_2767) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2763,U_2764) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
cnf(f_858_3,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2764,U_2763)),U_2765),U_2766) = U_2767
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2764),U_2765),U_2766) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2763),U_2765),U_2767)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2763,U_2764) ),
inference(clausify,[status(thm)],[f_858_2]) ).
cnf(f_858_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2764),U_2765),U_2766) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2763),U_2765),U_2767)
| 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_2764,U_2763)),U_2765),U_2766) != U_2767
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2763,U_2764) ),
inference(clausify,[status(thm)],[f_858_2]) ).
fof(f_859_1,plain,
! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2]) ).
fof(f_859_2,plain,
! [U_2772,U_2771,U_2770,U_2769,U_2768] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2768),U_2770),U_2771),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2769),U_2770),U_2772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2771,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_2769,U_2768)),U_2770),U_2772)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2771,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_2769,U_2768)),U_2770),U_2772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2768),U_2770),U_2771),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2769),U_2770),U_2772)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2768,U_2769) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
cnf(f_859_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2771,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_2769,U_2768)),U_2770),U_2772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2768),U_2770),U_2771),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2769),U_2770),U_2772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2768,U_2769) ),
inference(clausify,[status(thm)],[f_859_2]) ).
cnf(f_859_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2768),U_2770),U_2771),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2769),U_2770),U_2772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2771,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_2769,U_2768)),U_2770),U_2772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2768,U_2769) ),
inference(clausify,[status(thm)],[f_859_2]) ).
fof(f_860_1,plain,
! [V_n,V_m,V_u,V_j,V_i] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2]) ).
fof(f_860_2,plain,
! [U_2777,U_2776,U_2775,U_2774,U_2773] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2773),U_2775),U_2776),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2774),U_2775),U_2777)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2776,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_2774,U_2773)),U_2775),U_2777))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2773,U_2774) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
cnf(f_860_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2773),U_2775),U_2776),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2774),U_2775),U_2777)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2776,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_2774,U_2773)),U_2775),U_2777))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2773,U_2774) ),
inference(clausify,[status(thm)],[f_860_2]) ).
fof(f_861_1,plain,
! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)
| V_m_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2) )
& ( V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2]) ).
fof(f_861_2,plain,
! [U_2782,U_2781,U_2780,U_2779,U_2778] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2778),U_2780),U_2781) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2780),U_2782)
| U_2781 != 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_2779,U_2778)),U_2780),U_2782) )
& ( U_2781 = 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_2779,U_2778)),U_2780),U_2782)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2778),U_2780),U_2781) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2780),U_2782) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2778,U_2779) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
cnf(f_861_3,plain,
( U_2781 = 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_2779,U_2778)),U_2780),U_2782)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2778),U_2780),U_2781) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2780),U_2782)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2778,U_2779) ),
inference(clausify,[status(thm)],[f_861_2]) ).
cnf(f_861_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2778),U_2780),U_2781) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2780),U_2782)
| U_2781 != 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_2779,U_2778)),U_2780),U_2782)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2778,U_2779) ),
inference(clausify,[status(thm)],[f_861_2]) ).
fof(f_862_1,plain,
! [V_c,V_p,T_a] :
( c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__synthetic__div]) ).
fof(f_862_2,plain,
! [U_2785,U_2784,U_2783] :
( c_Polynomial_Odegree(U_2783,c_Polynomial_Osynthetic__div(U_2783,U_2784,U_2785)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(U_2783,U_2784),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(U_2783) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
cnf(f_862_3,plain,
( c_Polynomial_Odegree(U_2783,c_Polynomial_Osynthetic__div(U_2783,U_2784,U_2785)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(U_2783,U_2784),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__0(U_2783) ),
inference(clausify,[status(thm)],[f_862_2]) ).
fof(f_863_1,plain,
! [V_n] :
( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred_H]) ).
fof(f_863_2,plain,
! [U_2786] :
( U_2786 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2786,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2786) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
cnf(f_863_3,plain,
( U_2786 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2786,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2786) ),
inference(clausify,[status(thm)],[f_863_2]) ).
fof(f_864_1,plain,
! [V_n] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__diff__1]) ).
fof(f_864_2,plain,
! [U_2787] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2787,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2787
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2787) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
cnf(f_864_3,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2787,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2787
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2787) ),
inference(clausify,[status(thm)],[f_864_2]) ).
fof(f_865_1,plain,
! [V_n,V_m] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
| V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__if]) ).
fof(f_865_2,plain,
! [U_2789,U_2788] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2788,U_2789) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2788,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2789))
| U_2788 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2788,U_2789) = U_2789
| U_2788 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
fof(f_865_3,plain,
( ! [U_2793,U_2791] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2791,U_2793) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2791,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2793))
| U_2791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2792,U_2790] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2790,U_2792) = U_2792
| U_2790 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_865_2]) ).
cnf(f_865_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2790,U_2792) = U_2792
| U_2790 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_865_3]) ).
cnf(f_865_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2791,U_2793) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2791,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2793))
| U_2791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_865_3]) ).
fof(f_866_1,plain,
! [V_nb_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2]) ).
fof(f_866_2,plain,
! [U_2798,U_2797,U_2796,U_2795,U_2794] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2796),U_2797),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2795),U_2796),U_2798))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2797,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_2795,U_2794)),U_2796),U_2798)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2797,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_2795,U_2794)),U_2796),U_2798))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2796),U_2797),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2795),U_2796),U_2798)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2794,U_2795) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
cnf(f_866_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2797,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_2795,U_2794)),U_2796),U_2798))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2796),U_2797),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2795),U_2796),U_2798))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2794,U_2795) ),
inference(clausify,[status(thm)],[f_866_2]) ).
cnf(f_866_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2794),U_2796),U_2797),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2795),U_2796),U_2798))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2797,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_2795,U_2794)),U_2796),U_2798))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2794,U_2795) ),
inference(clausify,[status(thm)],[f_866_2]) ).
fof(f_867_1,plain,
! [V_nb_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_nb_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_nb_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1]) ).
fof(f_867_2,plain,
! [U_2803,U_2802,U_2801,U_2800,U_2799] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2800),U_2801),U_2802),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2799),U_2801),U_2803))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2800,U_2799)),U_2801),U_2802),U_2803) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2800,U_2799)),U_2801),U_2802),U_2803)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2800),U_2801),U_2802),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2799),U_2801),U_2803)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2799,U_2800) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
cnf(f_867_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2800,U_2799)),U_2801),U_2802),U_2803)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2800),U_2801),U_2802),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2799),U_2801),U_2803))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2799,U_2800) ),
inference(clausify,[status(thm)],[f_867_2]) ).
cnf(f_867_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2800),U_2801),U_2802),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2799),U_2801),U_2803))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2800,U_2799)),U_2801),U_2802),U_2803)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2799,U_2800) ),
inference(clausify,[status(thm)],[f_867_2]) ).
fof(f_868_1,plain,
! [V_n,V_m] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
| V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__if]) ).
fof(f_868_2,plain,
! [U_2805,U_2804] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2804),U_2805) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2804,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2805))
| U_2804 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2804),U_2805) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2804 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
fof(f_868_3,plain,
( ! [U_2809,U_2807] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2807,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2809))
| U_2807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2808,U_2806] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2806),U_2808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2806 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_868_2]) ).
cnf(f_868_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2806),U_2808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2806 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_868_3]) ).
cnf(f_868_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2807),U_2809) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2807,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2809))
| U_2807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_868_3]) ).
fof(f_869_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_869_2,plain,
! [U_2811,U_2810] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2811),U_2810) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2811),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2811),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2810,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2811),U_2810) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2810 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
fof(f_869_3,plain,
( ! [U_2815,U_2813] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2815),U_2813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2815),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2815),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2813,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2814,U_2812] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2814),U_2812) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_869_2]) ).
cnf(f_869_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2814),U_2812) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_869_3]) ).
cnf(f_869_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2815),U_2813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2815),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2815),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2813,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_869_3]) ).
fof(f_870_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__diff]) ).
fof(f_870_2,plain,
! [U_2818,U_2817,U_2816] :
( c_Groups_Ominus__class_Ominus(U_2816,hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2818),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2816),c_Groups_Ominus__class_Ominus(U_2816,U_2817,U_2818)),c_Groups_Oplus__class_Oplus(U_2816,U_2817,U_2818))
| ~ class_Rings_Ocomm__ring__1(U_2816) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
cnf(f_870_3,plain,
( c_Groups_Ominus__class_Ominus(U_2816,hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2817),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2816),U_2818),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2816),c_Groups_Ominus__class_Ominus(U_2816,U_2817,U_2818)),c_Groups_Oplus__class_Oplus(U_2816,U_2817,U_2818))
| ~ class_Rings_Ocomm__ring__1(U_2816) ),
inference(clausify,[status(thm)],[f_870_2]) ).
fof(f_871_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_871_2,plain,
! [U_2821,U_2820,U_2819] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2819),U_2821),U_2820) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2819),U_2821),hAPP(hAPP(c_Power_Opower__class_Opower(U_2819),U_2821),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2820,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2819),U_2821),U_2820) = c_Groups_Oone__class_Oone(U_2819)
| U_2820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Power_Opower(U_2819) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
cnf(f_871_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2819),U_2821),U_2820) = c_Groups_Oone__class_Oone(U_2819)
| U_2820 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(U_2819) ),
inference(clausify,[status(thm)],[f_871_2]) ).
cnf(f_871_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2819),U_2821),U_2820) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2819),U_2821),hAPP(hAPP(c_Power_Opower__class_Opower(U_2819),U_2821),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2820,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(U_2819) ),
inference(clausify,[status(thm)],[f_871_2]) ).
fof(f_872_1,plain,
! [V_y,V_n,V_p,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_lemma__realpow__diff]) ).
fof(f_872_2,plain,
! [U_2825,U_2824,U_2823,U_2822] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2822),U_2825),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2824),U_2823)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2822),hAPP(hAPP(c_Power_Opower__class_Opower(U_2822),U_2825),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2824,U_2823))),U_2825)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2823,U_2824)
| ~ class_Groups_Omonoid__mult(U_2822) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
cnf(f_872_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2822),U_2825),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2824),U_2823)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2822),hAPP(hAPP(c_Power_Opower__class_Opower(U_2822),U_2825),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2824,U_2823))),U_2825)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2823,U_2824)
| ~ class_Groups_Omonoid__mult(U_2822) ),
inference(clausify,[status(thm)],[f_872_2]) ).
fof(f_873_1,plain,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(f_873_2,plain,
! [U_2827,U_2826] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2826,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2827)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2826,U_2827),
inference(variable_rename,[status(thm)],[f_873_1]) ).
cnf(f_873_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2826,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2827)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2826,U_2827),
inference(clausify,[status(thm)],[f_873_2]) ).
fof(f_874_1,plain,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).
fof(f_874_2,plain,
! [U_2829,U_2828] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2828,U_2829) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2828,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2829)),
inference(variable_rename,[status(thm)],[f_874_1]) ).
cnf(f_874_3,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2828,U_2829) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2828,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2829)),
inference(clausify,[status(thm)],[f_874_2]) ).
fof(f_875_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).
fof(f_875_2,plain,
! [U_2831,U_2830] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2831)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2830,U_2831),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2830,U_2831),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2831) ) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
fof(f_875_3,plain,
( ! [U_2835,U_2833] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2833,U_2835)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2833,U_2835),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2834,U_2832] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2832,U_2834),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2832,U_2834) ) ),
inference(miniscope,[status(thm)],[f_875_2]) ).
cnf(f_875_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2832,U_2834),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2832,U_2834) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2833,U_2835)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2833,U_2835),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_875_3]) ).
fof(f_876_1,plain,
! [V_q,V_n,V_p,T_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__diff__less]) ).
fof(f_876_2,plain,
! [U_2839,U_2838,U_2837,U_2836] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_2836,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2836),U_2837,U_2839)),U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_2836,U_2839),U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_2836,U_2837),U_2838)
| ~ class_Groups_Oab__group__add(U_2836) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
cnf(f_876_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_2836,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2836),U_2837,U_2839)),U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_2836,U_2839),U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_2836,U_2837),U_2838)
| ~ class_Groups_Oab__group__add(U_2836) ),
inference(clausify,[status(thm)],[f_876_2]) ).
fof(f_877_1,plain,
! [V_q,V_n,V_p,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_degree__diff__le]) ).
fof(f_877_2,plain,
! [U_2843,U_2842,U_2841,U_2840] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2840,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2840),U_2841,U_2843)),U_2842)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2840,U_2843),U_2842)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2840,U_2841),U_2842)
| ~ class_Groups_Oab__group__add(U_2840) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
cnf(f_877_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2840,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2840),U_2841,U_2843)),U_2842)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2840,U_2843),U_2842)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Polynomial_Odegree(U_2840,U_2841),U_2842)
| ~ class_Groups_Oab__group__add(U_2840) ),
inference(clausify,[status(thm)],[f_877_2]) ).
fof(f_878_1,plain,
! [V_q,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J]) ).
fof(f_878_2,plain,
! [U_2845,U_2844] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2844),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2844)),U_2845) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2844),U_2845)
| ~ class_Groups_Oab__group__add(U_2844) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
cnf(f_878_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2844),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2844)),U_2845) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2844),U_2845)
| ~ class_Groups_Oab__group__add(U_2844) ),
inference(clausify,[status(thm)],[f_878_2]) ).
fof(f_879_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD]) ).
fof(f_879_2,plain,
! [U_2848,U_2847,U_2846] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2846),U_2847))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2846),U_2848))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2846),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2847,U_2848))) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
cnf(f_879_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2846),U_2847))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2846),U_2848))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2846),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2847,U_2848))) ),
inference(clausify,[status(thm)],[f_879_2]) ).
fof(f_880_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
| ( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
& V_x_2 != V_y_2 ) )
& ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def]) ).
fof(f_880_2,plain,
! [U_2851,U_2850,U_2849] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2849),U_2850,U_2851)
| ( ~ c_Polynomial_Opos__poly(U_2849,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2849),U_2851,U_2850))
& U_2850 != U_2851 ) )
& ( c_Polynomial_Opos__poly(U_2849,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2849),U_2851,U_2850))
| U_2850 = U_2851
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2849),U_2850,U_2851) ) )
| ~ class_Rings_Olinordered__idom(U_2849) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
cnf(f_880_3,plain,
( c_Polynomial_Opos__poly(U_2849,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2849),U_2851,U_2850))
| U_2850 = U_2851
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2849),U_2850,U_2851)
| ~ class_Rings_Olinordered__idom(U_2849) ),
inference(clausify,[status(thm)],[f_880_2]) ).
cnf(f_880_4,plain,
( U_2850 != U_2851
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2849),U_2850,U_2851)
| ~ class_Rings_Olinordered__idom(U_2849) ),
inference(clausify,[status(thm)],[f_880_2]) ).
cnf(f_880_5,plain,
( ~ c_Polynomial_Opos__poly(U_2849,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2849),U_2851,U_2850))
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2849),U_2850,U_2851)
| ~ class_Rings_Olinordered__idom(U_2849) ),
inference(clausify,[status(thm)],[f_880_2]) ).
fof(f_881_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
| ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) )
& ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__poly__def]) ).
fof(f_881_2,plain,
! [U_2854,U_2853,U_2852] :
( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2852),U_2853,U_2854)
| ~ c_Polynomial_Opos__poly(U_2852,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2852),U_2854,U_2853)) )
& ( c_Polynomial_Opos__poly(U_2852,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2852),U_2854,U_2853))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2852),U_2853,U_2854) ) )
| ~ class_Rings_Olinordered__idom(U_2852) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
cnf(f_881_3,plain,
( c_Polynomial_Opos__poly(U_2852,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2852),U_2854,U_2853))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2852),U_2853,U_2854)
| ~ class_Rings_Olinordered__idom(U_2852) ),
inference(clausify,[status(thm)],[f_881_2]) ).
cnf(f_881_4,plain,
( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_2852),U_2853,U_2854)
| ~ c_Polynomial_Opos__poly(U_2852,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2852),U_2854,U_2853))
| ~ class_Rings_Olinordered__idom(U_2852) ),
inference(clausify,[status(thm)],[f_881_2]) ).
fof(f_882_1,plain,
! [V_p,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J]) ).
fof(f_882_2,plain,
! [U_2856,U_2855] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2855),U_2856,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2855))) = U_2856
| ~ class_Groups_Oab__group__add(U_2855) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
cnf(f_882_3,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2855),U_2856,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2855))) = U_2856
| ~ class_Groups_Oab__group__add(U_2855) ),
inference(clausify,[status(thm)],[f_882_2]) ).
fof(f_883_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_883_2,plain,
! [U_2859,U_2858,U_2857] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2857,U_2858)),U_2859) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2857),U_2859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2858),U_2859)),
inference(variable_rename,[status(thm)],[f_883_1]) ).
cnf(f_883_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2857,U_2858)),U_2859) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2857),U_2859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2858),U_2859)),
inference(clausify,[status(thm)],[f_883_2]) ).
fof(f_884_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_884_2,plain,
! [U_2862,U_2861,U_2860] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2860),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2861,U_2862)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2860),U_2861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2860),U_2862)),
inference(variable_rename,[status(thm)],[f_884_1]) ).
cnf(f_884_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2860),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2861,U_2862)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2860),U_2861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2860),U_2862)),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).
fof(f_885_2,plain,
! [U_2864,U_2863] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2863,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2864,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2863,U_2864) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2863,U_2864)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2863,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2864,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
fof(f_885_3,plain,
( ! [U_2868,U_2866] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2866,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2868,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2866,U_2868) )
& ! [U_2867,U_2865] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2865,U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2865,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2867,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_885_2]) ).
cnf(f_885_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2865,U_2867)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2865,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2867,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2866,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2868,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2866,U_2868) ),
inference(clausify,[status(thm)],[f_885_3]) ).
fof(f_886_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus]) ).
fof(f_886_2,plain,
! [U_2871,U_2870,U_2869] :
( c_Groups_Ominus__class_Ominus(U_2869,c_Groups_Ouminus__class_Ouminus(U_2869,U_2870),c_Groups_Ouminus__class_Ouminus(U_2869,U_2871)) = c_Groups_Ouminus__class_Ouminus(U_2869,c_Groups_Ominus__class_Ominus(U_2869,U_2870,U_2871))
| ~ class_Groups_Oab__group__add(U_2869) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
cnf(f_886_3,plain,
( c_Groups_Ominus__class_Ominus(U_2869,c_Groups_Ouminus__class_Ouminus(U_2869,U_2870),c_Groups_Ouminus__class_Ouminus(U_2869,U_2871)) = c_Groups_Ouminus__class_Ouminus(U_2869,c_Groups_Ominus__class_Ominus(U_2869,U_2870,U_2871))
| ~ class_Groups_Oab__group__add(U_2869) ),
inference(clausify,[status(thm)],[f_886_2]) ).
fof(f_887_1,plain,
! [V_k,V_m] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ),
inference(fof_nnf,[status(thm)],[fact_int__power__div__base]) ).
fof(f_887_2,plain,
! [U_2873,U_2872] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2873),U_2872),U_2873) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2873),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2872,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2873)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2872) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
cnf(f_887_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2873),U_2872),U_2873) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2873),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2872,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2873)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2872) ),
inference(clausify,[status(thm)],[f_887_2]) ).
fof(f_888_1,plain,
! [V_k_2,V_i_2] :
( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff]) ).
fof(f_888_2,plain,
! [U_2875,U_2874] :
( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2874,U_2875) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2875,U_2874)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2874,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2874,U_2875)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2874) )
& U_2875 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2875,U_2874)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2874,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2874,U_2875)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2874) )
| U_2875 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2874,U_2875) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
fof(f_888_3,plain,
( ! [U_2879,U_2877] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2877,U_2879) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2879,U_2877)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2877,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2877,U_2879)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2877) )
& U_2879 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2878,U_2876] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2878,U_2876)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2876,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2876,U_2878)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2876) )
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2876,U_2878) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_888_2]) ).
cnf(f_888_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2876,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2876)
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2876,U_2878) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_888_3]) ).
cnf(f_888_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2878,U_2876)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2876)
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2876,U_2878) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_888_3]) ).
cnf(f_888_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2876,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2876,U_2878)
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2876,U_2878) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_888_3]) ).
cnf(f_888_7,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2878,U_2876)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2876,U_2878)
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2876,U_2878) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_888_3]) ).
cnf(f_888_8,plain,
( U_2879 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2877,U_2879) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_888_3]) ).
