%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 18:18:56 EDT 2024

% Result   : Theorem 0.97s 1.22s
% Output   : Proof 0.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.24  % Problem    : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% 0.13/0.25  % Command    : do_cvc5 %s %d
% 0.25/0.46  % Computer : n026.cluster.edu
% 0.25/0.46  % Model    : x86_64 x86_64
% 0.25/0.46  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.46  % Memory   : 8042.1875MB
% 0.25/0.46  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.25/0.46  % CPULimit   : 300
% 0.25/0.46  % WCLimit    : 300
% 0.25/0.46  % DateTime   : Sun May 26 06:49:54 EDT 2024
% 0.25/0.46  % CPUTime    : 
% 0.53/0.87  %----Proving TF0_NAR, FOF, or CNF
% 0.97/1.22  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.97/1.22  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.zIms5SNDm7/cvc5---1.0.5_29063.smt2
% 0.97/1.22  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.zIms5SNDm7/cvc5---1.0.5_29063.smt2
% 0.97/1.22  (assume a0 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))))
% 0.97/1.22  (assume a1 (=> (tptp.class_Rings_Oidom tptp.t_a) (not (forall ((B_z $$unsorted)) (=> (not (= B_z (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))))))
% 0.97/1.22  (assume a2 (=> (tptp.class_Rings_Oidom tptp.t_a) (not (forall ((B_z $$unsorted)) (=> (not (= B_z (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a tptp.v_p) B_z) (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))))))
% 0.97/1.22  (assume a3 (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))
% 0.97/1.22  (assume a4 (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))
% 0.97/1.22  (assume a5 (forall ((V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (and (=> (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_OpCons T_a V_a V_p)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_OpCons T_a V_a V_p)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree T_a V_p))))))))
% 0.97/1.22  (assume a6 (forall ((V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_OpCons T_a V_a V_p)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree T_a V_p)))))))
% 0.97/1.22  (assume a7 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a8 (forall ((V_x $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_OpCons T_a V_a V_p)) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)))))))
% 0.97/1.22  (assume a9 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (and (=> (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_p) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_p) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree T_a V_p))))))))
% 0.97/1.22  (assume a10 (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (forall ((B_z $$unsorted)) (=> (not (= B_z (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a tptp.v_cs____) B_z) (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= tptp.v_cs____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= tptp.v_cs____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a tptp.v_cs____)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a tptp.v_cs____) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))
% 0.97/1.22  (assume a11 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a12 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a13 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a14 (forall ((V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.c_Polynomial_OpCons T_b V_a_2 V_pa_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (and (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))))))))
% 0.97/1.22  (assume a15 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_p))))
% 0.97/1.22  (assume a16 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_q) V_q))))
% 0.97/1.22  (assume a17 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a18 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_q) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a19 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (not (= V_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p) (tptp.c_Polynomial_Odegree T_a V_q))))))))
% 0.97/1.22  (assume a20 (forall ((V_q_2 $$unsorted) (V_b_2 $$unsorted) (V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.c_Polynomial_OpCons T_b V_a_2 V_pa_2) (tptp.c_Polynomial_OpCons T_b V_b_2 V_q_2)) (and (= V_a_2 V_b_2) (= V_pa_2 V_q_2))))))
% 0.97/1.22  (assume a21 (forall ((V_q_2 $$unsorted) (V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_b) (tptp.class_Rings_Oidom T_b)) (= (= (tptp.c_Polynomial_Opoly T_b V_pa_2) (tptp.c_Polynomial_Opoly T_b V_q_2)) (= V_pa_2 V_q_2)))))
% 0.97/1.22  (assume a22 (forall ((V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_b V_pa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))))))
% 0.97/1.22  (assume a23 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a V_p) (tptp.c_Polynomial_OpCons T_a V_b V_q)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q))))))
% 0.97/1.22  (assume a24 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 0.97/1.22  (assume a25 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 0.97/1.22  (assume a26 (forall ((V_x $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) V_p) V_n)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) V_n)))))
% 0.97/1.22  (assume a27 (forall ((V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_b) (tptp.class_Rings_Oidom T_b)) (= (= (tptp.c_Polynomial_Opoly T_b V_pa_2) (tptp.c_Polynomial_Opoly T_b (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))))))
% 0.97/1.22  (assume a28 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 0.97/1.22  (assume a29 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 0.97/1.22  (assume a30 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_p)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_p V_q))))))
% 0.97/1.22  (assume a31 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 0.97/1.22  (assume a32 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q))))))
% 0.97/1.22  (assume a33 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q))))))
% 0.97/1.22  (assume a34 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) V_a)))))
% 0.97/1.22  (assume a35 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q))))))