cnf(f_888_9,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2877,U_2879)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2877)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2877,U_2879) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_888_3]) ).
cnf(f_888_10,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2879,U_2877)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2877,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2877,U_2879) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_888_3]) ).
fof(f_889_1,plain,
! [V_aa_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff]) ).
fof(f_889_2,plain,
! [U_2881,U_2880] :
( ( ( 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_2881,U_2880))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2881) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2881)
| ~ 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_2881,U_2880)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2880) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
cnf(f_889_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2881)
| ~ 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_2881,U_2880))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2880) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2881,U_2880))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2881)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2880) ),
inference(clausify,[status(thm)],[f_889_2]) ).
fof(f_890_1,plain,
! [V_i_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff]) ).
fof(f_890_2,plain,
! [U_2883,U_2882] :
( ( ( 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_2883,U_2882))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2882,U_2883) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2882,U_2883)
| ~ 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_2883,U_2882)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2882) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
cnf(f_890_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2882,U_2883)
| ~ 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_2883,U_2882))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2882) ),
inference(clausify,[status(thm)],[f_890_2]) ).
cnf(f_890_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2883,U_2882))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2882,U_2883)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2882) ),
inference(clausify,[status(thm)],[f_890_2]) ).
fof(f_891_1,plain,
! [V_b_2,V_aa_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_aa_2) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_aa_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2) ),
inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff]) ).
fof(f_891_2,plain,
! [U_2885,U_2884] :
( ( ( 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_2884,U_2885))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2885)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2885,U_2884) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2885)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2885,U_2884) )
| ~ 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_2884,U_2885)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2884) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
cnf(f_891_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2885,U_2884)
| ~ 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_2884,U_2885))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2884) ),
inference(clausify,[status(thm)],[f_891_2]) ).
cnf(f_891_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2885)
| ~ 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_2884,U_2885))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2884) ),
inference(clausify,[status(thm)],[f_891_2]) ).
cnf(f_891_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2884,U_2885))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2885)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2885,U_2884)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2884) ),
inference(clausify,[status(thm)],[f_891_2]) ).
fof(f_892_1,plain,
! [V_b,V_b_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2]) ).
fof(f_892_2,plain,
! [U_2888,U_2887,U_2886] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2886,U_2888),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2886,U_2887))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2887,U_2888)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2887)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2886) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
cnf(f_892_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2886,U_2888),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2886,U_2887))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2887,U_2888)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2887)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2886) ),
inference(clausify,[status(thm)],[f_892_2]) ).
fof(f_893_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0]) ).
fof(f_893_2,plain,
! [U_2890,U_2889] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2889,U_2890),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2890,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2889) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
cnf(f_893_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2889,U_2890),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2890,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2889) ),
inference(clausify,[status(thm)],[f_893_2]) ).
fof(f_894_1,plain,
! [V_b,V_a] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial]) ).
fof(f_894_2,plain,
! [U_2892,U_2891] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2891,U_2892) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2891,U_2892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2891) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
cnf(f_894_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2891,U_2892) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2891,U_2892)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2891) ),
inference(clausify,[status(thm)],[f_894_2]) ).
fof(f_895_1,plain,
! [V_aa_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff]) ).
fof(f_895_2,plain,
! [U_2894,U_2893] :
( ( ( 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_2894,U_2893))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2894,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2894,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2894,U_2893)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2893,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
cnf(f_895_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2894,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2894,U_2893))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2893,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_895_2]) ).
cnf(f_895_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2894,U_2893))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2894,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2893,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_895_2]) ).
fof(f_896_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0]) ).
fof(f_896_2,plain,
! [U_2896,U_2895] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2895,U_2896),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2896)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2895,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
cnf(f_896_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2895,U_2896),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2896)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2895,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_896_2]) ).
fof(f_897_1,plain,
! [V_b,V_b_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg]) ).
fof(f_897_2,plain,
! [U_2899,U_2898,U_2897] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2897,U_2898),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2897,U_2899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2898,U_2899)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2898)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2897,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
cnf(f_897_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2897,U_2898),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2897,U_2899))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2898,U_2899)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2898)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2897,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_897_2]) ).
fof(f_898_1,plain,
! [V_b,V_a] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial]) ).
fof(f_898_2,plain,
! [U_2901,U_2900] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2900,U_2901) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2901,U_2900)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2900,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
cnf(f_898_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2900,U_2901) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2901,U_2900)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2900,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_898_2]) ).
fof(f_899_1,plain,
! [V_b,V_a_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono1]) ).
fof(f_899_2,plain,
! [U_2904,U_2903,U_2902] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2902,U_2904),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2903,U_2904))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2902,U_2903) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
cnf(f_899_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2902,U_2904),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2903,U_2904))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2902,U_2903) ),
inference(clausify,[status(thm)],[f_899_2]) ).
fof(f_900_1,plain,
! [V_b,V_a_H,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg]) ).
fof(f_900_2,plain,
! [U_2907,U_2906,U_2905] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2906,U_2907),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2905,U_2907))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2907,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2905,U_2906) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
cnf(f_900_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2906,U_2907),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2905,U_2907))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2907,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2905,U_2906) ),
inference(clausify,[status(thm)],[f_900_2]) ).
fof(f_901_1,plain,
! [V_k,V_x] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_int__div__less__self]) ).
fof(f_901_2,plain,
! [U_2909,U_2908] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2908,U_2909),U_2908)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2909)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2908) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
cnf(f_901_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2908,U_2909),U_2908)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2909)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2908) ),
inference(clausify,[status(thm)],[f_901_2]) ).
fof(f_902_1,plain,
! [V_b,V_a,V_c] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),V_c)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_c) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq]) ).
fof(f_902_2,plain,
! [U_2912,U_2911,U_2910] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2911,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2912),U_2910)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2911,U_2912),U_2910)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2910) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
cnf(f_902_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2911,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2912),U_2910)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2911,U_2912),U_2910)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2910) ),
inference(clausify,[status(thm)],[f_902_2]) ).
fof(f_903_1,plain,
! [V_y,V_x,V_z,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__add]) ).
fof(f_903_2,plain,
! [U_2916,U_2915,U_2914,U_2913] :
( c_Divides_Odiv__class_Odiv(U_2913,c_Groups_Oplus__class_Oplus(U_2913,U_2915,U_2916),U_2914) = c_Groups_Oplus__class_Oplus(U_2913,c_Divides_Odiv__class_Odiv(U_2913,U_2915,U_2914),c_Divides_Odiv__class_Odiv(U_2913,U_2916,U_2914))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2913),U_2914),U_2916))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2913),U_2914),U_2915))
| ~ class_Divides_Osemiring__div(U_2913) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
cnf(f_903_3,plain,
( c_Divides_Odiv__class_Odiv(U_2913,c_Groups_Oplus__class_Oplus(U_2913,U_2915,U_2916),U_2914) = c_Groups_Oplus__class_Oplus(U_2913,c_Divides_Odiv__class_Odiv(U_2913,U_2915,U_2914),c_Divides_Odiv__class_Odiv(U_2913,U_2916,U_2914))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2913),U_2914),U_2916))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2913),U_2914),U_2915))
| ~ class_Divides_Osemiring__div(U_2913) ),
inference(clausify,[status(thm)],[f_903_2]) ).
fof(f_904_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J]) ).
fof(f_904_2,plain,
! [U_2918,U_2917] :
( 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_2917,U_2918))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2918)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2917) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
cnf(f_904_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2917,U_2918))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2918)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2917) ),
inference(clausify,[status(thm)],[f_904_2]) ).
fof(f_905_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_905_2,plain,
! [U_2922,U_2921,U_2920,U_2919] :
( c_Divides_Odiv__class_Odiv(U_2919,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2919),U_2920),U_2921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2919),U_2920),U_2922)) = c_Divides_Odiv__class_Odiv(U_2919,U_2921,U_2922)
| U_2920 = c_Groups_Ozero__class_Ozero(U_2919)
| ~ class_Divides_Osemiring__div(U_2919) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
cnf(f_905_3,plain,
( c_Divides_Odiv__class_Odiv(U_2919,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2919),U_2920),U_2921),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2919),U_2920),U_2922)) = c_Divides_Odiv__class_Odiv(U_2919,U_2921,U_2922)
| U_2920 = c_Groups_Ozero__class_Ozero(U_2919)
| ~ class_Divides_Osemiring__div(U_2919) ),
inference(clausify,[status(thm)],[f_905_2]) ).
fof(f_906_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_906_2,plain,
! [U_2926,U_2925,U_2924,U_2923] :
( c_Divides_Odiv__class_Odiv(U_2923,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2923),U_2925),U_2924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2923),U_2926),U_2924)) = c_Divides_Odiv__class_Odiv(U_2923,U_2925,U_2926)
| U_2924 = c_Groups_Ozero__class_Ozero(U_2923)
| ~ class_Divides_Osemiring__div(U_2923) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
cnf(f_906_3,plain,
( c_Divides_Odiv__class_Odiv(U_2923,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2923),U_2925),U_2924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2923),U_2926),U_2924)) = c_Divides_Odiv__class_Odiv(U_2923,U_2925,U_2926)
| U_2924 = c_Groups_Ozero__class_Ozero(U_2923)
| ~ class_Divides_Osemiring__div(U_2923) ),
inference(clausify,[status(thm)],[f_906_2]) ).
fof(f_907_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_907_2,plain,
! [U_2929,U_2928,U_2927] :
( c_Divides_Odiv__class_Odiv(U_2927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2927),U_2928),U_2929),U_2928) = U_2929
| U_2928 = c_Groups_Ozero__class_Ozero(U_2927)
| ~ class_Divides_Osemiring__div(U_2927) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
cnf(f_907_3,plain,
( c_Divides_Odiv__class_Odiv(U_2927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2927),U_2928),U_2929),U_2928) = U_2929
| U_2928 = c_Groups_Ozero__class_Ozero(U_2927)
| ~ class_Divides_Osemiring__div(U_2927) ),
inference(clausify,[status(thm)],[f_907_2]) ).
fof(f_908_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_908_2,plain,
! [U_2932,U_2931,U_2930] :
( c_Divides_Odiv__class_Odiv(U_2930,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2930),U_2932),U_2931),U_2931) = U_2932
| U_2931 = c_Groups_Ozero__class_Ozero(U_2930)
| ~ class_Divides_Osemiring__div(U_2930) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
cnf(f_908_3,plain,
( c_Divides_Odiv__class_Odiv(U_2930,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2930),U_2932),U_2931),U_2931) = U_2932
| U_2931 = c_Groups_Ozero__class_Ozero(U_2930)
| ~ class_Divides_Osemiring__div(U_2930) ),
inference(clausify,[status(thm)],[f_908_2]) ).
fof(f_909_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_909_2,plain,
! [U_2936,U_2935,U_2934,U_2933] :
( ( ( c_Divides_Odiv__class_Odiv(U_2933,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2936)) = c_Divides_Odiv__class_Odiv(U_2933,U_2935,U_2936)
| U_2934 = c_Groups_Ozero__class_Ozero(U_2933) )
& ( c_Divides_Odiv__class_Odiv(U_2933,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2936)) = c_Groups_Ozero__class_Ozero(U_2933)
| U_2934 != c_Groups_Ozero__class_Ozero(U_2933) ) )
| ~ class_Divides_Osemiring__div(U_2933) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
cnf(f_909_3,plain,
( c_Divides_Odiv__class_Odiv(U_2933,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2936)) = c_Groups_Ozero__class_Ozero(U_2933)
| U_2934 != c_Groups_Ozero__class_Ozero(U_2933)
| ~ class_Divides_Osemiring__div(U_2933) ),
inference(clausify,[status(thm)],[f_909_2]) ).
cnf(f_909_4,plain,
( c_Divides_Odiv__class_Odiv(U_2933,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2933),U_2934),U_2936)) = c_Divides_Odiv__class_Odiv(U_2933,U_2935,U_2936)
| U_2934 = c_Groups_Ozero__class_Ozero(U_2933)
| ~ class_Divides_Osemiring__div(U_2933) ),
inference(clausify,[status(thm)],[f_909_2]) ).
fof(f_910_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel]) ).
fof(f_910_2,plain,
! [U_2939,U_2938,U_2937] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2937),U_2938),c_Divides_Odiv__class_Odiv(U_2937,U_2939,U_2938)) = U_2939
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2937),U_2938),U_2939))
| ~ class_Divides_Osemiring__div(U_2937) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
cnf(f_910_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2937),U_2938),c_Divides_Odiv__class_Odiv(U_2937,U_2939,U_2938)) = U_2939
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2937),U_2938),U_2939))
| ~ class_Divides_Osemiring__div(U_2937) ),
inference(clausify,[status(thm)],[f_910_2]) ).
fof(f_911_1,plain,
! [V_a,V_b,V_c,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__swap]) ).
fof(f_911_2,plain,
! [U_2943,U_2942,U_2941,U_2940] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2940),U_2943),c_Divides_Odiv__class_Odiv(U_2940,U_2942,U_2941)) = c_Divides_Odiv__class_Odiv(U_2940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2940),U_2943),U_2942),U_2941)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2940),U_2941),U_2942))
| ~ class_Divides_Osemiring__div(U_2940) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
cnf(f_911_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2940),U_2943),c_Divides_Odiv__class_Odiv(U_2940,U_2942,U_2941)) = c_Divides_Odiv__class_Odiv(U_2940,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2940),U_2943),U_2942),U_2941)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2940),U_2941),U_2942))
| ~ class_Divides_Osemiring__div(U_2940) ),
inference(clausify,[status(thm)],[f_911_2]) ).
fof(f_912_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self]) ).
fof(f_912_2,plain,
! [U_2946,U_2945,U_2944] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2944),c_Divides_Odiv__class_Odiv(U_2944,U_2946,U_2945)),U_2945) = U_2946
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2944),U_2945),U_2946))
| ~ class_Divides_Osemiring__div(U_2944) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
cnf(f_912_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2944),c_Divides_Odiv__class_Odiv(U_2944,U_2946,U_2945)),U_2945) = U_2946
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2944),U_2945),U_2946))
| ~ class_Divides_Osemiring__div(U_2944) ),
inference(clausify,[status(thm)],[f_912_2]) ).
fof(f_913_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__mult]) ).
fof(f_913_2,plain,
! [U_2950,U_2949,U_2948,U_2947] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2947),c_Divides_Odiv__class_Odiv(U_2947,U_2949,U_2948)),U_2950) = c_Divides_Odiv__class_Odiv(U_2947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2947),U_2949),U_2950),U_2948)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2947),U_2948),U_2949))
| ~ class_Divides_Osemiring__div(U_2947) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
cnf(f_913_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2947),c_Divides_Odiv__class_Odiv(U_2947,U_2949,U_2948)),U_2950) = c_Divides_Odiv__class_Odiv(U_2947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2947),U_2949),U_2950),U_2948)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2947),U_2948),U_2949))
| ~ class_Divides_Osemiring__div(U_2947) ),
inference(clausify,[status(thm)],[f_913_2]) ).
fof(f_914_1,plain,
! [V_w,V_z,V_x,V_y,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd]) ).
fof(f_914_2,plain,
! [U_2955,U_2954,U_2953,U_2952,U_2951] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),c_Divides_Odiv__class_Odiv(U_2951,U_2953,U_2952)),c_Divides_Odiv__class_Odiv(U_2951,U_2955,U_2954)) = c_Divides_Odiv__class_Odiv(U_2951,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2953),U_2955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2952),U_2954))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2951),U_2954),U_2955))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2951),U_2952),U_2953))
| ~ class_Divides_Osemiring__div(U_2951) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
cnf(f_914_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),c_Divides_Odiv__class_Odiv(U_2951,U_2953,U_2952)),c_Divides_Odiv__class_Odiv(U_2951,U_2955,U_2954)) = c_Divides_Odiv__class_Odiv(U_2951,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2953),U_2955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2951),U_2952),U_2954))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2951),U_2954),U_2955))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2951),U_2952),U_2953))
| ~ class_Divides_Osemiring__div(U_2951) ),
inference(clausify,[status(thm)],[f_914_2]) ).
fof(f_915_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0]) ).
fof(f_915_2,plain,
! [U_2957,U_2956] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2956,U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2957)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2956,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
cnf(f_915_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2956,U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2957)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2956,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_915_2]) ).
fof(f_916_1,plain,
! [V_aa_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_aa_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff]) ).
fof(f_916_2,plain,
! [U_2959,U_2958] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2959,U_2958),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2959) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2959)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2959,U_2958),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2958,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
cnf(f_916_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2959)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2959,U_2958),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2958,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_916_2]) ).
cnf(f_916_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2959,U_2958),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2959)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2958,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_916_2]) ).
fof(f_917_1,plain,
! [V_aa_2,V_b_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_aa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ),
inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff]) ).
fof(f_917_2,plain,
! [U_2961,U_2960] :
( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2961,U_2960),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2961,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2961,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2961,U_2960),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2960) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
cnf(f_917_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2961,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2961,U_2960),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2960) ),
inference(clausify,[status(thm)],[f_917_2]) ).
cnf(f_917_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2961,U_2960),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2961,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2960) ),
inference(clausify,[status(thm)],[f_917_2]) ).
fof(f_918_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_918_2,plain,
! [U_2962] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2962) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_918_1]) ).
cnf(f_918_3,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2962) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_918_2]) ).
fof(f_919_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_919_2,plain,
! [U_2964,U_2963] :
( c_Divides_Odiv__class_Odiv(U_2963,U_2964,c_Groups_Ozero__class_Ozero(U_2963)) = c_Groups_Ozero__class_Ozero(U_2963)
| ~ class_Divides_Osemiring__div(U_2963) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
cnf(f_919_3,plain,
( c_Divides_Odiv__class_Odiv(U_2963,U_2964,c_Groups_Ozero__class_Ozero(U_2963)) = c_Groups_Ozero__class_Ozero(U_2963)
| ~ class_Divides_Osemiring__div(U_2963) ),
inference(clausify,[status(thm)],[f_919_2]) ).
fof(f_920_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_920_2,plain,
! [U_2966,U_2965] :
( c_Divides_Odiv__class_Odiv(U_2965,c_Groups_Ozero__class_Ozero(U_2965),U_2966) = c_Groups_Ozero__class_Ozero(U_2965)
| ~ class_Divides_Osemiring__div(U_2965) ),
inference(variable_rename,[status(thm)],[f_920_1]) ).
cnf(f_920_3,plain,
( c_Divides_Odiv__class_Odiv(U_2965,c_Groups_Ozero__class_Ozero(U_2965),U_2966) = c_Groups_Ozero__class_Ozero(U_2965)
| ~ class_Divides_Osemiring__div(U_2965) ),
inference(clausify,[status(thm)],[f_920_2]) ).
fof(f_921_1,plain,
! [V_m,V_n] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel]) ).
fof(f_921_2,plain,
! [U_2968,U_2967] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2967),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2968,U_2967)) = U_2968
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2967),U_2968)) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
cnf(f_921_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2967),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2968,U_2967)) = U_2968
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_2967),U_2968)) ),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_1,plain,
! [V_n,V_x,V_y,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__power]) ).
fof(f_922_2,plain,
! [U_2972,U_2971,U_2970,U_2969] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2969),c_Divides_Odiv__class_Odiv(U_2969,U_2971,U_2970)),U_2972) = c_Divides_Odiv__class_Odiv(U_2969,hAPP(hAPP(c_Power_Opower__class_Opower(U_2969),U_2971),U_2972),hAPP(hAPP(c_Power_Opower__class_Opower(U_2969),U_2970),U_2972))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2969),U_2970),U_2971))
| ~ class_Divides_Osemiring__div(U_2969) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
cnf(f_922_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2969),c_Divides_Odiv__class_Odiv(U_2969,U_2971,U_2970)),U_2972) = c_Divides_Odiv__class_Odiv(U_2969,hAPP(hAPP(c_Power_Opower__class_Opower(U_2969),U_2971),U_2972),hAPP(hAPP(c_Power_Opower__class_Opower(U_2969),U_2970),U_2972))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2969),U_2970),U_2971))
| ~ class_Divides_Osemiring__div(U_2969) ),
inference(clausify,[status(thm)],[f_922_2]) ).
fof(f_923_1,plain,
! [V_c_2,V_b_2,V_aa_2,T_a] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2)),c_Divides_Odiv__class_Odiv(T_a,V_c_2,V_aa_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b_2),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2)),c_Divides_Odiv__class_Odiv(T_a,V_c_2,V_aa_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__dvd__div]) ).
fof(f_923_2,plain,
! [U_2976,U_2975,U_2974,U_2973] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),c_Divides_Odiv__class_Odiv(U_2973,U_2975,U_2974)),c_Divides_Odiv__class_Odiv(U_2973,U_2976,U_2974)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2975),U_2976)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2975),U_2976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),c_Divides_Odiv__class_Odiv(U_2973,U_2975,U_2974)),c_Divides_Odiv__class_Odiv(U_2973,U_2976,U_2974))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2974),U_2976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2974),U_2975))
| ~ class_Divides_Osemiring__div(U_2973) ),
inference(variable_rename,[status(thm)],[f_923_1]) ).
cnf(f_923_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2975),U_2976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),c_Divides_Odiv__class_Odiv(U_2973,U_2975,U_2974)),c_Divides_Odiv__class_Odiv(U_2973,U_2976,U_2974)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2974),U_2976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2974),U_2975))
| ~ class_Divides_Osemiring__div(U_2973) ),
inference(clausify,[status(thm)],[f_923_2]) ).
cnf(f_923_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),c_Divides_Odiv__class_Odiv(U_2973,U_2975,U_2974)),c_Divides_Odiv__class_Odiv(U_2973,U_2976,U_2974)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2975),U_2976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2974),U_2976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2973),U_2974),U_2975))
| ~ class_Divides_Osemiring__div(U_2973) ),
inference(clausify,[status(thm)],[f_923_2]) ).
fof(f_924_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_924_2,plain,
! [U_2978,U_2977] :
( c_Divides_Odiv__class_Odiv(U_2977,U_2978,c_Groups_Oone__class_Oone(U_2977)) = U_2978
| ~ class_Divides_Osemiring__div(U_2977) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
cnf(f_924_3,plain,
( c_Divides_Odiv__class_Odiv(U_2977,U_2978,c_Groups_Oone__class_Oone(U_2977)) = U_2978
| ~ class_Divides_Osemiring__div(U_2977) ),
inference(clausify,[status(thm)],[f_924_2]) ).
fof(f_925_1,plain,
! [V_x,V_y,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__neg]) ).
fof(f_925_2,plain,
! [U_2981,U_2980,U_2979] :
( c_Divides_Odiv__class_Odiv(U_2979,U_2981,c_Groups_Ouminus__class_Ouminus(U_2979,U_2980)) = c_Groups_Ouminus__class_Ouminus(U_2979,c_Divides_Odiv__class_Odiv(U_2979,U_2981,U_2980))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2979),U_2980),U_2981))
| ~ class_Divides_Oring__div(U_2979) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
cnf(f_925_3,plain,
( c_Divides_Odiv__class_Odiv(U_2979,U_2981,c_Groups_Ouminus__class_Ouminus(U_2979,U_2980)) = c_Groups_Ouminus__class_Ouminus(U_2979,c_Divides_Odiv__class_Odiv(U_2979,U_2981,U_2980))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2979),U_2980),U_2981))
| ~ class_Divides_Oring__div(U_2979) ),
inference(clausify,[status(thm)],[f_925_2]) ).
fof(f_926_1,plain,
! [V_x,V_y,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__neg__div]) ).
fof(f_926_2,plain,
! [U_2984,U_2983,U_2982] :
( c_Divides_Odiv__class_Odiv(U_2982,c_Groups_Ouminus__class_Ouminus(U_2982,U_2984),U_2983) = c_Groups_Ouminus__class_Ouminus(U_2982,c_Divides_Odiv__class_Odiv(U_2982,U_2984,U_2983))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2982),U_2983),U_2984))
| ~ class_Divides_Oring__div(U_2982) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
cnf(f_926_3,plain,
( c_Divides_Odiv__class_Odiv(U_2982,c_Groups_Ouminus__class_Ouminus(U_2982,U_2984),U_2983) = c_Groups_Ouminus__class_Ouminus(U_2982,c_Divides_Odiv__class_Odiv(U_2982,U_2984,U_2983))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_2982),U_2983),U_2984))
| ~ class_Divides_Oring__div(U_2982) ),
inference(clausify,[status(thm)],[f_926_2]) ).
fof(f_927_1,plain,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus__zminus]) ).
fof(f_927_2,plain,
! [U_2986,U_2985] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2985),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2986)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2985,U_2986),
inference(variable_rename,[status(thm)],[f_927_1]) ).
cnf(f_927_3,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2985),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2986)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2985,U_2986),
inference(clausify,[status(thm)],[f_927_2]) ).
fof(f_928_1,plain,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_b)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_a),V_b),
inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2]) ).
fof(f_928_2,plain,
! [U_2988,U_2987] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2987,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2988)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2987),U_2988),
inference(variable_rename,[status(thm)],[f_928_1]) ).
cnf(f_928_3,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2987,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2988)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2987),U_2988),
inference(clausify,[status(thm)],[f_928_2]) ).
fof(f_929_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_929_2,plain,
! [U_2989] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2989,U_2989) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2989 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
cnf(f_929_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_2989,U_2989) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2989 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_929_2]) ).
fof(f_930_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_930_2,plain,
! [U_2991,U_2990] :
( c_Divides_Odiv__class_Odiv(U_2990,U_2991,U_2991) = c_Groups_Oone__class_Oone(U_2990)
| U_2991 = c_Groups_Ozero__class_Ozero(U_2990)
| ~ class_Divides_Osemiring__div(U_2990) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
cnf(f_930_3,plain,
( c_Divides_Odiv__class_Odiv(U_2990,U_2991,U_2991) = c_Groups_Oone__class_Oone(U_2990)
| U_2991 = c_Groups_Ozero__class_Ozero(U_2990)
| ~ class_Divides_Osemiring__div(U_2990) ),
inference(clausify,[status(thm)],[f_930_2]) ).
fof(f_931_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self2]) ).
fof(f_931_2,plain,
! [U_2995,U_2994,U_2993,U_2992] :
( c_Divides_Odiv__class_Odiv(U_2992,c_Groups_Oplus__class_Oplus(U_2992,U_2994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2992),U_2993),U_2995)),U_2993) = c_Groups_Oplus__class_Oplus(U_2992,U_2995,c_Divides_Odiv__class_Odiv(U_2992,U_2994,U_2993))
| U_2993 = c_Groups_Ozero__class_Ozero(U_2992)
| ~ class_Divides_Osemiring__div(U_2992) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
cnf(f_931_3,plain,
( c_Divides_Odiv__class_Odiv(U_2992,c_Groups_Oplus__class_Oplus(U_2992,U_2994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2992),U_2993),U_2995)),U_2993) = c_Groups_Oplus__class_Oplus(U_2992,U_2995,c_Divides_Odiv__class_Odiv(U_2992,U_2994,U_2993))
| U_2993 = c_Groups_Ozero__class_Ozero(U_2992)
| ~ class_Divides_Osemiring__div(U_2992) ),
inference(clausify,[status(thm)],[f_931_2]) ).
fof(f_932_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self1]) ).
fof(f_932_2,plain,
! [U_2999,U_2998,U_2997,U_2996] :
( c_Divides_Odiv__class_Odiv(U_2996,c_Groups_Oplus__class_Oplus(U_2996,U_2998,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2996),U_2999),U_2997)),U_2997) = c_Groups_Oplus__class_Oplus(U_2996,U_2999,c_Divides_Odiv__class_Odiv(U_2996,U_2998,U_2997))
| U_2997 = c_Groups_Ozero__class_Ozero(U_2996)
| ~ class_Divides_Osemiring__div(U_2996) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
cnf(f_932_3,plain,
( c_Divides_Odiv__class_Odiv(U_2996,c_Groups_Oplus__class_Oplus(U_2996,U_2998,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2996),U_2999),U_2997)),U_2997) = c_Groups_Oplus__class_Oplus(U_2996,U_2999,c_Divides_Odiv__class_Odiv(U_2996,U_2998,U_2997))
| U_2997 = c_Groups_Ozero__class_Ozero(U_2996)
| ~ class_Divides_Osemiring__div(U_2996) ),
inference(clausify,[status(thm)],[f_932_2]) ).
fof(f_933_1,plain,
! [V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__add__self2]) ).
fof(f_933_2,plain,
! [U_3002,U_3001,U_3000] :
( c_Divides_Odiv__class_Odiv(U_3000,c_Groups_Oplus__class_Oplus(U_3000,U_3002,U_3001),U_3001) = c_Groups_Oplus__class_Oplus(U_3000,c_Divides_Odiv__class_Odiv(U_3000,U_3002,U_3001),c_Groups_Oone__class_Oone(U_3000))
| U_3001 = c_Groups_Ozero__class_Ozero(U_3000)
| ~ class_Divides_Osemiring__div(U_3000) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
cnf(f_933_3,plain,
( c_Divides_Odiv__class_Odiv(U_3000,c_Groups_Oplus__class_Oplus(U_3000,U_3002,U_3001),U_3001) = c_Groups_Oplus__class_Oplus(U_3000,c_Divides_Odiv__class_Odiv(U_3000,U_3002,U_3001),c_Groups_Oone__class_Oone(U_3000))
| U_3001 = c_Groups_Ozero__class_Ozero(U_3000)
| ~ class_Divides_Osemiring__div(U_3000) ),
inference(clausify,[status(thm)],[f_933_2]) ).
fof(f_934_1,plain,
! [V_a,V_b,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__add__self1]) ).
fof(f_934_2,plain,
! [U_3005,U_3004,U_3003] :
( c_Divides_Odiv__class_Odiv(U_3003,c_Groups_Oplus__class_Oplus(U_3003,U_3004,U_3005),U_3004) = c_Groups_Oplus__class_Oplus(U_3003,c_Divides_Odiv__class_Odiv(U_3003,U_3005,U_3004),c_Groups_Oone__class_Oone(U_3003))
| U_3004 = c_Groups_Ozero__class_Ozero(U_3003)
| ~ class_Divides_Osemiring__div(U_3003) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
cnf(f_934_3,plain,
( c_Divides_Odiv__class_Odiv(U_3003,c_Groups_Oplus__class_Oplus(U_3003,U_3004,U_3005),U_3004) = c_Groups_Oplus__class_Oplus(U_3003,c_Divides_Odiv__class_Odiv(U_3003,U_3005,U_3004),c_Groups_Oone__class_Oone(U_3003))
| U_3004 = c_Groups_Ozero__class_Ozero(U_3003)
| ~ class_Divides_Osemiring__div(U_3003) ),
inference(clausify,[status(thm)],[f_934_2]) ).
fof(f_935_1,plain,
! [V_d_2,V_b_2,V_c_2,V_aa_2,T_a] :
( ( ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) = c_Divides_Odiv__class_Odiv(T_a,V_d_2,V_c_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_aa_2),V_d_2)
| c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) != c_Divides_Odiv__class_Odiv(T_a,V_d_2,V_c_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult]) ).
fof(f_935_2,plain,
! [U_3010,U_3009,U_3008,U_3007,U_3006] :
( ( ( c_Divides_Odiv__class_Odiv(U_3006,U_3009,U_3007) = c_Divides_Odiv__class_Odiv(U_3006,U_3010,U_3008)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3009),U_3008) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3007),U_3010) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3009),U_3008) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3007),U_3010)
| c_Divides_Odiv__class_Odiv(U_3006,U_3009,U_3007) != c_Divides_Odiv__class_Odiv(U_3006,U_3010,U_3008) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3006),U_3008),U_3010))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3006),U_3007),U_3009))
| U_3008 = c_Groups_Ozero__class_Ozero(U_3006)
| U_3007 = c_Groups_Ozero__class_Ozero(U_3006)
| ~ class_Divides_Osemiring__div(U_3006) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
cnf(f_935_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3009),U_3008) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3007),U_3010)
| c_Divides_Odiv__class_Odiv(U_3006,U_3009,U_3007) != c_Divides_Odiv__class_Odiv(U_3006,U_3010,U_3008)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3006),U_3008),U_3010))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3006),U_3007),U_3009))
| U_3008 = c_Groups_Ozero__class_Ozero(U_3006)
| U_3007 = c_Groups_Ozero__class_Ozero(U_3006)
| ~ class_Divides_Osemiring__div(U_3006) ),
inference(clausify,[status(thm)],[f_935_2]) ).
cnf(f_935_4,plain,
( c_Divides_Odiv__class_Odiv(U_3006,U_3009,U_3007) = c_Divides_Odiv__class_Odiv(U_3006,U_3010,U_3008)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3009),U_3008) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3006),U_3007),U_3010)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3006),U_3008),U_3010))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3006),U_3007),U_3009))
| U_3008 = c_Groups_Ozero__class_Ozero(U_3006)
| U_3007 = c_Groups_Ozero__class_Ozero(U_3006)
| ~ class_Divides_Osemiring__div(U_3006) ),
inference(clausify,[status(thm)],[f_935_2]) ).
fof(f_936_1,plain,
! [V_c_2,V_b_2,V_aa_2,T_a] :
( ( ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) = V_c_2
| V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_aa_2)
| c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_aa_2) != V_c_2 ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_aa_2),V_b_2))
| V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult]) ).
fof(f_936_2,plain,
! [U_3014,U_3013,U_3012,U_3011] :
( ( ( c_Divides_Odiv__class_Odiv(U_3011,U_3013,U_3012) = U_3014
| U_3013 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3011),U_3014),U_3012) )
& ( U_3013 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3011),U_3014),U_3012)
| c_Divides_Odiv__class_Odiv(U_3011,U_3013,U_3012) != U_3014 ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3011),U_3012),U_3013))
| U_3012 = c_Groups_Ozero__class_Ozero(U_3011)
| ~ class_Divides_Osemiring__div(U_3011) ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
cnf(f_936_3,plain,
( U_3013 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3011),U_3014),U_3012)
| c_Divides_Odiv__class_Odiv(U_3011,U_3013,U_3012) != U_3014
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3011),U_3012),U_3013))
| U_3012 = c_Groups_Ozero__class_Ozero(U_3011)
| ~ class_Divides_Osemiring__div(U_3011) ),
inference(clausify,[status(thm)],[f_936_2]) ).
cnf(f_936_4,plain,
( c_Divides_Odiv__class_Odiv(U_3011,U_3013,U_3012) = U_3014
| U_3013 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3011),U_3014),U_3012)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_3011),U_3012),U_3013))
| U_3012 = c_Groups_Ozero__class_Ozero(U_3011)
| ~ class_Divides_Osemiring__div(U_3011) ),
inference(clausify,[status(thm)],[f_936_2]) ).
fof(f_937_1,plain,
! [V_k_2,V_nb_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2)))
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& ? [B_j] :
( V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& ? [B_j] :
( V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [B_i] :
( hBOOL(hAPP(V_P_2,B_i))
| ! [B_j] :
( V_nb_2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [B_i] :
( hBOOL(hAPP(V_P_2,B_i))
| ! [B_j] :
( V_nb_2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,B_j,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),B_j) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).
fof(f_937_2,plain,
! [U_3025,U_3024,U_3023] :
( ( hBOOL(hAPP(U_3023,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3024,U_3025)))
| ( ? [U_3022] :
( ~ hBOOL(hAPP(U_3023,U_3022))
& ? [U_3021] :
( U_3024 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),U_3022),U_3021)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3025,U_3021) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3025,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ? [U_3020] :
( ~ hBOOL(hAPP(U_3023,U_3020))
& ? [U_3019] :
( U_3024 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),U_3020),U_3019)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3019,U_3025)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3019) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3025) )
| ( ~ hBOOL(hAPP(U_3023,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3025 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_3018] :
( hBOOL(hAPP(U_3023,U_3018))
| ! [U_3017] :
( U_3024 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),U_3018),U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3025,U_3017) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3025,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3016] :
( hBOOL(hAPP(U_3023,U_3016))
| ! [U_3015] :
( U_3024 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3015,U_3025)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3025) )
& ( hBOOL(hAPP(U_3023,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3025 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3023,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3024,U_3025))) ) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
( ! [U_3031,U_3029,U_3027] :
( hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031)))
| ( ? [U_3022] :
( ~ hBOOL(hAPP(U_3027,U_3022))
& ? [U_3021] :
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),U_3022),U_3021)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,U_3021) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ? [U_3020] :
( ~ hBOOL(hAPP(U_3027,U_3020))
& ? [U_3019] :
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),U_3020),U_3019)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3019,U_3031)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3019) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031) )
| ( ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3030,U_3028,U_3026] :
( ( ( ! [U_3018] :
( hBOOL(hAPP(U_3026,U_3018))
| ! [U_3017] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3018),U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,U_3017) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3016] :
( hBOOL(hAPP(U_3026,U_3016))
| ! [U_3015] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3015,U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3030) )
& ( hBOOL(hAPP(U_3026,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3030 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ) ),
inference(miniscope,[status(thm)],[f_937_2]) ).
fof(f_937_4,plain,
( ! [U_3031,U_3029,U_3027] :
( hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031)))
| ( ? [U_3022] :
( ~ hBOOL(hAPP(U_3027,U_3022))
& ? [U_3021] :
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),U_3022),U_3021)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,U_3021) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
& ? [U_3019] :
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),U_3019)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3019,U_3031)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3019) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031) )
| ( ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3030,U_3028,U_3026] :
( ( ( ! [U_3018] :
( hBOOL(hAPP(U_3026,U_3018))
| ! [U_3017] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3018),U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,U_3017) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3016] :
( hBOOL(hAPP(U_3026,U_3016))
| ! [U_3015] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3015,U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3030) )
& ( hBOOL(hAPP(U_3026,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3030 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_3020,sK19(U_3031,U_3029,U_3027))],[f_937_3]) ).
fof(f_937_5,plain,
( ! [U_3031,U_3029,U_3027] :
( hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031)))
| ( ? [U_3022] :
( ~ hBOOL(hAPP(U_3027,U_3022))
& ? [U_3021] :
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),U_3022),U_3021)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,U_3021) ) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
& U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031) )
| ( ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3030,U_3028,U_3026] :
( ( ( ! [U_3018] :
( hBOOL(hAPP(U_3026,U_3018))
| ! [U_3017] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3018),U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,U_3017) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3016] :
( hBOOL(hAPP(U_3026,U_3016))
| ! [U_3015] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3015,U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3030) )
& ( hBOOL(hAPP(U_3026,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3030 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_3019,sK20(U_3031,U_3029,U_3027))],[f_937_4]) ).
fof(f_937_6,plain,
( ! [U_3031,U_3029,U_3027] :
( hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031)))
| ( ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
& ? [U_3021] :
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),U_3021)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3021,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,U_3021) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
& U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031) )
| ( ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3030,U_3028,U_3026] :
( ( ( ! [U_3018] :
( hBOOL(hAPP(U_3026,U_3018))
| ! [U_3017] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3018),U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,U_3017) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3016] :
( hBOOL(hAPP(U_3026,U_3016))
| ! [U_3015] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3015,U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3030) )
& ( hBOOL(hAPP(U_3026,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3030 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_3022,sK21(U_3031,U_3029,U_3027))],[f_937_5]) ).
fof(f_937_7,plain,
( ! [U_3031,U_3029,U_3027] :
( hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031)))
| ( ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
& U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
& U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031) )
| ( ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3030,U_3028,U_3026] :
( ( ( ! [U_3018] :
( hBOOL(hAPP(U_3026,U_3018))
| ! [U_3017] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3018),U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,U_3017) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ! [U_3016] :
( hBOOL(hAPP(U_3026,U_3016))
| ! [U_3015] :
( U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3015,U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3030) )
& ( hBOOL(hAPP(U_3026,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3030 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_3021,sK22(U_3031,U_3029,U_3027))],[f_937_6]) ).
cnf(f_937_8,plain,
( hBOOL(hAPP(U_3026,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3030 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_9,plain,
( hBOOL(hAPP(U_3026,U_3016))
| U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3016),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3015,U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3015)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3030)
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_10,plain,
( hBOOL(hAPP(U_3026,U_3018))
| U_3028 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3030),U_3018),U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3017,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,U_3017)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3030,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(U_3026,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3028,U_3030))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_11,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_12,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_13,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_14,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_15,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_16,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_17,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_18,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_19,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_20,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_21,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_22,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_23,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_24,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_25,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_26,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_27,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_28,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_29,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_30,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_31,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_32,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_33,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_34,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_35,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_36,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_37,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_38,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_39,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_40,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| U_3031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_41,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_42,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_43,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_44,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_45,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3031,sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_46,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_47,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_48,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_49,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_50,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK22(U_3031,U_3029,U_3027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_51,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_52,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_53,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_54,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_55,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK21(U_3031,U_3029,U_3027)),sK22(U_3031,U_3029,U_3027))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_56,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_57,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_58,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,sK20(U_3031,U_3029,U_3027),U_3031)
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_59,plain,
( U_3029 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3031),sK19(U_3031,U_3029,U_3027)),sK20(U_3031,U_3029,U_3027))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
cnf(f_937_60,plain,
( ~ hBOOL(hAPP(U_3027,sK19(U_3031,U_3029,U_3027)))
| ~ hBOOL(hAPP(U_3027,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_3027,sK21(U_3031,U_3029,U_3027)))
| hBOOL(hAPP(U_3027,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3029,U_3031))) ),
inference(clausify,[status(thm)],[f_937_7]) ).