% 0.97/1.22  (assume a36 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 0.97/1.22  (assume a37 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a38 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Power_Opower T_b) (tptp.class_Rings_Omult__zero T_b) (tptp.class_Rings_Ono__zero__divisors T_b) (tptp.class_Rings_Ozero__neq__one T_b)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) V_a_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (and (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 0.97/1.22  (assume a39 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_d)))))))))
% 0.97/1.22  (assume a40 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_r) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_q) V_r))))))
% 0.97/1.22  (assume a41 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a42 (forall ((V_m_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_m_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_x_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 0.97/1.22  (assume a43 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)))))
% 0.97/1.22  (assume a44 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ry))))))
% 0.97/1.22  (assume a45 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ry)))))
% 0.97/1.22  (assume a46 (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_rx))))))
% 0.97/1.22  (assume a47 (forall ((V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) V_ly)))))
% 0.97/1.22  (assume a48 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)))))))
% 0.97/1.22  (assume a49 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_ry))))))
% 0.97/1.22  (assume a50 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_ry))))))
% 0.97/1.22  (assume a51 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))
% 0.97/1.22  (assume a52 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))))
% 0.97/1.22  (assume a53 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))))
% 0.97/1.22  (assume a54 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 0.97/1.22  (assume a55 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))))
% 0.97/1.22  (assume a56 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))))
% 0.97/1.22  (assume a57 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a58 (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a59 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a60 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a61 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a62 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) V_n)))))
% 0.97/1.22  (assume a63 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_p)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) V_q))))))
% 0.97/1.22  (assume a64 (forall ((V_n $$unsorted)) (not (= V_n (tptp.c_Nat_OSuc V_n)))))
% 0.97/1.22  (assume a65 (forall ((V_n $$unsorted)) (not (= (tptp.c_Nat_OSuc V_n) V_n))))
% 0.97/1.22  (assume a66 (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.c_Nat_OSuc V_nat_2) (tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))))
% 0.97/1.22  (assume a67 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Nat_OSuc V_x) (tptp.c_Nat_OSuc V_y)) (= V_x V_y))))
% 0.97/1.22  (assume a68 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (= V_m_2 V_n_2))))
% 0.97/1.22  (assume a69 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 0.97/1.22  (assume a70 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))))
% 0.97/1.22  (assume a71 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))))
% 0.97/1.22  (assume a72 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (= V_m_2 V_n_2))))
% 0.97/1.22  (assume a73 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (= V_m_2 V_n_2))))
% 0.97/1.22  (assume a74 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 0.97/1.22  (assume a75 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 0.97/1.22  (assume a76 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a77 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a78 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 0.97/1.22  (assume a79 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 0.97/1.22  (assume a80 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_b) (= (= V_b_2 (tptp.c_Groups_Oplus__class_Oplus T_b V_b_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a81 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_z))))))
% 0.97/1.22  (assume a82 (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_b) (= (and (not (= V_a_2 V_b_2)) (not (= V_ca_2 V_d_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_d_2)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_d_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_ca_2))))))))
% 0.97/1.22  (assume a83 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 0.97/1.22  (assume a84 (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_m)))))
% 0.97/1.22  (assume a85 (forall ((V_z_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (V_w_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_w_2) V_y_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_x_2) V_z_2)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_w_2) V_z_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_x_2) V_y_2))) (or (= V_w_2 V_x_2) (= V_y_2 V_z_2))))))
% 0.97/1.22  (assume a86 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a87 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 0.97/1.22  (assume a88 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))
% 0.97/1.22  (assume a89 (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_q))))))
% 0.97/1.22  (assume a90 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 0.97/1.22  (assume a91 (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_nat_H)))))
% 0.97/1.22  (assume a92 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a93 (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a94 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)))))
% 0.97/1.22  (assume a95 (forall ((V_m $$unsorted)) (not (= (tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a96 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 0.97/1.22  (assume a97 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)))