fof(f_938_1,plain,
! [V_r_1,V_y,V_b_1,V_a_1] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_1,V_b_1) = V_y
| V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r_1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_1,V_r_1) )
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) )
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_1,V_b_1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_1) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_1) )
| V_a_1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y),V_r_1) ),
inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__eq]) ).
fof(f_938_2,plain,
! [U_3035,U_3034,U_3033,U_3032] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3032,U_3033) = U_3034
| U_3033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3033,U_3035) )
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3033) )
| ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3035,U_3033)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3035) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3033) )
| U_3032 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3034),U_3035) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
cnf(f_938_3,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3033)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3033)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3032,U_3033) = U_3034
| U_3033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3032 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3034),U_3035) ),
inference(clausify,[status(thm)],[f_938_2]) ).
cnf(f_938_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3033,U_3035)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3033)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3032,U_3033) = U_3034
| U_3033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3032 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3034),U_3035) ),
inference(clausify,[status(thm)],[f_938_2]) ).
cnf(f_938_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3033)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3035,U_3033)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3035)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3032,U_3033) = U_3034
| U_3033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3032 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3034),U_3035) ),
inference(clausify,[status(thm)],[f_938_2]) ).
cnf(f_938_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3033,U_3035)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3035,U_3033)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3035)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3032,U_3033) = U_3034
| U_3033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3032 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3034),U_3035) ),
inference(clausify,[status(thm)],[f_938_2]) ).
fof(f_939_1,plain,
! [V_k,V_l] :
( ( c_SMT_Oz3div(V_k,V_l) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_l)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l) )
& ( c_SMT_Oz3div(V_k,V_l) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_k,V_l)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_l) ) ),
inference(fof_nnf,[status(thm)],[fact_z3div__def]) ).
fof(f_939_2,plain,
! [U_3037,U_3036] :
( ( c_SMT_Oz3div(U_3037,U_3036) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3037,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_3036)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3036) )
& ( c_SMT_Oz3div(U_3037,U_3036) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3037,U_3036)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3036) ) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
fof(f_939_3,plain,
( ! [U_3041,U_3039] :
( c_SMT_Oz3div(U_3041,U_3039) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3041,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_3039)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3039) )
& ! [U_3040,U_3038] :
( c_SMT_Oz3div(U_3040,U_3038) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3040,U_3038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3038) ) ),
inference(miniscope,[status(thm)],[f_939_2]) ).
cnf(f_939_4,plain,
( c_SMT_Oz3div(U_3040,U_3038) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3040,U_3038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3038) ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_5,plain,
( c_SMT_Oz3div(U_3041,U_3039) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3041,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_3039)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3039) ),
inference(clausify,[status(thm)],[f_939_3]) ).
fof(f_940_1,plain,
! [V_x,V_y] :
( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) )
& ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ) ),
inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).
fof(f_940_2,plain,
! [U_3043,U_3042] :
( ( c_Nat__Transfer_Otsub(U_3043,U_3042) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3042,U_3043) )
& ( c_Nat__Transfer_Otsub(U_3043,U_3042) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3043,U_3042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3042,U_3043) ) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
fof(f_940_3,plain,
( ! [U_3047,U_3045] :
( c_Nat__Transfer_Otsub(U_3047,U_3045) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3045,U_3047) )
& ! [U_3046,U_3044] :
( c_Nat__Transfer_Otsub(U_3046,U_3044) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3046,U_3044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3044,U_3046) ) ),
inference(miniscope,[status(thm)],[f_940_2]) ).
cnf(f_940_4,plain,
( c_Nat__Transfer_Otsub(U_3046,U_3044) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3046,U_3044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3044,U_3046) ),
inference(clausify,[status(thm)],[f_940_3]) ).
cnf(f_940_5,plain,
( c_Nat__Transfer_Otsub(U_3047,U_3045) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3045,U_3047) ),
inference(clausify,[status(thm)],[f_940_3]) ).
fof(f_941_1,plain,
! [V_k,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_n),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_k,V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ),
inference(fof_nnf,[status(thm)],[fact_div__le__mono2]) ).
fof(f_941_2,plain,
! [U_3050,U_3049,U_3048] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3050,U_3049),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3050,U_3048))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3048,U_3049)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3048) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
cnf(f_941_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3050,U_3049),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3050,U_3048))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3048,U_3049)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3048) ),
inference(clausify,[status(thm)],[f_941_2]) ).
fof(f_942_1,plain,
! [V_m,V_n] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),V_n) = V_m
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m]) ).
fof(f_942_2,plain,
! [U_3052,U_3051] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3051),U_3052),U_3051) = U_3052
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3051) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
cnf(f_942_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3051),U_3052),U_3051) = U_3052
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3051) ),
inference(clausify,[status(thm)],[f_942_2]) ).
fof(f_943_1,plain,
! [V_m,V_n] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n),V_n) = V_m
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m]) ).
fof(f_943_2,plain,
! [U_3054,U_3053] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3054),U_3053),U_3053) = U_3054
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3053) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
cnf(f_943_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3054),U_3053),U_3053) = U_3054
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3053) ),
inference(clausify,[status(thm)],[f_943_2]) ).
fof(f_944_1,plain,
! [V_n,V_m,V_k] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1]) ).
fof(f_944_2,plain,
! [U_3057,U_3056,U_3055] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3055),U_3056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3055),U_3057)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3056,U_3057)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3055) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
cnf(f_944_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3055),U_3056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3055),U_3057)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3056,U_3057)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3055) ),
inference(clausify,[status(thm)],[f_944_2]) ).
fof(f_945_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__less__dividend]) ).
fof(f_945_2,plain,
! [U_3059,U_3058] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3059,U_3058),U_3059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3058) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
cnf(f_945_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3059,U_3058),U_3059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_3058) ),
inference(clausify,[status(thm)],[f_945_2]) ).
fof(f_946_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n),V_m),
inference(fof_nnf,[status(thm)],[fact_div__le__dividend]) ).
fof(f_946_2,plain,
! [U_3061,U_3060] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3060,U_3061),U_3060),
inference(variable_rename,[status(thm)],[f_946_1]) ).
cnf(f_946_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3060,U_3061),U_3060),
inference(clausify,[status(thm)],[f_946_2]) ).
fof(f_947_1,plain,
! [V_k,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_k),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_n,V_k))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__le__mono]) ).
fof(f_947_2,plain,
! [U_3064,U_3063,U_3062] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3062,U_3064),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3063,U_3064))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3062,U_3063) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
cnf(f_947_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3062,U_3064),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3063,U_3064))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3062,U_3063) ),
inference(clausify,[status(thm)],[f_947_2]) ).
fof(f_948_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_948_2,plain,
! [U_3065] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3065,
inference(variable_rename,[status(thm)],[f_948_1]) ).
cnf(f_948_3,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3065,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3065,
inference(clausify,[status(thm)],[f_948_2]) ).
fof(f_949_1,plain,
! [V_n,V_m] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__less]) ).
fof(f_949_2,plain,
! [U_3067,U_3066] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3066,U_3067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3066,U_3067) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
cnf(f_949_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3066,U_3067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3066,U_3067) ),
inference(clausify,[status(thm)],[f_949_2]) ).
fof(f_950_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_950_2,plain,
! [U_3070,U_3069,U_3068] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3068,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3069),U_3070)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3068,U_3069),U_3070),
inference(variable_rename,[status(thm)],[f_950_1]) ).
cnf(f_950_3,plain,
c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3068,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3069),U_3070)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3068,U_3069),U_3070),
inference(clausify,[status(thm)],[f_950_2]) ).
fof(f_951_1,plain,
! [V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__div__minus__right]) ).
fof(f_951_2,plain,
! [U_3073,U_3072,U_3071] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3071),U_3072,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3071),U_3073)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3071),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3071),U_3072,U_3073))
| ~ class_Fields_Ofield(U_3071) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
cnf(f_951_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3071),U_3072,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3071),U_3073)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3071),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3071),U_3072,U_3073))
| ~ class_Fields_Ofield(U_3071) ),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_1,plain,
! [V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__div__minus__left]) ).
fof(f_952_2,plain,
! [U_3076,U_3075,U_3074] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3074),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3074),U_3075),U_3076) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3074),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3074),U_3075,U_3076))
| ~ class_Fields_Ofield(U_3074) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
cnf(f_952_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3074),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3074),U_3075),U_3076) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3074),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3074),U_3075,U_3076))
| ~ class_Fields_Ofield(U_3074) ),
inference(clausify,[status(thm)],[f_952_2]) ).
fof(f_953_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_y),V_z)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y),V_z)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__div__mult__right]) ).
fof(f_953_2,plain,
! [U_3080,U_3079,U_3078,U_3077] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3077),U_3078,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_3077)),U_3079),U_3080)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3077),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3077),U_3078,U_3079),U_3080)
| ~ class_Fields_Ofield(U_3077) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
cnf(f_953_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3077),U_3078,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_3077)),U_3079),U_3080)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3077),c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3077),U_3078,U_3079),U_3080)
| ~ class_Fields_Ofield(U_3077) ),
inference(clausify,[status(thm)],[f_953_2]) ).
fof(f_954_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_954_2,plain,
! [U_3083,U_3082,U_3081] :
( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3081),U_3082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3081),U_3083)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3082,U_3083)
| U_3081 = 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_3081),U_3082),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3081),U_3083)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3081 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
fof(f_954_3,plain,
( ! [U_3089,U_3087,U_3085] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3089)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3087,U_3089)
| U_3085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_3088,U_3086,U_3084] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3084),U_3086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3084),U_3088)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3084 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_954_2]) ).
cnf(f_954_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3084),U_3086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3084),U_3088)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3084 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_954_3]) ).
cnf(f_954_5,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3087),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3085),U_3089)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3087,U_3089)
| U_3085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_954_3]) ).
fof(f_955_1,plain,
! [V_r,V_q,V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = V_q
| ~ c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__poly__eq]) ).
fof(f_955_2,plain,
! [U_3094,U_3093,U_3092,U_3091,U_3090] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,U_3092) = U_3093
| ~ c_Polynomial_Opdivmod__rel(U_3090,U_3091,U_3092,U_3093,U_3094)
| ~ class_Fields_Ofield(U_3090) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
cnf(f_955_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3090),U_3091,U_3092) = U_3093
| ~ c_Polynomial_Opdivmod__rel(U_3090,U_3091,U_3092,U_3093,U_3094)
| ~ class_Fields_Ofield(U_3090) ),
inference(clausify,[status(thm)],[f_955_2]) ).
fof(f_956_1,plain,
! [V_y,V_x,T_a] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(T_a),V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__poly__less]) ).
fof(f_956_2,plain,
! [U_3097,U_3096,U_3095] :
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3095),U_3096,U_3097) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3095))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_3095,U_3096),c_Polynomial_Odegree(U_3095,U_3097))
| ~ class_Fields_Ofield(U_3095) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
cnf(f_956_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(U_3095),U_3096,U_3097) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3095))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(U_3095,U_3096),c_Polynomial_Odegree(U_3095,U_3097))
| ~ class_Fields_Ofield(U_3095) ),
inference(clausify,[status(thm)],[f_956_2]) ).
fof(f_957_1,plain,
! [V_m,V_n] :
( ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
& ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__if]) ).
fof(f_957_2,plain,
! [U_3099,U_3098] :
( ( ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3099,U_3098) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3099,U_3098),U_3098))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3099,U_3098) )
& ( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3099,U_3098) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3099,U_3098) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3098) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
cnf(f_957_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3099,U_3098) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3099,U_3098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3098) ),
inference(clausify,[status(thm)],[f_957_2]) ).
cnf(f_957_4,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3099,U_3098) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3099,U_3098),U_3098))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3099,U_3098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3098) ),
inference(clausify,[status(thm)],[f_957_2]) ).
fof(f_958_1,plain,
! [V_m,V_n] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_div__geq]) ).
fof(f_958_2,plain,
! [U_3101,U_3100] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3101,U_3100) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3101,U_3100),U_3100))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3101,U_3100)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3100) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
cnf(f_958_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3101,U_3100) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3101,U_3100),U_3100))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3101,U_3100)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3100) ),
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_1,plain,
! [V_k_2,V_nb_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_nb_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) )
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_P_2,B_i))
| V_nb_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i),B_j)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_nb_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div]) ).
fof(f_959_2,plain,
! [U_3108,U_3107,U_3106] :
( ( hBOOL(hAPP(U_3106,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3107,U_3108)))
| ( ? [U_3105,U_3104] :
( ~ hBOOL(hAPP(U_3106,U_3105))
& U_3107 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3108),U_3105),U_3104)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3104,U_3108) )
& U_3108 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3106,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_3103,U_3102] :
( hBOOL(hAPP(U_3106,U_3103))
| U_3107 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3108),U_3103),U_3102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3102,U_3108) )
| U_3108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3106,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3108 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3106,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3107,U_3108))) ) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
fof(f_959_3,plain,
( ! [U_3114,U_3112,U_3110] :
( hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114)))
| ( ? [U_3105,U_3104] :
( ~ hBOOL(hAPP(U_3110,U_3105))
& U_3112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3114),U_3105),U_3104)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3104,U_3114) )
& U_3114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3110,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3113,U_3111,U_3109] :
( ( ( ! [U_3103,U_3102] :
( hBOOL(hAPP(U_3109,U_3103))
| U_3111 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3113),U_3103),U_3102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3102,U_3113) )
| U_3113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3109,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3113 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3109,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3111,U_3113))) ) ),
inference(miniscope,[status(thm)],[f_959_2]) ).
fof(f_959_4,plain,
( ! [U_3114,U_3112,U_3110] :
( hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114)))
| ( ? [U_3104] :
( ~ hBOOL(hAPP(U_3110,sK23(U_3114,U_3112,U_3110)))
& U_3112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3114),sK23(U_3114,U_3112,U_3110)),U_3104)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3104,U_3114) )
& U_3114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3110,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3113,U_3111,U_3109] :
( ( ( ! [U_3103,U_3102] :
( hBOOL(hAPP(U_3109,U_3103))
| U_3111 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3113),U_3103),U_3102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3102,U_3113) )
| U_3113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3109,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3113 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3109,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3111,U_3113))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_3105,sK23(U_3114,U_3112,U_3110))],[f_959_3]) ).
fof(f_959_5,plain,
( ! [U_3114,U_3112,U_3110] :
( hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114)))
| ( ~ hBOOL(hAPP(U_3110,sK23(U_3114,U_3112,U_3110)))
& U_3112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3114),sK23(U_3114,U_3112,U_3110)),sK24(U_3114,U_3112,U_3110))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(U_3114,U_3112,U_3110),U_3114)
& U_3114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3110,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3113,U_3111,U_3109] :
( ( ( ! [U_3103,U_3102] :
( hBOOL(hAPP(U_3109,U_3103))
| U_3111 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3113),U_3103),U_3102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3102,U_3113) )
| U_3113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3109,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3113 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3109,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3111,U_3113))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_3104,sK24(U_3114,U_3112,U_3110))],[f_959_4]) ).
cnf(f_959_6,plain,
( hBOOL(hAPP(U_3109,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3113 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3109,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3111,U_3113))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_7,plain,
( hBOOL(hAPP(U_3109,U_3103))
| U_3111 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3113),U_3103),U_3102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3102,U_3113)
| U_3113 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3109,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3111,U_3113))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_8,plain,
( U_3114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(U_3114,U_3112,U_3110),U_3114)
| U_3114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_10,plain,
( U_3112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3114),sK23(U_3114,U_3112,U_3110)),sK24(U_3114,U_3112,U_3110))
| U_3114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_11,plain,
( ~ hBOOL(hAPP(U_3110,sK23(U_3114,U_3112,U_3110)))
| U_3114 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_12,plain,
( U_3114 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3110,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_13,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK24(U_3114,U_3112,U_3110),U_3114)
| ~ hBOOL(hAPP(U_3110,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_14,plain,
( U_3112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3114),sK23(U_3114,U_3112,U_3110)),sK24(U_3114,U_3112,U_3110))
| ~ hBOOL(hAPP(U_3110,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
cnf(f_959_15,plain,
( ~ hBOOL(hAPP(U_3110,sK23(U_3114,U_3112,U_3110)))
| ~ hBOOL(hAPP(U_3110,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3110,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3112,U_3114))) ),
inference(clausify,[status(thm)],[f_959_5]) ).
fof(f_960_1,plain,
! [V_nb_2,V_m_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_nb_2)))
| ( ! [B_q] :
( ~ hBOOL(hAPP(V_P_2,B_q))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(B_q)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),B_q),V_m_2) )
& ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_nb_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [B_q] :
( hBOOL(hAPP(V_P_2,B_q))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(B_q)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),B_q),V_m_2) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_nb_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_nb_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).
fof(f_960_2,plain,
! [U_3119,U_3118,U_3117] :
( ( hBOOL(hAPP(U_3117,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3118,U_3119)))
| ( ! [U_3116] :
( ~ hBOOL(hAPP(U_3117,U_3116))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3119),c_Nat_OSuc(U_3116)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3119),U_3116),U_3118) )
& ( ~ hBOOL(hAPP(U_3117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3119 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [U_3115] :
( hBOOL(hAPP(U_3117,U_3115))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3119),c_Nat_OSuc(U_3115)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3119),U_3115),U_3118) )
| ( hBOOL(hAPP(U_3117,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3119 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_3117,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3118,U_3119))) ) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
fof(f_960_3,plain,
( ! [U_3125,U_3123,U_3121] :
( hBOOL(hAPP(U_3121,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3123,U_3125)))
| ( ! [U_3116] :
( ~ hBOOL(hAPP(U_3121,U_3116))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3125),c_Nat_OSuc(U_3116)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3125),U_3116),U_3123) )
& ( ~ hBOOL(hAPP(U_3121,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3125 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_3124,U_3122,U_3120] :
( ? [U_3115] :
( hBOOL(hAPP(U_3120,U_3115))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),c_Nat_OSuc(U_3115)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),U_3115),U_3122) )
| ( hBOOL(hAPP(U_3120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ) ),
inference(miniscope,[status(thm)],[f_960_2]) ).
fof(f_960_4,plain,
( ! [U_3125,U_3123,U_3121] :
( hBOOL(hAPP(U_3121,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3123,U_3125)))
| ( ! [U_3116] :
( ~ hBOOL(hAPP(U_3121,U_3116))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3125),c_Nat_OSuc(U_3116)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3125),U_3116),U_3123) )
& ( ~ hBOOL(hAPP(U_3121,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3125 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_3124,U_3122,U_3120] :
( ( hBOOL(hAPP(U_3120,sK25(U_3124,U_3122,U_3120)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),c_Nat_OSuc(sK25(U_3124,U_3122,U_3120))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),sK25(U_3124,U_3122,U_3120)),U_3122) )
| ( hBOOL(hAPP(U_3120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_3115,sK25(U_3124,U_3122,U_3120))],[f_960_3]) ).
cnf(f_960_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),sK25(U_3124,U_3122,U_3120)),U_3122)
| U_3124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),c_Nat_OSuc(sK25(U_3124,U_3122,U_3120))))
| U_3124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_7,plain,
( hBOOL(hAPP(U_3120,sK25(U_3124,U_3122,U_3120)))
| U_3124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),sK25(U_3124,U_3122,U_3120)),U_3122)
| hBOOL(hAPP(U_3120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3122,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3124),c_Nat_OSuc(sK25(U_3124,U_3122,U_3120))))
| hBOOL(hAPP(U_3120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_10,plain,
( hBOOL(hAPP(U_3120,sK25(U_3124,U_3122,U_3120)))
| hBOOL(hAPP(U_3120,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_3120,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3122,U_3124))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_11,plain,
( ~ hBOOL(hAPP(U_3121,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3125 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3121,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3123,U_3125))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_12,plain,
( ~ hBOOL(hAPP(U_3121,U_3116))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3125),c_Nat_OSuc(U_3116)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3125),U_3116),U_3123)
| hBOOL(hAPP(U_3121,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3123,U_3125))) ),
inference(clausify,[status(thm)],[f_960_4]) ).
fof(f_961_1,plain,
! [V_m_2,V_qb_2,V_nb_2] :
( ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(V_qb_2)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_qb_2),V_m_2) )
| V_qb_2 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_nb_2) )
& ( V_qb_2 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m_2,V_nb_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),c_Nat_OSuc(V_qb_2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_nb_2),V_qb_2),V_m_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_nb_2) ),
inference(fof_nnf,[status(thm)],[fact_split__div__lemma]) ).
fof(f_961_2,plain,
! [U_3128,U_3127,U_3126] :
( ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),c_Nat_OSuc(U_3127)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),U_3127),U_3128) )
| U_3127 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3128,U_3126) )
& ( U_3127 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3128,U_3126)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),c_Nat_OSuc(U_3127)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),U_3127),U_3128) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3126) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
cnf(f_961_3,plain,
( U_3127 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3128,U_3126)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),c_Nat_OSuc(U_3127)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),U_3127),U_3128)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3126) ),
inference(clausify,[status(thm)],[f_961_2]) ).
cnf(f_961_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),U_3127),U_3128)
| U_3127 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3128,U_3126)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3126) ),
inference(clausify,[status(thm)],[f_961_2]) ).
cnf(f_961_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3126),c_Nat_OSuc(U_3127)))
| U_3127 != c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3128,U_3126)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3126) ),
inference(clausify,[status(thm)],[f_961_2]) ).
fof(f_962_1,plain,
! [V_m,V_n] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_le__div__geq]) ).
fof(f_962_2,plain,
! [U_3130,U_3129] :
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3130,U_3129) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3130,U_3129),U_3129))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3129,U_3130)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3129) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
cnf(f_962_3,plain,
( c_Divides_Odiv__class_Odiv(tc_Nat_Onat,U_3130,U_3129) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3130,U_3129),U_3129))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3129,U_3130)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3129) ),
inference(clausify,[status(thm)],[f_962_2]) ).
fof(f_963_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).
fof(f_963_2,plain,
! [U_3132,U_3131] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_3131,U_3132))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3132)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3131) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
cnf(f_963_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_3131,U_3132))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3132)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3131) ),
inference(clausify,[status(thm)],[f_963_2]) ).
fof(f_964_1,plain,
! [V_x,V_y] :
( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ),
inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).
fof(f_964_2,plain,
! [U_3134,U_3133] :
( c_Nat__Transfer_Otsub(U_3134,U_3133) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3134,U_3133)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3133,U_3134) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
cnf(f_964_3,plain,
( c_Nat__Transfer_Otsub(U_3134,U_3133) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3134,U_3133)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3133,U_3134) ),
inference(clausify,[status(thm)],[f_964_2]) ).
fof(f_965_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add]) ).
fof(f_965_2,plain,
! [U_3139,U_3138,U_3137,U_3136,U_3135] :
( c_Groups_Ominus__class_Ominus(U_3135,c_Groups_Oplus__class_Oplus(U_3135,U_3136,U_3137),c_Groups_Oplus__class_Oplus(U_3135,U_3138,U_3139)) = c_Groups_Oplus__class_Oplus(U_3135,c_Groups_Ominus__class_Ominus(U_3135,U_3136,U_3138),c_Groups_Ominus__class_Ominus(U_3135,U_3137,U_3139))
| ~ class_Groups_Oab__group__add(U_3135) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
cnf(f_965_3,plain,
( c_Groups_Ominus__class_Ominus(U_3135,c_Groups_Oplus__class_Oplus(U_3135,U_3136,U_3137),c_Groups_Oplus__class_Oplus(U_3135,U_3138,U_3139)) = c_Groups_Oplus__class_Oplus(U_3135,c_Groups_Ominus__class_Ominus(U_3135,U_3136,U_3138),c_Groups_Ominus__class_Ominus(U_3135,U_3137,U_3139))
| ~ class_Groups_Oab__group__add(U_3135) ),
inference(clausify,[status(thm)],[f_965_2]) ).
fof(f_966_1,plain,
! [V_x,T_a] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) ) )
| V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__poly__def]) ).
fof(f_966_2,plain,
! [U_3141,U_3140] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_3140),U_3141) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3140),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_3140)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_3140),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140)),U_3141) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_3140),U_3141) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_3140))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_3140),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140)),U_3141) ) )
| U_3141 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140)) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_3140),U_3141) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140))
| U_3141 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140)) ) )
| ~ class_Rings_Olinordered__idom(U_3140) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
cnf(f_966_3,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_3140),U_3141) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140))
| U_3141 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140))
| ~ class_Rings_Olinordered__idom(U_3140) ),
inference(clausify,[status(thm)],[f_966_2]) ).
cnf(f_966_4,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_3140),U_3141) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_3140))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_3140),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140)),U_3141)
| U_3141 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140))
| ~ class_Rings_Olinordered__idom(U_3140) ),
inference(clausify,[status(thm)],[f_966_2]) ).
cnf(f_966_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_3140),U_3141) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3140),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_3140)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_3140),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140)),U_3141)
| U_3141 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3140))
| ~ class_Rings_Olinordered__idom(U_3140) ),
inference(clausify,[status(thm)],[f_966_2]) ).
fof(f_967_1,plain,
! [V_x,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__minus]) ).
fof(f_967_2,plain,
! [U_3143,U_3142] :
( c_Groups_Osgn__class_Osgn(U_3142,c_Groups_Ouminus__class_Ouminus(U_3142,U_3143)) = c_Groups_Ouminus__class_Ouminus(U_3142,c_Groups_Osgn__class_Osgn(U_3142,U_3143))
| ~ class_RealVector_Oreal__normed__vector(U_3142) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
cnf(f_967_3,plain,
( c_Groups_Osgn__class_Osgn(U_3142,c_Groups_Ouminus__class_Ouminus(U_3142,U_3143)) = c_Groups_Ouminus__class_Ouminus(U_3142,c_Groups_Osgn__class_Osgn(U_3142,U_3143))
| ~ class_RealVector_Oreal__normed__vector(U_3142) ),
inference(clausify,[status(thm)],[f_967_2]) ).
fof(f_968_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_968_2,plain,
! [U_3144] :
( c_Groups_Osgn__class_Osgn(U_3144,c_Groups_Oone__class_Oone(U_3144)) = c_Groups_Oone__class_Oone(U_3144)
| ~ class_RealVector_Oreal__normed__algebra__1(U_3144) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
cnf(f_968_3,plain,
( c_Groups_Osgn__class_Osgn(U_3144,c_Groups_Oone__class_Oone(U_3144)) = c_Groups_Oone__class_Oone(U_3144)
| ~ class_RealVector_Oreal__normed__algebra__1(U_3144) ),
inference(clausify,[status(thm)],[f_968_2]) ).
fof(f_969_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_969_2,plain,
! [U_3146,U_3145] :
( c_Groups_Osgn__class_Osgn(U_3145,c_Groups_Osgn__class_Osgn(U_3145,U_3146)) = c_Groups_Osgn__class_Osgn(U_3145,U_3146)
| ~ class_Rings_Olinordered__idom(U_3145) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
cnf(f_969_3,plain,
( c_Groups_Osgn__class_Osgn(U_3145,c_Groups_Osgn__class_Osgn(U_3145,U_3146)) = c_Groups_Osgn__class_Osgn(U_3145,U_3146)
| ~ class_Rings_Olinordered__idom(U_3145) ),
inference(clausify,[status(thm)],[f_969_2]) ).
fof(f_970_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_970_2,plain,
! [U_3149,U_3148,U_3147] :
( c_Groups_Osgn__class_Osgn(U_3147,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3147),U_3148),U_3149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3147),c_Groups_Osgn__class_Osgn(U_3147,U_3148)),c_Groups_Osgn__class_Osgn(U_3147,U_3149))
| ~ class_RealVector_Oreal__normed__div__algebra(U_3147) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
cnf(f_970_3,plain,
( c_Groups_Osgn__class_Osgn(U_3147,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3147),U_3148),U_3149)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3147),c_Groups_Osgn__class_Osgn(U_3147,U_3148)),c_Groups_Osgn__class_Osgn(U_3147,U_3149))
| ~ class_RealVector_Oreal__normed__div__algebra(U_3147) ),
inference(clausify,[status(thm)],[f_970_2]) ).
fof(f_971_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_971_2,plain,
! [U_3152,U_3151,U_3150] :
( c_Groups_Osgn__class_Osgn(U_3150,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3150),U_3151),U_3152)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3150),c_Groups_Osgn__class_Osgn(U_3150,U_3151)),c_Groups_Osgn__class_Osgn(U_3150,U_3152))
| ~ class_Rings_Olinordered__idom(U_3150) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
cnf(f_971_3,plain,
( c_Groups_Osgn__class_Osgn(U_3150,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3150),U_3151),U_3152)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3150),c_Groups_Osgn__class_Osgn(U_3150,U_3151)),c_Groups_Osgn__class_Osgn(U_3150,U_3152))
| ~ class_Rings_Olinordered__idom(U_3150) ),
inference(clausify,[status(thm)],[f_971_2]) ).
fof(f_972_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_972_2,plain,
! [U_3153] :
( c_Groups_Osgn__class_Osgn(U_3153,c_Groups_Ozero__class_Ozero(U_3153)) = c_Groups_Ozero__class_Ozero(U_3153)
| ~ class_Groups_Osgn__if(U_3153) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
cnf(f_972_3,plain,
( c_Groups_Osgn__class_Osgn(U_3153,c_Groups_Ozero__class_Ozero(U_3153)) = c_Groups_Ozero__class_Ozero(U_3153)
| ~ class_Groups_Osgn__if(U_3153) ),
inference(clausify,[status(thm)],[f_972_2]) ).
fof(f_973_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_973_2,plain,
! [U_3154] :
( c_Groups_Osgn__class_Osgn(U_3154,c_Groups_Ozero__class_Ozero(U_3154)) = c_Groups_Ozero__class_Ozero(U_3154)
| ~ class_RealVector_Oreal__normed__vector(U_3154) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
cnf(f_973_3,plain,
( c_Groups_Osgn__class_Osgn(U_3154,c_Groups_Ozero__class_Ozero(U_3154)) = c_Groups_Ozero__class_Ozero(U_3154)
| ~ class_RealVector_Oreal__normed__vector(U_3154) ),
inference(clausify,[status(thm)],[f_973_2]) ).
fof(f_974_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_974_2,plain,
! [U_3156,U_3155] :
( ( ( c_Groups_Osgn__class_Osgn(U_3155,U_3156) = c_Groups_Ozero__class_Ozero(U_3155)
| U_3156 != c_Groups_Ozero__class_Ozero(U_3155) )
& ( U_3156 = c_Groups_Ozero__class_Ozero(U_3155)
| c_Groups_Osgn__class_Osgn(U_3155,U_3156) != c_Groups_Ozero__class_Ozero(U_3155) ) )
| ~ class_RealVector_Oreal__normed__vector(U_3155) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
cnf(f_974_3,plain,
( U_3156 = c_Groups_Ozero__class_Ozero(U_3155)
| c_Groups_Osgn__class_Osgn(U_3155,U_3156) != c_Groups_Ozero__class_Ozero(U_3155)
| ~ class_RealVector_Oreal__normed__vector(U_3155) ),
inference(clausify,[status(thm)],[f_974_2]) ).
cnf(f_974_4,plain,
( c_Groups_Osgn__class_Osgn(U_3155,U_3156) = c_Groups_Ozero__class_Ozero(U_3155)
| U_3156 != c_Groups_Ozero__class_Ozero(U_3155)
| ~ class_RealVector_Oreal__normed__vector(U_3155) ),
inference(clausify,[status(thm)],[f_974_2]) ).
fof(f_975_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_aa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_aa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Osgn__class_Osgn(T_a,V_aa_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_975_2,plain,
! [U_3158,U_3157] :
( ( ( c_Groups_Osgn__class_Osgn(U_3157,U_3158) = c_Groups_Ozero__class_Ozero(U_3157)
| U_3158 != c_Groups_Ozero__class_Ozero(U_3157) )
& ( U_3158 = c_Groups_Ozero__class_Ozero(U_3157)
| c_Groups_Osgn__class_Osgn(U_3157,U_3158) != c_Groups_Ozero__class_Ozero(U_3157) ) )
| ~ class_Rings_Olinordered__idom(U_3157) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
cnf(f_975_3,plain,
( U_3158 = c_Groups_Ozero__class_Ozero(U_3157)
| c_Groups_Osgn__class_Osgn(U_3157,U_3158) != c_Groups_Ozero__class_Ozero(U_3157)
| ~ class_Rings_Olinordered__idom(U_3157) ),
inference(clausify,[status(thm)],[f_975_2]) ).
cnf(f_975_4,plain,
( c_Groups_Osgn__class_Osgn(U_3157,U_3158) = c_Groups_Ozero__class_Ozero(U_3157)
| U_3158 != c_Groups_Ozero__class_Ozero(U_3157)
| ~ class_Rings_Olinordered__idom(U_3157) ),
inference(clausify,[status(thm)],[f_975_2]) ).
fof(f_976_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).
fof(f_976_2,plain,
! [U_3160,U_3159] :
( ( ( c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),c_Groups_Osgn__class_Osgn(U_3159,U_3160))
| ~ c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),U_3160) )
& ( c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),U_3160)
| ~ c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),c_Groups_Osgn__class_Osgn(U_3159,U_3160)) ) )
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
cnf(f_976_3,plain,
( c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),U_3160)
| ~ c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),c_Groups_Osgn__class_Osgn(U_3159,U_3160))
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(clausify,[status(thm)],[f_976_2]) ).
cnf(f_976_4,plain,
( c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),c_Groups_Osgn__class_Osgn(U_3159,U_3160))
| ~ c_Orderings_Oord__class_Oless(U_3159,c_Groups_Ozero__class_Ozero(U_3159),U_3160)
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(clausify,[status(thm)],[f_976_2]) ).
fof(f_977_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).
fof(f_977_2,plain,
! [U_3162,U_3161] :
( ( ( c_Orderings_Oord__class_Oless(U_3161,c_Groups_Osgn__class_Osgn(U_3161,U_3162),c_Groups_Ozero__class_Ozero(U_3161))
| ~ c_Orderings_Oord__class_Oless(U_3161,U_3162,c_Groups_Ozero__class_Ozero(U_3161)) )
& ( c_Orderings_Oord__class_Oless(U_3161,U_3162,c_Groups_Ozero__class_Ozero(U_3161))
| ~ c_Orderings_Oord__class_Oless(U_3161,c_Groups_Osgn__class_Osgn(U_3161,U_3162),c_Groups_Ozero__class_Ozero(U_3161)) ) )
| ~ class_Rings_Olinordered__idom(U_3161) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
cnf(f_977_3,plain,
( c_Orderings_Oord__class_Oless(U_3161,U_3162,c_Groups_Ozero__class_Ozero(U_3161))
| ~ c_Orderings_Oord__class_Oless(U_3161,c_Groups_Osgn__class_Osgn(U_3161,U_3162),c_Groups_Ozero__class_Ozero(U_3161))
| ~ class_Rings_Olinordered__idom(U_3161) ),
inference(clausify,[status(thm)],[f_977_2]) ).
cnf(f_977_4,plain,
( c_Orderings_Oord__class_Oless(U_3161,c_Groups_Osgn__class_Osgn(U_3161,U_3162),c_Groups_Ozero__class_Ozero(U_3161))
| ~ c_Orderings_Oord__class_Oless(U_3161,U_3162,c_Groups_Ozero__class_Ozero(U_3161))
| ~ class_Rings_Olinordered__idom(U_3161) ),
inference(clausify,[status(thm)],[f_977_2]) ).
fof(f_978_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)
| c_Groups_Osgn__class_Osgn(T_a,V_aa_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_978_2,plain,
! [U_3164,U_3163] :
( ( ( c_Groups_Osgn__class_Osgn(U_3163,U_3164) = c_Groups_Oone__class_Oone(U_3163)
| ~ c_Orderings_Oord__class_Oless(U_3163,c_Groups_Ozero__class_Ozero(U_3163),U_3164) )
& ( c_Orderings_Oord__class_Oless(U_3163,c_Groups_Ozero__class_Ozero(U_3163),U_3164)
| c_Groups_Osgn__class_Osgn(U_3163,U_3164) != c_Groups_Oone__class_Oone(U_3163) ) )
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
cnf(f_978_3,plain,
( c_Orderings_Oord__class_Oless(U_3163,c_Groups_Ozero__class_Ozero(U_3163),U_3164)
| c_Groups_Osgn__class_Osgn(U_3163,U_3164) != c_Groups_Oone__class_Oone(U_3163)
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(clausify,[status(thm)],[f_978_2]) ).
cnf(f_978_4,plain,
( c_Groups_Osgn__class_Osgn(U_3163,U_3164) = c_Groups_Oone__class_Oone(U_3163)
| ~ c_Orderings_Oord__class_Oless(U_3163,c_Groups_Ozero__class_Ozero(U_3163),U_3164)
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(clausify,[status(thm)],[f_978_2]) ).
fof(f_979_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__pos]) ).
fof(f_979_2,plain,
! [U_3166,U_3165] :
( c_Groups_Osgn__class_Osgn(U_3165,U_3166) = c_Groups_Oone__class_Oone(U_3165)
| ~ c_Orderings_Oord__class_Oless(U_3165,c_Groups_Ozero__class_Ozero(U_3165),U_3166)
| ~ class_Rings_Olinordered__idom(U_3165) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
cnf(f_979_3,plain,
( c_Groups_Osgn__class_Osgn(U_3165,U_3166) = c_Groups_Oone__class_Oone(U_3165)
| ~ c_Orderings_Oord__class_Oless(U_3165,c_Groups_Ozero__class_Ozero(U_3165),U_3166)
| ~ class_Rings_Olinordered__idom(U_3165) ),
inference(clausify,[status(thm)],[f_979_2]) ).
fof(f_980_1,plain,
! [V_x,T_a] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) )
& ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) ) )
| V_x = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)
| V_x != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Osgn__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__if]) ).
fof(f_980_2,plain,
! [U_3168,U_3167] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_3167,U_3168) = c_Groups_Ouminus__class_Ouminus(U_3167,c_Groups_Oone__class_Oone(U_3167))
| c_Orderings_Oord__class_Oless(U_3167,c_Groups_Ozero__class_Ozero(U_3167),U_3168) )
& ( c_Groups_Osgn__class_Osgn(U_3167,U_3168) = c_Groups_Oone__class_Oone(U_3167)
| ~ c_Orderings_Oord__class_Oless(U_3167,c_Groups_Ozero__class_Ozero(U_3167),U_3168) ) )
| U_3168 = c_Groups_Ozero__class_Ozero(U_3167) )
& ( c_Groups_Osgn__class_Osgn(U_3167,U_3168) = c_Groups_Ozero__class_Ozero(U_3167)
| U_3168 != c_Groups_Ozero__class_Ozero(U_3167) ) )
| ~ class_Groups_Osgn__if(U_3167) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
cnf(f_980_3,plain,
( c_Groups_Osgn__class_Osgn(U_3167,U_3168) = c_Groups_Ozero__class_Ozero(U_3167)
| U_3168 != c_Groups_Ozero__class_Ozero(U_3167)
| ~ class_Groups_Osgn__if(U_3167) ),
inference(clausify,[status(thm)],[f_980_2]) ).
cnf(f_980_4,plain,
( c_Groups_Osgn__class_Osgn(U_3167,U_3168) = c_Groups_Oone__class_Oone(U_3167)
| ~ c_Orderings_Oord__class_Oless(U_3167,c_Groups_Ozero__class_Ozero(U_3167),U_3168)
| U_3168 = c_Groups_Ozero__class_Ozero(U_3167)
| ~ class_Groups_Osgn__if(U_3167) ),
inference(clausify,[status(thm)],[f_980_2]) ).
cnf(f_980_5,plain,
( c_Groups_Osgn__class_Osgn(U_3167,U_3168) = c_Groups_Ouminus__class_Ouminus(U_3167,c_Groups_Oone__class_Oone(U_3167))
| c_Orderings_Oord__class_Oless(U_3167,c_Groups_Ozero__class_Ozero(U_3167),U_3168)
| U_3168 = c_Groups_Ozero__class_Ozero(U_3167)
| ~ class_Groups_Osgn__if(U_3167) ),
inference(clausify,[status(thm)],[f_980_2]) ).