% 0.97/1.22  (assume a98 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 0.97/1.22  (assume a99 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a100 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a101 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a102 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a103 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 0.97/1.22  (assume a104 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 0.97/1.22  (assume a105 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_m)) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 0.97/1.22  (assume a106 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Opcompose T_a (tptp.c_Polynomial_OpCons T_a V_a V_p) V_q) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_q) (tptp.c_Polynomial_Opcompose T_a V_p V_q)))))))
% 0.97/1.22  (assume a107 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero T_b)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_b)))))))
% 0.97/1.22  (assume a108 (forall ((V_a_2 $$unsorted) (V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_b V_pa_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (or (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (not (= (tptp.c_Polynomial_Oorder T_b V_a_2 V_pa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 0.97/1.22  (assume a109 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_b_H)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 0.97/1.22  (assume a110 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 0.97/1.22  (assume a111 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 0.97/1.22  (assume a112 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 0.97/1.22  (assume a113 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 0.97/1.22  (assume a114 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_e) V_c)))))
% 0.97/1.22  (assume a115 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 0.97/1.22  (assume a116 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m))))
% 0.97/1.22  (assume a117 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 0.97/1.22  (assume a118 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Opcompose T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_q) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a119 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Opcompose T_a V_p V_q)) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 0.97/1.22  (assume a120 (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.c_Groups_Ozero__class_Ozero T_b) V_x_2) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a121 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 0.97/1.22  (assume a122 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))))
% 0.97/1.22  (assume a123 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 0.97/1.22  (assume a124 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 0.97/1.22  (assume a125 (forall ((V_ca_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b V_b_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_b V_ca_2 V_a_2)) (= V_b_2 V_ca_2)))))
% 0.97/1.22  (assume a126 (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_b_2) (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_ca_2)) (= V_b_2 V_ca_2)))))
% 0.97/1.22  (assume a127 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 0.97/1.22  (assume a128 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a129 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 0.97/1.22  (assume a130 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oring__no__zero__divisors T_b) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_b)))))))
% 0.97/1.22  (assume a131 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a132 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a133 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a134 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a135 (forall ((V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a136 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Omult__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a137 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 0.97/1.22  (assume a138 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 0.97/1.22  (assume a139 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_b) (= (= (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a140 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 0.97/1.22  (assume a141 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j)) V_u) V_k))))
% 0.97/1.22  (assume a142 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m_2 V_n_2)))))
% 0.97/1.22  (assume a143 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a144 (forall ((V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted)) (=> (tptp.class_Groups_Ozero T_c) (=> (= (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 (tptp.c_Groups_Ozero__class_Ozero T_c)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_c))) V_z_2) V_z_2) (= (tptp.c_Polynomial_Opoly__rec T_b T_c V_z_2 V_f_2 (tptp.c_Polynomial_OpCons T_c V_a_2 V_pa_2)) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 V_a_2) V_pa_2) (tptp.c_Polynomial_Opoly__rec T_b T_c V_z_2 V_f_2 V_pa_2)))))))
% 0.97/1.22  (assume a145 (forall ((V_ca_2 $$unsorted) (V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_b) (= (= (tptp.c_Polynomial_Osynthetic__div T_b V_pa_2 V_ca_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (= (tptp.c_Polynomial_Odegree T_b V_pa_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a146 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) V_n)) V_n))))
% 0.97/1.22  (assume a147 (forall ((V_nat $$unsorted)) (= (tptp.c_Nat_Onat_Onat__size (tptp.c_Nat_OSuc V_nat)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_Onat_Onat__size V_nat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a148 (forall ((V_pa_2 $$unsorted) (V_a_2 $$unsorted) (V_f_2 $$unsorted) (V_z_2 $$unsorted) (T_b $$unsorted) (T_c $$unsorted)) (=> (tptp.class_Groups_Ozero T_c) (= (tptp.c_Polynomial_Opoly__rec T_b T_c V_z_2 V_f_2 (tptp.c_Polynomial_OpCons T_c V_a_2 V_pa_2)) (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 V_a_2) V_pa_2) (tptp.c_If T_b (tptp.c_fequal V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_c))) V_z_2 (tptp.c_Polynomial_Opoly__rec T_b T_c V_z_2 V_f_2 V_pa_2)))))))
% 0.97/1.22  (assume a149 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a V_a V_p)) V_q) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_q) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)))))))
% 0.97/1.22  (assume a150 (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oone T_b) (= (= (tptp.c_Groups_Oone__class_Oone T_b) V_x_2) (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_b))))))
% 0.97/1.22  (assume a151 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a152 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Oone__class_Oone T_a) V_p) V_p))))
% 0.97/1.22  (assume a153 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 0.97/1.22  (assume a154 (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Polynomial_Osmult T_a V_b V_p)) (tptp.c_Polynomial_Osmult T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_p)))))
% 0.97/1.22  (assume a155 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a156 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a157 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))))
% 0.97/1.22  (assume a158 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 0.97/1.22  (assume a159 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))))
% 0.97/1.22  (assume a160 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))))
% 0.97/1.22  (assume a161 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 0.97/1.22  (assume a162 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 0.97/1.22  (assume a163 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_n) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a164 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_a))))
% 0.97/1.22  (assume a165 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_x))))
% 0.97/1.22  (assume a166 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a167 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a168 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 0.97/1.22  (assume a169 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a170 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) V_n)))
% 0.97/1.22  (assume a171 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p) (tptp.c_Polynomial_Osmult T_a V_a V_q))))))
% 0.97/1.22  (assume a172 (forall ((V_q $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) (tptp.c_Polynomial_Osmult T_a V_a V_q)) (tptp.c_Polynomial_Osmult T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))))))
% 0.97/1.22  (assume a173 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a V_p)) V_q) (tptp.c_Polynomial_Osmult T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))))))
% 0.97/1.22  (assume a174 (= (tptp.c_Nat_Onat_Onat__size (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 0.97/1.22  (assume a175 (forall ((V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 0.97/1.22  (assume a176 (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 0.97/1.22  (assume a177 (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 0.97/1.22  (assume a178 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_p) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a179 (forall ((V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (= (tptp.c_Polynomial_Osmult T_b V_a_2 V_pa_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))))))))
% 0.97/1.22  (assume a180 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a181 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a182 (forall ((V_c $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Polynomial_Osmult T_a V_c (tptp.c_Polynomial_Osynthetic__div T_a V_p V_c))) (tptp.c_Polynomial_OpCons T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_c) (tptp.c_Polynomial_Osynthetic__div T_a V_p V_c))))))
% 0.97/1.22  (assume a183 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_c $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Polynomial_Osmult T_a V_c V_q)) (tptp.c_Polynomial_OpCons T_a V_r V_q)) (and (= V_r (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_c)) (= V_q (tptp.c_Polynomial_Osynthetic__div T_a V_p V_c)))))))
% 0.97/1.22  (assume a184 (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Polynomial_OpCons T_a V_b V_p)) (tptp.c_Polynomial_OpCons T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Polynomial_Osmult T_a V_a V_p))))))
% 0.97/1.22  (assume a185 (forall ((V_x $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x))))))
% 0.97/1.22  (assume a186 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a187 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n))))
% 0.97/1.22  (assume a188 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a189 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (or (= V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a190 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a191 (forall ((V_a $$unsorted) (V_p $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (=> (= (tptp.c_Polynomial_Osmult T_a V_c V_p) (tptp.c_Polynomial_OpCons T_a V_a V_p)) (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 0.97/1.22  (assume a192 (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_p) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p) (tptp.c_Polynomial_Osmult T_a V_b V_p))))))
% 0.97/1.22  (assume a193 (forall ((V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osynthetic__div T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_c) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a194 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a195 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))))
% 0.97/1.22  (assume a196 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_z)))))
% 0.97/1.22  (assume a197 (forall ((V_a $$unsorted) (V_p $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_c V_p) (tptp.c_Polynomial_OpCons T_a V_a V_p)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 0.97/1.22  (assume a198 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_y) V_z)))))
% 0.97/1.22  (assume a199 (forall ((V_c $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osynthetic__div T_a (tptp.c_Polynomial_OpCons T_a V_a V_p) V_c) (tptp.c_Polynomial_OpCons T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_c) (tptp.c_Polynomial_Osynthetic__div T_a V_p V_c))))))