fof(f_981_1,plain,
! [V_aa_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Groups_Osgn__class_Osgn(T_a,V_aa_2) != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).
fof(f_981_2,plain,
! [U_3170,U_3169] :
( ( ( c_Groups_Osgn__class_Osgn(U_3169,U_3170) = c_Groups_Ouminus__class_Ouminus(U_3169,c_Groups_Oone__class_Oone(U_3169))
| ~ c_Orderings_Oord__class_Oless(U_3169,U_3170,c_Groups_Ozero__class_Ozero(U_3169)) )
& ( c_Orderings_Oord__class_Oless(U_3169,U_3170,c_Groups_Ozero__class_Ozero(U_3169))
| c_Groups_Osgn__class_Osgn(U_3169,U_3170) != c_Groups_Ouminus__class_Ouminus(U_3169,c_Groups_Oone__class_Oone(U_3169)) ) )
| ~ class_Rings_Olinordered__idom(U_3169) ),
inference(variable_rename,[status(thm)],[f_981_1]) ).
cnf(f_981_3,plain,
( c_Orderings_Oord__class_Oless(U_3169,U_3170,c_Groups_Ozero__class_Ozero(U_3169))
| c_Groups_Osgn__class_Osgn(U_3169,U_3170) != c_Groups_Ouminus__class_Ouminus(U_3169,c_Groups_Oone__class_Oone(U_3169))
| ~ class_Rings_Olinordered__idom(U_3169) ),
inference(clausify,[status(thm)],[f_981_2]) ).
cnf(f_981_4,plain,
( c_Groups_Osgn__class_Osgn(U_3169,U_3170) = c_Groups_Ouminus__class_Ouminus(U_3169,c_Groups_Oone__class_Oone(U_3169))
| ~ c_Orderings_Oord__class_Oless(U_3169,U_3170,c_Groups_Ozero__class_Ozero(U_3169))
| ~ class_Rings_Olinordered__idom(U_3169) ),
inference(clausify,[status(thm)],[f_981_2]) ).
fof(f_982_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__neg]) ).
fof(f_982_2,plain,
! [U_3172,U_3171] :
( c_Groups_Osgn__class_Osgn(U_3171,U_3172) = c_Groups_Ouminus__class_Ouminus(U_3171,c_Groups_Oone__class_Oone(U_3171))
| ~ c_Orderings_Oord__class_Oless(U_3171,U_3172,c_Groups_Ozero__class_Ozero(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
cnf(f_982_3,plain,
( c_Groups_Osgn__class_Osgn(U_3171,U_3172) = c_Groups_Ouminus__class_Ouminus(U_3171,c_Groups_Oone__class_Oone(U_3171))
| ~ c_Orderings_Oord__class_Oless(U_3171,U_3172,c_Groups_Ozero__class_Ozero(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(clausify,[status(thm)],[f_982_2]) ).
fof(f_983_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
| ~ hBOOL(hAPP(V_P_2,B_x)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,B_x,V_d_2)))
& hBOOL(hAPP(V_P_2,B_x)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma]) ).
fof(f_983_2,plain,
! [U_3177,U_3176,U_3175] :
( ! [U_3174] :
( hBOOL(hAPP(U_3176,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3177),U_3175))))
| ~ hBOOL(hAPP(U_3176,U_3174)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3177)
| ? [U_3173] :
( ~ hBOOL(hAPP(U_3176,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3173,U_3175)))
& hBOOL(hAPP(U_3176,U_3173)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3175) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
fof(f_983_3,plain,
! [U_3177,U_3176,U_3175] :
( ! [U_3174] :
( hBOOL(hAPP(U_3176,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3177),U_3175))))
| ~ hBOOL(hAPP(U_3176,U_3174)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3177)
| ( ~ hBOOL(hAPP(U_3176,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK26(U_3177,U_3176,U_3175),U_3175)))
& hBOOL(hAPP(U_3176,sK26(U_3177,U_3176,U_3175))) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3175) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_3173,sK26(U_3177,U_3176,U_3175))],[f_983_2]) ).
cnf(f_983_4,plain,
( hBOOL(hAPP(U_3176,sK26(U_3177,U_3176,U_3175)))
| hBOOL(hAPP(U_3176,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3177),U_3175))))
| ~ hBOOL(hAPP(U_3176,U_3174))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3177)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3175) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_5,plain,
( ~ hBOOL(hAPP(U_3176,c_Groups_Ominus__class_Ominus(tc_Int_Oint,sK26(U_3177,U_3176,U_3175),U_3175)))
| hBOOL(hAPP(U_3176,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3177),U_3175))))
| ~ hBOOL(hAPP(U_3176,U_3174))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3177)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3175) ),
inference(clausify,[status(thm)],[f_983_3]) ).
fof(f_984_1,plain,
! [V_nb_2,V_P_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_nb_2,V_k_2)))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
& V_nb_2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) ) )
& ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
| V_nb_2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i),B_j)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B_j,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,B_j) )
| ~ hBOOL(hAPP(hAPP(V_P_2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_nb_2,V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_nb_2,V_k_2))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_split__neg__lemma]) ).
fof(f_984_2,plain,
! [U_3184,U_3183,U_3182] :
( ( ( hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ? [U_3181,U_3180] :
( ~ hBOOL(hAPP(hAPP(U_3183,U_3181),U_3180))
& U_3184 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),U_3181),U_3180)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3180,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,U_3180) ) )
& ( ! [U_3179,U_3178] :
( hBOOL(hAPP(hAPP(U_3183,U_3179),U_3178))
| U_3184 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),U_3179),U_3178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3178,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,U_3178) )
| ~ hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
fof(f_984_3,plain,
! [U_3184,U_3183,U_3182] :
( ( ( hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ? [U_3180] :
( ~ hBOOL(hAPP(hAPP(U_3183,sK27(U_3184,U_3183,U_3182)),U_3180))
& U_3184 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),sK27(U_3184,U_3183,U_3182)),U_3180)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3180,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,U_3180) ) )
& ( ! [U_3179,U_3178] :
( hBOOL(hAPP(hAPP(U_3183,U_3179),U_3178))
| U_3184 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),U_3179),U_3178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3178,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,U_3178) )
| ~ hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_3181,sK27(U_3184,U_3183,U_3182))],[f_984_2]) ).
fof(f_984_4,plain,
! [U_3184,U_3183,U_3182] :
( ( ( hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ( ~ hBOOL(hAPP(hAPP(U_3183,sK27(U_3184,U_3183,U_3182)),sK28(U_3184,U_3183,U_3182)))
& U_3184 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),sK27(U_3184,U_3183,U_3182)),sK28(U_3184,U_3183,U_3182))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK28(U_3184,U_3183,U_3182),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,sK28(U_3184,U_3183,U_3182)) ) )
& ( ! [U_3179,U_3178] :
( hBOOL(hAPP(hAPP(U_3183,U_3179),U_3178))
| U_3184 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),U_3179),U_3178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3178,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,U_3178) )
| ~ hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182))) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_3180,sK28(U_3184,U_3183,U_3182))],[f_984_3]) ).
cnf(f_984_5,plain,
( hBOOL(hAPP(hAPP(U_3183,U_3179),U_3178))
| U_3184 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),U_3179),U_3178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3178,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,U_3178)
| ~ hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_984_4]) ).
cnf(f_984_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,sK28(U_3184,U_3183,U_3182))
| hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_984_4]) ).
cnf(f_984_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK28(U_3184,U_3183,U_3182),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_984_4]) ).
cnf(f_984_8,plain,
( U_3184 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),sK27(U_3184,U_3183,U_3182)),sK28(U_3184,U_3183,U_3182))
| hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_984_4]) ).
cnf(f_984_9,plain,
( ~ hBOOL(hAPP(hAPP(U_3183,sK27(U_3184,U_3183,U_3182)),sK28(U_3184,U_3183,U_3182)))
| hBOOL(hAPP(hAPP(U_3183,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3184,U_3182)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3184,U_3182)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_984_4]) ).
fof(f_985_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mod__equality]) ).
fof(f_985_2,plain,
! [U_3188,U_3187,U_3186,U_3185] :
( c_Groups_Oplus__class_Oplus(U_3185,c_Groups_Oplus__class_Oplus(U_3185,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3185),c_Divides_Odiv__class_Odiv(U_3185,U_3186,U_3187)),U_3187),c_Divides_Odiv__class_Omod(U_3185,U_3186,U_3187)),U_3188) = c_Groups_Oplus__class_Oplus(U_3185,U_3186,U_3188)
| ~ class_Divides_Osemiring__div(U_3185) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
cnf(f_985_3,plain,
( c_Groups_Oplus__class_Oplus(U_3185,c_Groups_Oplus__class_Oplus(U_3185,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3185),c_Divides_Odiv__class_Odiv(U_3185,U_3186,U_3187)),U_3187),c_Divides_Odiv__class_Omod(U_3185,U_3186,U_3187)),U_3188) = c_Groups_Oplus__class_Oplus(U_3185,U_3186,U_3188)
| ~ class_Divides_Osemiring__div(U_3185) ),
inference(clausify,[status(thm)],[f_985_2]) ).
fof(f_986_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mod__equality2]) ).
fof(f_986_2,plain,
! [U_3192,U_3191,U_3190,U_3189] :
( c_Groups_Oplus__class_Oplus(U_3189,c_Groups_Oplus__class_Oplus(U_3189,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),U_3190),c_Divides_Odiv__class_Odiv(U_3189,U_3191,U_3190)),c_Divides_Odiv__class_Omod(U_3189,U_3191,U_3190)),U_3192) = c_Groups_Oplus__class_Oplus(U_3189,U_3191,U_3192)
| ~ class_Divides_Osemiring__div(U_3189) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
cnf(f_986_3,plain,
( c_Groups_Oplus__class_Oplus(U_3189,c_Groups_Oplus__class_Oplus(U_3189,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3189),U_3190),c_Divides_Odiv__class_Odiv(U_3189,U_3191,U_3190)),c_Divides_Odiv__class_Omod(U_3189,U_3191,U_3190)),U_3192) = c_Groups_Oplus__class_Oplus(U_3189,U_3191,U_3192)
| ~ class_Divides_Osemiring__div(U_3189) ),
inference(clausify,[status(thm)],[f_986_2]) ).
fof(f_987_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__equality]) ).
fof(f_987_2,plain,
! [U_3195,U_3194,U_3193] :
( c_Groups_Oplus__class_Oplus(U_3193,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3193),c_Divides_Odiv__class_Odiv(U_3193,U_3194,U_3195)),U_3195),c_Divides_Odiv__class_Omod(U_3193,U_3194,U_3195)) = U_3194
| ~ class_Divides_Osemiring__div(U_3193) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
cnf(f_987_3,plain,
( c_Groups_Oplus__class_Oplus(U_3193,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3193),c_Divides_Odiv__class_Odiv(U_3193,U_3194,U_3195)),U_3195),c_Divides_Odiv__class_Omod(U_3193,U_3194,U_3195)) = U_3194
| ~ class_Divides_Osemiring__div(U_3193) ),
inference(clausify,[status(thm)],[f_987_2]) ).
fof(f_988_1,plain,
! [V_a,V_b,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__equality2]) ).
fof(f_988_2,plain,
! [U_3198,U_3197,U_3196] :
( c_Groups_Oplus__class_Oplus(U_3196,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3196),U_3197),c_Divides_Odiv__class_Odiv(U_3196,U_3198,U_3197)),c_Divides_Odiv__class_Omod(U_3196,U_3198,U_3197)) = U_3198
| ~ class_Divides_Osemiring__div(U_3196) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
cnf(f_988_3,plain,
( c_Groups_Oplus__class_Oplus(U_3196,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3196),U_3197),c_Divides_Odiv__class_Odiv(U_3196,U_3198,U_3197)),c_Divides_Odiv__class_Omod(U_3196,U_3198,U_3197)) = U_3198
| ~ class_Divides_Osemiring__div(U_3196) ),
inference(clausify,[status(thm)],[f_988_2]) ).
fof(f_989_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)),V_b)) = V_a
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H]) ).
fof(f_989_2,plain,
! [U_3201,U_3200,U_3199] :
( c_Groups_Oplus__class_Oplus(U_3199,c_Divides_Odiv__class_Omod(U_3199,U_3200,U_3201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3199),c_Divides_Odiv__class_Odiv(U_3199,U_3200,U_3201)),U_3201)) = U_3200
| ~ class_Divides_Osemiring__div(U_3199) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
cnf(f_989_3,plain,
( c_Groups_Oplus__class_Oplus(U_3199,c_Divides_Odiv__class_Omod(U_3199,U_3200,U_3201),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3199),c_Divides_Odiv__class_Odiv(U_3199,U_3200,U_3201)),U_3201)) = U_3200
| ~ class_Divides_Osemiring__div(U_3199) ),
inference(clausify,[status(thm)],[f_989_2]) ).
fof(f_990_1,plain,
! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)),
inference(fof_nnf,[status(thm)],[fact_zdiv__zadd1__eq]) ).
fof(f_990_2,plain,
! [U_3204,U_3203,U_3202] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_3202,U_3203),U_3204) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3202,U_3204),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3203,U_3204)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3202,U_3204),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3203,U_3204)),U_3204)),
inference(variable_rename,[status(thm)],[f_990_1]) ).
cnf(f_990_3,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_3202,U_3203),U_3204) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3202,U_3204),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3203,U_3204)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3202,U_3204),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3203,U_3204)),U_3204)),
inference(clausify,[status(thm)],[f_990_2]) ).
fof(f_991_1,plain,
! [V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__trivial]) ).
fof(f_991_2,plain,
! [U_3206,U_3205] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3205,U_3206),U_3206) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_991_1]) ).
cnf(f_991_3,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3205,U_3206),U_3206) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_991_2]) ).
fof(f_992_1,plain,
! [V_b,V_a,T_a] :
( c_Divides_Odiv__class_Odiv(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__trivial]) ).
fof(f_992_2,plain,
! [U_3209,U_3208,U_3207] :
( c_Divides_Odiv__class_Odiv(U_3207,c_Divides_Odiv__class_Omod(U_3207,U_3208,U_3209),U_3209) = c_Groups_Ozero__class_Ozero(U_3207)
| ~ class_Divides_Osemiring__div(U_3207) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
cnf(f_992_3,plain,
( c_Divides_Odiv__class_Odiv(U_3207,c_Divides_Odiv__class_Omod(U_3207,U_3208,U_3209),U_3209) = c_Groups_Ozero__class_Ozero(U_3207)
| ~ class_Divides_Osemiring__div(U_3207) ),
inference(clausify,[status(thm)],[f_992_2]) ).
fof(f_993_1,plain,
! [V_a] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
& c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_DIVISION__BY__ZERO]) ).
fof(f_993_2,plain,
! [U_3210] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3210,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3210
& c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3210,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
fof(f_993_3,plain,
( ! [U_3212] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3212,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3212
& ! [U_3211] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3211,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(miniscope,[status(thm)],[f_993_2]) ).
cnf(f_993_4,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3211,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_993_3]) ).
cnf(f_993_5,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3212,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3212,
inference(clausify,[status(thm)],[f_993_3]) ).
fof(f_994_1,plain,
! [V_b,V_a] : V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__equality]) ).
fof(f_994_2,plain,
! [U_3214,U_3213] : U_3213 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3214),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3213,U_3214)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3213,U_3214)),
inference(variable_rename,[status(thm)],[f_994_1]) ).
cnf(f_994_3,plain,
U_3213 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3214),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3213,U_3214)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3213,U_3214)),
inference(clausify,[status(thm)],[f_994_2]) ).
fof(f_995_1,plain,
! [V_c,V_b,V_a] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_b,V_c)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c)),
inference(fof_nnf,[status(thm)],[fact_zdiv__zmult1__eq]) ).
fof(f_995_2,plain,
! [U_3217,U_3216,U_3215] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3215),U_3216),U_3217) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3215),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3216,U_3217)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3215),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3216,U_3217)),U_3217)),
inference(variable_rename,[status(thm)],[f_995_1]) ).
cnf(f_995_3,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3215),U_3216),U_3217) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3215),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3216,U_3217)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3215),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3216,U_3217)),U_3217)),
inference(clausify,[status(thm)],[f_995_2]) ).
fof(f_996_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_996_2,plain,
! [U_3218] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3218))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3218) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
cnf(f_996_3,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3218))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3218) ),
inference(clausify,[status(thm)],[f_996_2]) ).
fof(f_997_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_997_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_997_1]) ).
fof(f_998_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_998_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_998_1]) ).
fof(f_999_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_999_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_999_1]) ).
fof(f_1000_1,plain,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra]) ).
fof(f_1000_2,plain,
! [U_3220,U_3219] :
( class_Lattices_Oboolean__algebra(tc_fun(U_3220,U_3219))
| ~ class_Lattices_Oboolean__algebra(U_3219) ),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
cnf(f_1000_3,plain,
( class_Lattices_Oboolean__algebra(tc_fun(U_3220,U_3219))
| ~ class_Lattices_Oboolean__algebra(U_3219) ),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_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_1001_2,plain,
! [U_3222,U_3221] :
( class_Orderings_Opreorder(tc_fun(U_3222,U_3221))
| ~ class_Orderings_Opreorder(U_3221) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
cnf(f_1001_3,plain,
( class_Orderings_Opreorder(tc_fun(U_3222,U_3221))
| ~ class_Orderings_Opreorder(U_3221) ),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_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_1002_2,plain,
! [U_3224,U_3223] :
( class_Orderings_Oorder(tc_fun(U_3224,U_3223))
| ~ class_Orderings_Oorder(U_3223) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
cnf(f_1002_3,plain,
( class_Orderings_Oorder(tc_fun(U_3224,U_3223))
| ~ class_Orderings_Oorder(U_3223) ),
inference(clausify,[status(thm)],[f_1002_2]) ).
fof(f_1003_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_1003_2,plain,
! [U_3226,U_3225] :
( class_Orderings_Oord(tc_fun(U_3226,U_3225))
| ~ class_Orderings_Oord(U_3225) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
cnf(f_1003_3,plain,
( class_Orderings_Oord(tc_fun(U_3226,U_3225))
| ~ class_Orderings_Oord(U_3225) ),
inference(clausify,[status(thm)],[f_1003_2]) ).
fof(f_1004_1,plain,
! [T_2,T_1] :
( class_Groups_Ouminus(tc_fun(T_2,T_1))
| ~ class_Groups_Ouminus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus]) ).
fof(f_1004_2,plain,
! [U_3228,U_3227] :
( class_Groups_Ouminus(tc_fun(U_3228,U_3227))
| ~ class_Groups_Ouminus(U_3227) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
cnf(f_1004_3,plain,
( class_Groups_Ouminus(tc_fun(U_3228,U_3227))
| ~ class_Groups_Ouminus(U_3227) ),
inference(clausify,[status(thm)],[f_1004_2]) ).
fof(f_1005_1,plain,
! [T_2,T_1] :
( class_Groups_Ominus(tc_fun(T_2,T_1))
| ~ class_Groups_Ominus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus]) ).
fof(f_1005_2,plain,
! [U_3230,U_3229] :
( class_Groups_Ominus(tc_fun(U_3230,U_3229))
| ~ class_Groups_Ominus(U_3229) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
cnf(f_1005_3,plain,
( class_Groups_Ominus(tc_fun(U_3230,U_3229))
| ~ class_Groups_Ominus(U_3229) ),
inference(clausify,[status(thm)],[f_1005_2]) ).
fof(f_1006_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_1006_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1006_1]) ).
fof(f_1007_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_1007_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1007_1]) ).
fof(f_1008_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_1008_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1008_1]) ).
fof(f_1009_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_1009_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1009_1]) ).
fof(f_1010_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_1010_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1010_1]) ).
fof(f_1011_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).
cnf(f_1011_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1011_1]) ).
fof(f_1012_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_1012_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1012_1]) ).
fof(f_1013_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_1013_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1013_1]) ).
fof(f_1014_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_1014_2,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1014_1]) ).
fof(f_1015_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_1015_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1015_1]) ).
fof(f_1016_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_1016_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1016_1]) ).
fof(f_1017_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).
cnf(f_1017_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1017_1]) ).
fof(f_1018_1,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).
cnf(f_1018_2,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1018_1]) ).