% 0.97/1.22  (assume a200 (forall ((T_b $$unsorted) (V_z_2 $$unsorted) (V_f_2 $$unsorted) (T_c $$unsorted)) (=> (tptp.class_Groups_Ozero T_c) (=> (= (tptp.hAPP (tptp.hAPP (tptp.hAPP V_f_2 (tptp.c_Groups_Ozero__class_Ozero T_c)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_c))) V_z_2) V_z_2) (= (tptp.c_Polynomial_Opoly__rec T_b T_c V_z_2 V_f_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_c))) V_z_2)))))
% 0.97/1.22  (assume a201 (forall ((V_q $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) (tptp.c_Polynomial_OpCons T_a V_a V_q)) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)))))))
% 0.97/1.22  (assume a202 (forall ((T_b $$unsorted)) (=> (tptp.class_Power_Opower T_b) (= (tptp.c_Power_Opower__class_Opower T_b) (tptp.c_Power_Opower_Opower T_b (tptp.c_Groups_Oone__class_Oone T_b) (tptp.c_Groups_Otimes__class_Otimes T_b))))))
% 0.97/1.22  (assume a203 (forall ((V_p $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_c) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (tptp.c_Polynomial_Osynthetic__div T_a V_p V_c)) (tptp.c_Polynomial_OpCons T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_c) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) V_p))))
% 0.97/1.22  (assume a204 (forall ((V_nat $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_nat)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Nat_Osize__class_Osize tptp.tc_Nat_Onat V_nat) (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a205 (forall ((V_x $$unsorted) (V_p $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Oone__class_Oone T_a) V_n)) V_p)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x))))))
% 0.97/1.22  (assume a206 (forall ((V_h $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_a (tptp.c_Polynomial_OpCons T_a V_a V_p) V_h) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_h (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_a V_p V_h)) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_a V_p V_h)))))))
% 0.97/1.22  (assume a207 (= (tptp.c_HOL_Obool_Obool__size tptp.c_fTrue) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 0.97/1.22  (assume a208 (= (tptp.c_HOL_Obool_Obool__size tptp.c_fFalse) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 0.97/1.22  (assume a209 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) V_n)) V_n) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a210 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z) V_z)))
% 0.97/1.22  (assume a211 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)))
% 0.97/1.22  (assume a212 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z))))
% 0.97/1.22  (assume a213 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 0.97/1.22  (assume a214 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_w) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) V_w)))))
% 0.97/1.22  (assume a215 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_z3)))))
% 0.97/1.22  (assume a216 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 0.97/1.22  (assume a217 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_p) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p))))))
% 0.97/1.22  (assume a218 (forall ((V_b_2 $$unsorted) (V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.c_Polynomial_Omonom T_b V_a_2 V_n_2) (tptp.c_Polynomial_Omonom T_b V_b_2 V_n_2)) (= V_a_2 V_b_2)))))
% 0.97/1.22  (assume a219 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.c_Polynomial_Ocoeff T_b V_x_2) (tptp.c_Polynomial_Ocoeff T_b V_y_2)) (= V_x_2 V_y_2)))))
% 0.97/1.22  (assume a220 (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_p)) V_n) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n))))))
% 0.97/1.22  (assume a221 (forall ((V_q_2 $$unsorted) (V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= V_pa_2 V_q_2) (forall ((B_n $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_b V_pa_2) B_n) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_b V_q_2) B_n)))))))
% 0.97/1.22  (assume a222 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Omonom T_a V_a V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_n)))))
% 0.97/1.22  (assume a223 (forall ((V_a $$unsorted) (V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (and (=> (= V_m V_n) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_Omonom T_a V_a V_m)) V_n) V_a)) (=> (not (= V_m V_n)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_Omonom T_a V_a V_m)) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a224 (forall ((V_x $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_p)) V_x) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x))))))
% 0.97/1.22  (assume a225 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_b) (= (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_b) (tptp.c_Polynomial_OpCons T_b V_a V_p)) (tptp.c_Polynomial_OpCons T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_b) V_p))))))
% 0.97/1.22  (assume a226 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a V_p)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_p))))))
% 0.97/1.22  (assume a227 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2)) (= V_a_2 V_b_2)))))
% 0.97/1.22  (assume a228 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) V_b_2) (= (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2) V_a_2)))))
% 0.97/1.22  (assume a229 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2)) (= V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2))))))
% 0.97/1.22  (assume a230 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_a))))
% 0.97/1.22  (assume a231 (forall ((V_n $$unsorted)) (= (tptp.c_Nat_Osize__class_Osize tptp.tc_Nat_Onat V_n) V_n)))
% 0.97/1.22  (assume a232 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_b) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) V_a_2) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a233 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a234 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_b) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a235 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2)) (= (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))
% 0.97/1.22  (assume a236 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a237 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_b_2)) (or (= V_a_2 V_b_2) (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2)))))))