fof(f_1019_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_1019_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1019_1]) ).
fof(f_1020_1,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).
cnf(f_1020_2,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1020_1]) ).
fof(f_1021_1,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).
cnf(f_1021_2,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1021_1]) ).
fof(f_1022_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_1022_2,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1022_1]) ).
fof(f_1023_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).
cnf(f_1023_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1023_1]) ).
fof(f_1024_1,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).
cnf(f_1024_2,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1024_1]) ).
fof(f_1025_1,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).
cnf(f_1025_2,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1025_1]) ).
fof(f_1026_1,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).
cnf(f_1026_2,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1026_1]) ).
fof(f_1027_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).
cnf(f_1027_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1027_1]) ).
fof(f_1028_1,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).
cnf(f_1028_2,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1028_1]) ).
fof(f_1029_1,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).
cnf(f_1029_2,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1029_1]) ).
fof(f_1030_1,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).
cnf(f_1030_2,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1030_1]) ).
fof(f_1031_1,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).
cnf(f_1031_2,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1031_1]) ).
fof(f_1032_1,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).
cnf(f_1032_2,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1032_1]) ).
fof(f_1033_1,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).
cnf(f_1033_2,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1033_1]) ).
fof(f_1034_1,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).
cnf(f_1034_2,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1034_1]) ).
fof(f_1035_1,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]) ).
cnf(f_1035_2,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1035_1]) ).
fof(f_1036_1,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).
cnf(f_1036_2,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1036_1]) ).
fof(f_1037_1,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).
cnf(f_1037_2,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1037_1]) ).
fof(f_1038_1,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).
cnf(f_1038_2,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1038_1]) ).
fof(f_1039_1,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).
cnf(f_1039_2,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1039_1]) ).
fof(f_1040_1,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).
cnf(f_1040_2,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1040_1]) ).
fof(f_1041_1,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).
cnf(f_1041_2,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1041_1]) ).
fof(f_1042_1,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
cnf(f_1042_2,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1042_1]) ).
fof(f_1043_1,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).
cnf(f_1043_2,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1043_1]) ).
fof(f_1044_1,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).
cnf(f_1044_2,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1044_1]) ).
fof(f_1045_1,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).
cnf(f_1045_2,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1045_1]) ).
fof(f_1046_1,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).
cnf(f_1046_2,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1046_1]) ).
fof(f_1047_1,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).
cnf(f_1047_2,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1047_1]) ).
fof(f_1048_1,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Oring__div]) ).
cnf(f_1048_2,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1048_1]) ).
fof(f_1049_1,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).
cnf(f_1049_2,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1049_1]) ).
fof(f_1050_1,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).
cnf(f_1050_2,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1050_1]) ).
fof(f_1051_1,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).
cnf(f_1051_2,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1051_1]) ).
fof(f_1052_1,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).
cnf(f_1052_2,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1052_1]) ).
fof(f_1053_1,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).
cnf(f_1053_2,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1053_1]) ).
fof(f_1054_1,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).
cnf(f_1054_2,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1054_1]) ).
fof(f_1055_1,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).
cnf(f_1055_2,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1055_1]) ).
fof(f_1056_1,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).
cnf(f_1056_2,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1056_1]) ).
fof(f_1057_1,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).
cnf(f_1057_2,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1057_1]) ).
fof(f_1058_1,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).
cnf(f_1058_2,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1058_1]) ).
fof(f_1059_1,plain,
class_Power_Opower(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).
cnf(f_1059_2,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1059_1]) ).
fof(f_1060_1,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).
cnf(f_1060_2,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1060_1]) ).
fof(f_1061_1,plain,
class_Rings_Oring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).
cnf(f_1061_2,plain,
class_Rings_Oring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1061_1]) ).
fof(f_1062_1,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).
cnf(f_1062_2,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1062_1]) ).
fof(f_1063_1,plain,
class_Groups_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).
cnf(f_1063_2,plain,
class_Groups_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1063_1]) ).
fof(f_1064_1,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Odvd]) ).
cnf(f_1064_2,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1064_1]) ).
fof(f_1065_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_1065_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1065_1]) ).
fof(f_1066_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_1066_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1066_1]) ).
fof(f_1067_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_1067_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1067_1]) ).
fof(f_1068_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_1068_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1068_1]) ).
fof(f_1069_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).
cnf(f_1069_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1069_1]) ).
fof(f_1070_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_1070_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1070_1]) ).
fof(f_1071_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_1071_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1071_1]) ).
fof(f_1072_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_1072_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1072_1]) ).
fof(f_1073_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).
cnf(f_1073_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1073_1]) ).
fof(f_1074_1,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).
cnf(f_1074_2,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1074_1]) ).
fof(f_1075_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
cnf(f_1075_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1075_1]) ).
fof(f_1076_1,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).
cnf(f_1076_2,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1076_1]) ).
fof(f_1077_1,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
cnf(f_1077_2,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1077_1]) ).
fof(f_1078_1,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).
cnf(f_1078_2,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1078_1]) ).
fof(f_1079_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).
cnf(f_1079_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1079_1]) ).
fof(f_1080_1,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).
cnf(f_1080_2,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1080_1]) ).
fof(f_1081_1,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).
cnf(f_1081_2,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1081_1]) ).
fof(f_1082_1,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).
cnf(f_1082_2,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1082_1]) ).
fof(f_1083_1,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).
cnf(f_1083_2,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1083_1]) ).
fof(f_1084_1,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
cnf(f_1084_2,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1084_1]) ).
fof(f_1085_1,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]) ).
cnf(f_1085_2,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1085_1]) ).
fof(f_1086_1,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).
cnf(f_1086_2,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1086_1]) ).
fof(f_1087_1,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).
cnf(f_1087_2,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1087_1]) ).
fof(f_1088_1,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).
cnf(f_1088_2,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1088_1]) ).
fof(f_1089_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(f_1089_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1089_1]) ).
fof(f_1090_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
cnf(f_1090_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1090_1]) ).
fof(f_1091_1,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).
cnf(f_1091_2,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1091_1]) ).
fof(f_1092_1,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).
cnf(f_1092_2,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1092_1]) ).
fof(f_1093_1,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).
cnf(f_1093_2,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1093_1]) ).
fof(f_1094_1,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).
cnf(f_1094_2,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1094_1]) ).
fof(f_1095_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
cnf(f_1095_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1095_1]) ).
fof(f_1096_1,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).
cnf(f_1096_2,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1096_1]) ).
fof(f_1097_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
cnf(f_1097_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1097_1]) ).
fof(f_1098_1,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).
cnf(f_1098_2,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1098_1]) ).
fof(f_1099_1,plain,
class_Power_Opower(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).
cnf(f_1099_2,plain,
class_Power_Opower(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1099_1]) ).
fof(f_1100_1,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).
cnf(f_1100_2,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1100_1]) ).
fof(f_1101_1,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).
cnf(f_1101_2,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1101_1]) ).
fof(f_1102_1,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Odvd]) ).
cnf(f_1102_2,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1102_1]) ).
fof(f_1103_1,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
cnf(f_1103_2,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1103_1]) ).
fof(f_1104_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
cnf(f_1104_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1104_1]) ).
fof(f_1105_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
cnf(f_1105_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1105_1]) ).
fof(f_1106_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
cnf(f_1106_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1106_1]) ).
fof(f_1107_1,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).
cnf(f_1107_2,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1107_1]) ).
fof(f_1108_1,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).
cnf(f_1108_2,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1108_1]) ).
fof(f_1109_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_1109_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1109_1]) ).
fof(f_1110_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_1110_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1110_1]) ).
fof(f_1111_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_1111_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1111_1]) ).
fof(f_1112_1,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
cnf(f_1112_2,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1112_1]) ).
fof(f_1113_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_1113_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1113_1]) ).
fof(f_1114_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_1114_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1114_1]) ).
fof(f_1115_1,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(f_1115_2,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1115_1]) ).
fof(f_1116_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_1116_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1116_1]) ).
fof(f_1117_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).
cnf(f_1117_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1117_1]) ).
fof(f_1118_1,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).
cnf(f_1118_2,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1118_1]) ).
fof(f_1119_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).
cnf(f_1119_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1119_1]) ).
fof(f_1120_1,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).
cnf(f_1120_2,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1120_1]) ).
fof(f_1121_1,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
cnf(f_1121_2,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1121_1]) ).
fof(f_1122_1,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
cnf(f_1122_2,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1122_1]) ).
fof(f_1123_1,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(f_1123_2,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1123_1]) ).
fof(f_1124_1,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
cnf(f_1124_2,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1124_1]) ).
fof(f_1125_1,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).
cnf(f_1125_2,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1125_1]) ).
fof(f_1126_1,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
cnf(f_1126_2,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1126_1]) ).
fof(f_1127_1,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
cnf(f_1127_2,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1127_1]) ).
fof(f_1128_1,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
cnf(f_1128_2,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1128_1]) ).
fof(f_1129_1,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
cnf(f_1129_2,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1129_1]) ).
fof(f_1130_1,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).
cnf(f_1130_2,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1130_1]) ).
fof(f_1131_1,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).
cnf(f_1131_2,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1131_1]) ).
fof(f_1132_1,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(f_1132_2,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1132_1]) ).
fof(f_1133_1,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
cnf(f_1133_2,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1133_1]) ).
fof(f_1134_1,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]) ).
cnf(f_1134_2,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1134_1]) ).
fof(f_1135_1,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(f_1135_2,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1135_1]) ).
fof(f_1136_1,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).
cnf(f_1136_2,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1136_1]) ).
fof(f_1137_1,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]) ).
cnf(f_1137_2,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1137_1]) ).
fof(f_1138_1,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).
cnf(f_1138_2,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1138_1]) ).
fof(f_1139_1,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]) ).
cnf(f_1139_2,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1139_1]) ).
fof(f_1140_1,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
cnf(f_1140_2,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1140_1]) ).
fof(f_1141_1,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
cnf(f_1141_2,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1141_1]) ).
fof(f_1142_1,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
cnf(f_1142_2,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1142_1]) ).
fof(f_1143_1,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).
cnf(f_1143_2,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1143_1]) ).
fof(f_1144_1,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(f_1144_2,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1144_1]) ).
fof(f_1145_1,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).
cnf(f_1145_2,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1145_1]) ).
fof(f_1146_1,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]) ).
cnf(f_1146_2,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1146_1]) ).
fof(f_1147_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_1147_2,plain,
! [U_3231] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3231))
| ~ class_Rings_Oidom(U_3231) ),
inference(variable_rename,[status(thm)],[f_1147_1]) ).
cnf(f_1147_3,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3231))
| ~ class_Rings_Oidom(U_3231) ),
inference(clausify,[status(thm)],[f_1147_2]) ).
fof(f_1148_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_1148_2,plain,
! [U_3232] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3232))
| ~ class_Rings_Olinordered__idom(U_3232) ),
inference(variable_rename,[status(thm)],[f_1148_1]) ).
cnf(f_1148_3,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3232))
| ~ class_Rings_Olinordered__idom(U_3232) ),
inference(clausify,[status(thm)],[f_1148_2]) ).
fof(f_1149_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_1149_2,plain,
! [U_3233] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3233))
| ~ class_Rings_Olinordered__idom(U_3233) ),
inference(variable_rename,[status(thm)],[f_1149_1]) ).
cnf(f_1149_3,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3233))
| ~ class_Rings_Olinordered__idom(U_3233) ),
inference(clausify,[status(thm)],[f_1149_2]) ).
fof(f_1150_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_1150_2,plain,
! [U_3234] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3234))
| ~ class_Rings_Olinordered__idom(U_3234) ),
inference(variable_rename,[status(thm)],[f_1150_1]) ).
cnf(f_1150_3,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3234))
| ~ class_Rings_Olinordered__idom(U_3234) ),
inference(clausify,[status(thm)],[f_1150_2]) ).
fof(f_1151_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_1151_2,plain,
! [U_3235] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3235))
| ~ class_Rings_Olinordered__idom(U_3235) ),
inference(variable_rename,[status(thm)],[f_1151_1]) ).
cnf(f_1151_3,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3235))
| ~ class_Rings_Olinordered__idom(U_3235) ),
inference(clausify,[status(thm)],[f_1151_2]) ).
fof(f_1152_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_1152_2,plain,
! [U_3236] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3236))
| ~ class_Rings_Olinordered__idom(U_3236) ),
inference(variable_rename,[status(thm)],[f_1152_1]) ).
cnf(f_1152_3,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3236))
| ~ class_Rings_Olinordered__idom(U_3236) ),
inference(clausify,[status(thm)],[f_1152_2]) ).
fof(f_1153_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_1153_2,plain,
! [U_3237] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3237))
| ~ class_Rings_Olinordered__idom(U_3237) ),
inference(variable_rename,[status(thm)],[f_1153_1]) ).
cnf(f_1153_3,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3237))
| ~ class_Rings_Olinordered__idom(U_3237) ),
inference(clausify,[status(thm)],[f_1153_2]) ).
fof(f_1154_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_1154_2,plain,
! [U_3238] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3238))
| ~ class_Rings_Olinordered__idom(U_3238) ),
inference(variable_rename,[status(thm)],[f_1154_1]) ).
cnf(f_1154_3,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3238))
| ~ class_Rings_Olinordered__idom(U_3238) ),
inference(clausify,[status(thm)],[f_1154_2]) ).
fof(f_1155_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_1155_2,plain,
! [U_3239] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3239))
| ~ class_Rings_Olinordered__idom(U_3239) ),
inference(variable_rename,[status(thm)],[f_1155_1]) ).
cnf(f_1155_3,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3239))
| ~ class_Rings_Olinordered__idom(U_3239) ),
inference(clausify,[status(thm)],[f_1155_2]) ).
fof(f_1156_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_1156_2,plain,
! [U_3240] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3240))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3240) ),
inference(variable_rename,[status(thm)],[f_1156_1]) ).
cnf(f_1156_3,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3240))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3240) ),
inference(clausify,[status(thm)],[f_1156_2]) ).
fof(f_1157_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_1157_2,plain,
! [U_3241] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3241))
| ~ class_Rings_Oidom(U_3241) ),
inference(variable_rename,[status(thm)],[f_1157_1]) ).
cnf(f_1157_3,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3241))
| ~ class_Rings_Oidom(U_3241) ),
inference(clausify,[status(thm)],[f_1157_2]) ).
fof(f_1158_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_1158_2,plain,
! [U_3242] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3242))
| ~ class_Rings_Olinordered__idom(U_3242) ),
inference(variable_rename,[status(thm)],[f_1158_1]) ).
cnf(f_1158_3,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3242))
| ~ class_Rings_Olinordered__idom(U_3242) ),
inference(clausify,[status(thm)],[f_1158_2]) ).
fof(f_1159_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_1159_2,plain,
! [U_3243] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3243))
| ~ class_Rings_Olinordered__idom(U_3243) ),
inference(variable_rename,[status(thm)],[f_1159_1]) ).
cnf(f_1159_3,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3243))
| ~ class_Rings_Olinordered__idom(U_3243) ),
inference(clausify,[status(thm)],[f_1159_2]) ).
fof(f_1160_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_1160_2,plain,
! [U_3244] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3244))
| ~ class_Rings_Oidom(U_3244) ),
inference(variable_rename,[status(thm)],[f_1160_1]) ).
cnf(f_1160_3,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3244))
| ~ class_Rings_Oidom(U_3244) ),
inference(clausify,[status(thm)],[f_1160_2]) ).
fof(f_1161_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_1161_2,plain,
! [U_3245] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3245))
| ~ class_Rings_Olinordered__idom(U_3245) ),
inference(variable_rename,[status(thm)],[f_1161_1]) ).
cnf(f_1161_3,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3245))
| ~ class_Rings_Olinordered__idom(U_3245) ),
inference(clausify,[status(thm)],[f_1161_2]) ).
fof(f_1162_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_1162_2,plain,
! [U_3246] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3246))
| ~ class_Rings_Olinordered__idom(U_3246) ),
inference(variable_rename,[status(thm)],[f_1162_1]) ).
cnf(f_1162_3,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3246))
| ~ class_Rings_Olinordered__idom(U_3246) ),
inference(clausify,[status(thm)],[f_1162_2]) ).
fof(f_1163_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_1163_2,plain,
! [U_3247] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3247))
| ~ class_Rings_Olinordered__idom(U_3247) ),
inference(variable_rename,[status(thm)],[f_1163_1]) ).
cnf(f_1163_3,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3247))
| ~ class_Rings_Olinordered__idom(U_3247) ),
inference(clausify,[status(thm)],[f_1163_2]) ).
fof(f_1164_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_1164_2,plain,
! [U_3248] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3248))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3248) ),
inference(variable_rename,[status(thm)],[f_1164_1]) ).
cnf(f_1164_3,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3248))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3248) ),
inference(clausify,[status(thm)],[f_1164_2]) ).
fof(f_1165_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_1165_2,plain,
! [U_3249] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3249))
| ~ class_Rings_Olinordered__idom(U_3249) ),
inference(variable_rename,[status(thm)],[f_1165_1]) ).
cnf(f_1165_3,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3249))
| ~ class_Rings_Olinordered__idom(U_3249) ),
inference(clausify,[status(thm)],[f_1165_2]) ).
fof(f_1166_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_1166_2,plain,
! [U_3250] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3250))
| ~ class_Rings_Olinordered__idom(U_3250) ),
inference(variable_rename,[status(thm)],[f_1166_1]) ).
cnf(f_1166_3,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3250))
| ~ class_Rings_Olinordered__idom(U_3250) ),
inference(clausify,[status(thm)],[f_1166_2]) ).
fof(f_1167_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_1167_2,plain,
! [U_3251] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3251))
| ~ class_Rings_Ocomm__semiring__0(U_3251) ),
inference(variable_rename,[status(thm)],[f_1167_1]) ).
cnf(f_1167_3,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3251))
| ~ class_Rings_Ocomm__semiring__0(U_3251) ),
inference(clausify,[status(thm)],[f_1167_2]) ).
fof(f_1168_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_1168_2,plain,
! [U_3252] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3252))
| ~ class_Rings_Ocomm__semiring__1(U_3252) ),
inference(variable_rename,[status(thm)],[f_1168_1]) ).
cnf(f_1168_3,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3252))
| ~ class_Rings_Ocomm__semiring__1(U_3252) ),
inference(clausify,[status(thm)],[f_1168_2]) ).
fof(f_1169_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_1169_2,plain,
! [U_3253] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3253))
| ~ class_Groups_Ocomm__monoid__add(U_3253) ),
inference(variable_rename,[status(thm)],[f_1169_1]) ).
cnf(f_1169_3,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3253))
| ~ class_Groups_Ocomm__monoid__add(U_3253) ),
inference(clausify,[status(thm)],[f_1169_2]) ).
fof(f_1170_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_1170_2,plain,
! [U_3254] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3254))
| ~ class_Rings_Olinordered__idom(U_3254) ),
inference(variable_rename,[status(thm)],[f_1170_1]) ).
cnf(f_1170_3,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3254))
| ~ class_Rings_Olinordered__idom(U_3254) ),
inference(clausify,[status(thm)],[f_1170_2]) ).
fof(f_1171_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_1171_2,plain,
! [U_3255] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3255))
| ~ class_Rings_Oidom(U_3255) ),
inference(variable_rename,[status(thm)],[f_1171_1]) ).
cnf(f_1171_3,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3255))
| ~ class_Rings_Oidom(U_3255) ),
inference(clausify,[status(thm)],[f_1171_2]) ).
fof(f_1172_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_1172_2,plain,
! [U_3256] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3256))
| ~ class_Groups_Ocomm__monoid__add(U_3256) ),
inference(variable_rename,[status(thm)],[f_1172_1]) ).
cnf(f_1172_3,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3256))
| ~ class_Groups_Ocomm__monoid__add(U_3256) ),
inference(clausify,[status(thm)],[f_1172_2]) ).
fof(f_1173_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_1173_2,plain,
! [U_3257] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3257))
| ~ class_Rings_Olinordered__idom(U_3257) ),
inference(variable_rename,[status(thm)],[f_1173_1]) ).
cnf(f_1173_3,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3257))
| ~ class_Rings_Olinordered__idom(U_3257) ),
inference(clausify,[status(thm)],[f_1173_2]) ).
fof(f_1174_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_1174_2,plain,
! [U_3258] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3258))
| ~ class_Rings_Olinordered__idom(U_3258) ),
inference(variable_rename,[status(thm)],[f_1174_1]) ).
cnf(f_1174_3,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3258))
| ~ class_Rings_Olinordered__idom(U_3258) ),
inference(clausify,[status(thm)],[f_1174_2]) ).
fof(f_1175_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_1175_2,plain,
! [U_3259] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3259))
| ~ class_Rings_Ocomm__semiring__1(U_3259) ),
inference(variable_rename,[status(thm)],[f_1175_1]) ).
cnf(f_1175_3,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3259))
| ~ class_Rings_Ocomm__semiring__1(U_3259) ),
inference(clausify,[status(thm)],[f_1175_2]) ).
fof(f_1176_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_1176_2,plain,
! [U_3260] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3260))
| ~ class_Rings_Ocomm__semiring__0(U_3260) ),
inference(variable_rename,[status(thm)],[f_1176_1]) ).
cnf(f_1176_3,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3260))
| ~ class_Rings_Ocomm__semiring__0(U_3260) ),
inference(clausify,[status(thm)],[f_1176_2]) ).
fof(f_1177_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_1177_2,plain,
! [U_3261] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3261))
| ~ class_Fields_Ofield(U_3261) ),
inference(variable_rename,[status(thm)],[f_1177_1]) ).
cnf(f_1177_3,plain,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3261))
| ~ class_Fields_Ofield(U_3261) ),
inference(clausify,[status(thm)],[f_1177_2]) ).
fof(f_1178_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_1178_2,plain,
! [U_3262] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3262))
| ~ class_Rings_Ocomm__semiring__0(U_3262) ),
inference(variable_rename,[status(thm)],[f_1178_1]) ).
cnf(f_1178_3,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3262))
| ~ class_Rings_Ocomm__semiring__0(U_3262) ),
inference(clausify,[status(thm)],[f_1178_2]) ).
fof(f_1179_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_1179_2,plain,
! [U_3263] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3263))
| ~ class_Groups_Oab__group__add(U_3263) ),
inference(variable_rename,[status(thm)],[f_1179_1]) ).
cnf(f_1179_3,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3263))
| ~ class_Groups_Oab__group__add(U_3263) ),
inference(clausify,[status(thm)],[f_1179_2]) ).
fof(f_1180_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_1180_2,plain,
! [U_3264] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3264))
| ~ class_Rings_Ocomm__semiring__1(U_3264) ),
inference(variable_rename,[status(thm)],[f_1180_1]) ).
cnf(f_1180_3,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3264))
| ~ class_Rings_Ocomm__semiring__1(U_3264) ),
inference(clausify,[status(thm)],[f_1180_2]) ).
fof(f_1181_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_1181_2,plain,
! [U_3265] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3265))
| ~ class_Rings_Olinordered__idom(U_3265) ),
inference(variable_rename,[status(thm)],[f_1181_1]) ).
cnf(f_1181_3,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3265))
| ~ class_Rings_Olinordered__idom(U_3265) ),
inference(clausify,[status(thm)],[f_1181_2]) ).
fof(f_1182_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_1182_2,plain,
! [U_3266] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3266))
| ~ class_Rings_Olinordered__idom(U_3266) ),
inference(variable_rename,[status(thm)],[f_1182_1]) ).
cnf(f_1182_3,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3266))
| ~ class_Rings_Olinordered__idom(U_3266) ),
inference(clausify,[status(thm)],[f_1182_2]) ).
fof(f_1183_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_1183_2,plain,
! [U_3267] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3267))
| ~ class_Rings_Olinordered__idom(U_3267) ),
inference(variable_rename,[status(thm)],[f_1183_1]) ).
cnf(f_1183_3,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3267))
| ~ class_Rings_Olinordered__idom(U_3267) ),
inference(clausify,[status(thm)],[f_1183_2]) ).
fof(f_1184_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_1184_2,plain,
! [U_3268] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3268))
| ~ class_Rings_Ocomm__semiring__1(U_3268) ),
inference(variable_rename,[status(thm)],[f_1184_1]) ).
cnf(f_1184_3,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3268))
| ~ class_Rings_Ocomm__semiring__1(U_3268) ),
inference(clausify,[status(thm)],[f_1184_2]) ).
fof(f_1185_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_1185_2,plain,
! [U_3269] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3269))
| ~ class_Rings_Ocomm__ring__1(U_3269) ),
inference(variable_rename,[status(thm)],[f_1185_1]) ).
cnf(f_1185_3,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3269))
| ~ class_Rings_Ocomm__ring__1(U_3269) ),
inference(clausify,[status(thm)],[f_1185_2]) ).
fof(f_1186_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_1186_2,plain,
! [U_3270] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3270))
| ~ class_Groups_Ocomm__monoid__add(U_3270) ),
inference(variable_rename,[status(thm)],[f_1186_1]) ).
cnf(f_1186_3,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3270))
| ~ class_Groups_Ocomm__monoid__add(U_3270) ),
inference(clausify,[status(thm)],[f_1186_2]) ).
fof(f_1187_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_1187_2,plain,
! [U_3271] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3271))
| ~ class_Rings_Ocomm__semiring__0(U_3271) ),
inference(variable_rename,[status(thm)],[f_1187_1]) ).
cnf(f_1187_3,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3271))
| ~ class_Rings_Ocomm__semiring__0(U_3271) ),
inference(clausify,[status(thm)],[f_1187_2]) ).
fof(f_1188_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_1188_2,plain,
! [U_3272] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3272))
| ~ class_Groups_Oab__group__add(U_3272) ),
inference(variable_rename,[status(thm)],[f_1188_1]) ).
cnf(f_1188_3,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3272))
| ~ class_Groups_Oab__group__add(U_3272) ),
inference(clausify,[status(thm)],[f_1188_2]) ).
fof(f_1189_1,plain,
! [T_1] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Fields_Ofield(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Oring__div]) ).
fof(f_1189_2,plain,
! [U_3273] :
( class_Divides_Oring__div(tc_Polynomial_Opoly(U_3273))
| ~ class_Fields_Ofield(U_3273) ),
inference(variable_rename,[status(thm)],[f_1189_1]) ).
cnf(f_1189_3,plain,
( class_Divides_Oring__div(tc_Polynomial_Opoly(U_3273))
| ~ class_Fields_Ofield(U_3273) ),
inference(clausify,[status(thm)],[f_1189_2]) ).
fof(f_1190_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_1190_2,plain,
! [U_3274] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3274))
| ~ class_Rings_Ocomm__semiring__0(U_3274) ),
inference(variable_rename,[status(thm)],[f_1190_1]) ).
cnf(f_1190_3,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3274))
| ~ class_Rings_Ocomm__semiring__0(U_3274) ),
inference(clausify,[status(thm)],[f_1190_2]) ).
fof(f_1191_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_1191_2,plain,
! [U_3275] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3275))
| ~ class_Rings_Ocomm__ring(U_3275) ),
inference(variable_rename,[status(thm)],[f_1191_1]) ).
cnf(f_1191_3,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3275))
| ~ class_Rings_Ocomm__ring(U_3275) ),
inference(clausify,[status(thm)],[f_1191_2]) ).
fof(f_1192_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_1192_2,plain,
! [U_3276] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3276))
| ~ class_Rings_Olinordered__idom(U_3276) ),
inference(variable_rename,[status(thm)],[f_1192_1]) ).
cnf(f_1192_3,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3276))
| ~ class_Rings_Olinordered__idom(U_3276) ),
inference(clausify,[status(thm)],[f_1192_2]) ).
fof(f_1193_1,plain,
! [T_1] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0]) ).
fof(f_1193_2,plain,
! [U_3277] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3277))
| ~ class_Rings_Olinordered__idom(U_3277) ),
inference(variable_rename,[status(thm)],[f_1193_1]) ).
cnf(f_1193_3,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3277))
| ~ class_Rings_Olinordered__idom(U_3277) ),
inference(clausify,[status(thm)],[f_1193_2]) ).
fof(f_1194_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_1194_2,plain,
! [U_3278] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3278))
| ~ class_Rings_Ocomm__semiring__0(U_3278) ),
inference(variable_rename,[status(thm)],[f_1194_1]) ).
cnf(f_1194_3,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3278))
| ~ class_Rings_Ocomm__semiring__0(U_3278) ),
inference(clausify,[status(thm)],[f_1194_2]) ).
fof(f_1195_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_1195_2,plain,
! [U_3279] :
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3279))
| ~ class_Rings_Olinordered__idom(U_3279) ),
inference(variable_rename,[status(thm)],[f_1195_1]) ).
cnf(f_1195_3,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3279))
| ~ class_Rings_Olinordered__idom(U_3279) ),
inference(clausify,[status(thm)],[f_1195_2]) ).
fof(f_1196_1,plain,
! [T_1] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus]) ).
fof(f_1196_2,plain,
! [U_3280] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3280))
| ~ class_Groups_Oab__group__add(U_3280) ),
inference(variable_rename,[status(thm)],[f_1196_1]) ).
cnf(f_1196_3,plain,
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3280))
| ~ class_Groups_Oab__group__add(U_3280) ),
inference(clausify,[status(thm)],[f_1196_2]) ).
fof(f_1197_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_1197_2,plain,
! [U_3281] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3281))
| ~ class_Rings_Olinordered__idom(U_3281) ),
inference(variable_rename,[status(thm)],[f_1197_1]) ).
cnf(f_1197_3,plain,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3281))
| ~ class_Rings_Olinordered__idom(U_3281) ),
inference(clausify,[status(thm)],[f_1197_2]) ).
fof(f_1198_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_1198_2,plain,
! [U_3282] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3282))
| ~ class_Rings_Ocomm__ring__1(U_3282) ),
inference(variable_rename,[status(thm)],[f_1198_1]) ).
cnf(f_1198_3,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3282))
| ~ class_Rings_Ocomm__ring__1(U_3282) ),
inference(clausify,[status(thm)],[f_1198_2]) ).
fof(f_1199_1,plain,
! [T_1] :
( class_Groups_Ominus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus]) ).
fof(f_1199_2,plain,
! [U_3283] :
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3283))
| ~ class_Groups_Oab__group__add(U_3283) ),
inference(variable_rename,[status(thm)],[f_1199_1]) ).
cnf(f_1199_3,plain,
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3283))
| ~ class_Groups_Oab__group__add(U_3283) ),
inference(clausify,[status(thm)],[f_1199_2]) ).
fof(f_1200_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_1200_2,plain,
! [U_3284] :
( class_Power_Opower(tc_Polynomial_Opoly(U_3284))
| ~ class_Rings_Ocomm__semiring__1(U_3284) ),
inference(variable_rename,[status(thm)],[f_1200_1]) ).
cnf(f_1200_3,plain,
( class_Power_Opower(tc_Polynomial_Opoly(U_3284))
| ~ class_Rings_Ocomm__semiring__1(U_3284) ),
inference(clausify,[status(thm)],[f_1200_2]) ).
fof(f_1201_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_1201_2,plain,
! [U_3285] :
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3285))
| ~ class_Groups_Ozero(U_3285) ),
inference(variable_rename,[status(thm)],[f_1201_1]) ).
cnf(f_1201_3,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3285))
| ~ class_Groups_Ozero(U_3285) ),
inference(clausify,[status(thm)],[f_1201_2]) ).
fof(f_1202_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_1202_2,plain,
! [U_3286] :
( class_Rings_Oring(tc_Polynomial_Opoly(U_3286))
| ~ class_Rings_Ocomm__ring(U_3286) ),
inference(variable_rename,[status(thm)],[f_1202_1]) ).
cnf(f_1202_3,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(U_3286))
| ~ class_Rings_Ocomm__ring(U_3286) ),
inference(clausify,[status(thm)],[f_1202_2]) ).
fof(f_1203_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_1203_2,plain,
! [U_3287] :
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3287))
| ~ class_Rings_Oidom(U_3287) ),
inference(variable_rename,[status(thm)],[f_1203_1]) ).
cnf(f_1203_3,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3287))
| ~ class_Rings_Oidom(U_3287) ),
inference(clausify,[status(thm)],[f_1203_2]) ).
fof(f_1204_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_1204_2,plain,
! [U_3288] :
( class_Groups_Oone(tc_Polynomial_Opoly(U_3288))
| ~ class_Rings_Ocomm__semiring__1(U_3288) ),
inference(variable_rename,[status(thm)],[f_1204_1]) ).
cnf(f_1204_3,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(U_3288))
| ~ class_Rings_Ocomm__semiring__1(U_3288) ),
inference(clausify,[status(thm)],[f_1204_2]) ).
fof(f_1205_1,plain,
! [T_1] :
( class_Rings_Odvd(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd]) ).
fof(f_1205_2,plain,
! [U_3289] :
( class_Rings_Odvd(tc_Polynomial_Opoly(U_3289))
| ~ class_Rings_Ocomm__semiring__1(U_3289) ),
inference(variable_rename,[status(thm)],[f_1205_1]) ).
cnf(f_1205_3,plain,
( class_Rings_Odvd(tc_Polynomial_Opoly(U_3289))
| ~ class_Rings_Ocomm__semiring__1(U_3289) ),
inference(clausify,[status(thm)],[f_1205_2]) ).
fof(f_1206_1,plain,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(c_fequal(V_x_2,V_y_2)) ),
inference(fof_nnf,[status(thm)],[help_c__fequal__1]) ).
fof(f_1206_2,plain,
! [U_3291,U_3290] :
( U_3290 = U_3291
| ~ hBOOL(c_fequal(U_3290,U_3291)) ),
inference(variable_rename,[status(thm)],[f_1206_1]) ).
cnf(f_1206_3,plain,
( U_3290 = U_3291
| ~ hBOOL(c_fequal(U_3290,U_3291)) ),
inference(clausify,[status(thm)],[f_1206_2]) ).
fof(f_1207_1,plain,
! [V_y_2,V_x_2] :
( hBOOL(c_fequal(V_x_2,V_y_2))
| V_x_2 != V_y_2 ),
inference(fof_nnf,[status(thm)],[help_c__fequal__2]) ).
fof(f_1207_2,plain,
! [U_3293,U_3292] :
( hBOOL(c_fequal(U_3292,U_3293))
| U_3292 != U_3293 ),
inference(variable_rename,[status(thm)],[f_1207_1]) ).
cnf(f_1207_3,plain,
( hBOOL(c_fequal(U_3292,U_3293))
| U_3292 != U_3293 ),
inference(clausify,[status(thm)],[f_1207_2]) ).
fof(f_1208_1,plain,
( v_thesis____
| ! [B_r] : v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),B_r) ),
inference(fof_nnf,[status(thm)],[conj_0]) ).
fof(f_1208_2,plain,
( v_thesis____
| ! [U_3294] : v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),U_3294) ),
inference(variable_rename,[status(thm)],[f_1208_1]) ).
cnf(f_1208_3,plain,
( v_thesis____
| v_qa____ != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,v_a____),c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))),U_3294) ),
inference(clausify,[status(thm)],[f_1208_2]) ).
fof(f_1209_1,negated_conjecture,
~ v_thesis____,
inference(negate,[status(cth)],[conj_1]) ).
cnf(f_1209_2,negated_conjecture,
~ v_thesis____,
inference(clausify,[status(thm)],[f_1209_1]) ).
cnf(f_195_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_195_4]) ).
cnf(f_195_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_195_6]) ).
cnf(f_196_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_196_4]) ).
cnf(f_196_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_196_6]) ).
cnf(f_197_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_197_3]) ).
cnf(f_200_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_200_3]) ).
cnf(f_201_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_201_3]) ).
cnf(f_210_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_210_3]) ).
cnf(f_211_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_211_3]) ).
cnf(f_212_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_212_3]) ).
cnf(f_217_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_217_3]) ).
cnf(f_219_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_219_3]) ).
cnf(f_221_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_221_4]) ).
cnf(f_221_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_221_5]) ).
cnf(f_221_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_221_6]) ).
cnf(f_221_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_221_7]) ).
cnf(f_221_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_221_8]) ).
cnf(f_221_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_221_9]) ).
cnf(f_221_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_221_10]) ).
cnf(f_644_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_644_6]) ).
cnf(f_756_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_756_4]) ).
cnf(f_756_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_756_5]) ).
cnf(f_756_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_756_10]) ).
cnf(f_756_11_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_756_11]) ).
cnf(f_756_16_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_756_16]) ).
cnf(f_756_17_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_756_17]) ).
cnf(f_938_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_938_3]) ).
cnf(f_959_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_959_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,
( tc_Polynomial_Opoly(Eq_x_0) = tc_Polynomial_Opoly(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,axiom,
( c_Rings_Odvd__class_Odvd(Eq_x_0) = c_Rings_Odvd__class_Odvd(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( c_Groups_Ouminus__class_Ouminus(Eq_x_0,Eq_x_1) = c_Groups_Ouminus__class_Ouminus(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_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_Polynomial_OpCons(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_OpCons(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( c_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_12,axiom,
( c_Polynomial_Oorder(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Oorder(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( c_Polynomial_Opoly(Eq_x_0,Eq_x_1) = c_Polynomial_Opoly(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( c_Polynomial_Odegree(Eq_x_0,Eq_x_1) = c_Polynomial_Odegree(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_Nat_OSuc(Eq_x_0) = c_Nat_OSuc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,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_19,axiom,
( c_Polynomial_Opcompose(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opcompose(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_20,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_21,axiom,
( c_Polynomial_Omonom(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Omonom(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_22,axiom,
( c_Polynomial_Opoly__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Polynomial_Opoly__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,axiom,
( c_Polynomial_Osynthetic__div(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Osynthetic__div(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_24,axiom,
( c_Polynomial_Ocoeff(Eq_x_0,Eq_x_1) = c_Polynomial_Ocoeff(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_25,axiom,
( c_fequal(Eq_x_0,Eq_x_1) = c_fequal(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( c_If(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_If(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_27,axiom,
( c_Groups_Oplus__class_Oplus(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Oplus__class_Oplus(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_Polynomial_Opoly__gcd(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opoly__gcd(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,axiom,
( c_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_30,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_31,axiom,
( c_SMT_Oz3div(Eq_x_0,Eq_x_1) = c_SMT_Oz3div(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,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_33,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_34,axiom,
( c_Divides_Odiv__class_Omod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Omod(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,
( 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_36,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(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,
( 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_38,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK5(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_40,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(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_41,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(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,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(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,
( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_44,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(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,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK13(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_48,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(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,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,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_51,axiom,
( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(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_54,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(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_55,axiom,
( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(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_56,axiom,
( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(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_60,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(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_61,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(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_62,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_63,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,axiom,
( class_Rings_Odvd(Eq_y_0)
| ~ class_Rings_Odvd(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,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_81,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_82,axiom,
( class_Int_Oring__char__0(Eq_y_0)
| ~ class_Int_Oring__char__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_83,axiom,
( class_Rings_Ocomm__ring(Eq_y_0)
| ~ class_Rings_Ocomm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_84,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_85,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_86,axiom,
( c_Orderings_Oord__class_Oless__eq(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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_96,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_97,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_98,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_99,axiom,
( c_Orderings_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Orderings_Oord__class_Oless(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_100,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_101,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_102,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_103,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_104,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_105,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_106,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_107,axiom,
( c_Polynomial_Opos__poly(Eq_y_0,Eq_y_1)
| ~ c_Polynomial_Opos__poly(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_108,axiom,
( class_Lattices_Oboolean__algebra(Eq_y_0)
| ~ class_Lattices_Oboolean__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_109,axiom,
( class_Lattices_Oab__semigroup__idem__mult(Eq_y_0)
| ~ class_Lattices_Oab__semigroup__idem__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_110,axiom,
( class_Groups_Ouminus(Eq_y_0)
| ~ class_Groups_Ouminus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_111,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_112,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_113,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_114,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_115,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_116,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_117,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_118,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_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_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_123,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_124,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_125,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_126,axiom,
( c_Polynomial_Opdivmod__rel(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ c_Polynomial_Opdivmod__rel(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_127,axiom,
( c_Orderings_Oorder_Omono(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Orderings_Oorder_Omono(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_128,axiom,
( class_Groups_Ominus(Eq_y_0)
| ~ class_Groups_Ominus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_129,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_130,axiom,
( class_Divides_Oring__div(Eq_y_0)
| ~ class_Divides_Oring__div(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_131,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_132,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_133,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_134,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_135,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW271+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.39 % Computer : n008.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Sun Sep 20 05:17:53 UTC 2026
% 0.09/10.39 % CPUTime :
% 228.30/238.64 % SZS status Theorem for theBenchmark
% 228.30/238.64 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------