% 0.97/1.22  (assume a238 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))
% 0.97/1.22  (assume a239 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 0.97/1.22  (assume a240 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y))))))
% 0.97/1.22  (assume a241 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))
% 0.97/1.22  (assume a242 (forall ((V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x))))))
% 0.97/1.22  (assume a243 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))
% 0.97/1.22  (assume a244 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_b)))))
% 0.97/1.22  (assume a245 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 0.97/1.22  (assume a246 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_b))))
% 0.97/1.22  (assume a247 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)) V_b))))
% 0.97/1.22  (assume a248 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))))
% 0.97/1.22  (assume a249 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 0.97/1.22  (assume a250 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a251 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))
% 0.97/1.22  (assume a252 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_p)) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p))))))
% 0.97/1.22  (assume a253 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))))
% 0.97/1.22  (assume a254 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a255 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a256 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a257 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a258 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) V_x)))))
% 0.97/1.22  (assume a259 (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_b) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_x_2) V_x_2) (tptp.c_Groups_Oone__class_Oone T_b)) (or (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_b)) (= V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b (tptp.c_Groups_Oone__class_Oone T_b))))))))
% 0.97/1.22  (assume a260 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a261 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_OpCons T_a V_a V_p)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_a))))
% 0.97/1.22  (assume a262 (forall ((V_n $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_OpCons T_a V_a V_p)) (tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n)))))
% 0.97/1.22  (assume a263 (forall ((V_n $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n))))))
% 0.97/1.22  (assume a264 (forall ((V_n $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_n) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) V_n))))))
% 0.97/1.22  (assume a265 (forall ((V_h_2 $$unsorted) (V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_b) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_b V_pa_2 V_h_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))))))
% 0.97/1.22  (assume a266 (forall ((V_h $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_h) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a267 (forall ((V_h $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_a V_p V_h)) (tptp.c_Polynomial_Odegree T_a V_p)))))
% 0.97/1.22  (assume a268 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.c_Polynomial_Omonom T_b V_a_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a269 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_n) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a270 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Omonom T_a V_a V_n)) V_n)))))
% 0.97/1.22  (assume a271 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_n)))))
% 0.97/1.22  (assume a272 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Omonom T_a V_a V_n) (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_n)))))
% 0.97/1.22  (assume a273 (= (tptp.c_Nat_Osize__class_Osize tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 0.97/1.22  (assume a274 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 0.97/1.22  (assume a275 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a276 (forall ((V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_b V_one_2 V_times_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_one_2)))
% 0.97/1.22  (assume a277 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_b V_one_2 V_times_2) V_a_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.hAPP (tptp.hAPP V_times_2 V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_b V_one_2 V_times_2) V_a_2) V_n_2)))))
% 0.97/1.22  (assume a278 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (not (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a279 (forall ((V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_b V_pa_2) (tptp.c_Polynomial_Odegree T_b V_pa_2)) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))))))
% 0.97/1.22  (assume a280 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Omonom T_a V_a (tptp.c_Nat_OSuc V_n)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Polynomial_Omonom T_a V_a V_n))))))
% 0.97/1.22  (assume a281 (forall ((V_x $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Omonom T_a V_a V_n)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 0.97/1.22  (assume a282 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Omonom T_a V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 0.97/1.22  (assume a283 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a V_a V_m)) (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n))))))
% 0.97/1.22  (assume a284 (forall ((V_x $$unsorted) (V_h $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_a V_p V_h)) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) (tptp.c_Groups_Oplus__class_Oplus T_a V_h V_x))))))
% 0.97/1.22  (assume a285 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p) (tptp.c_Polynomial_Odegree T_a V_q))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) (tptp.c_Polynomial_Odegree T_a V_p))) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) (tptp.c_Polynomial_Odegree T_a V_q)))))))
% 0.97/1.22  (assume a286 (forall ((V_h $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly T_a (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_h) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 0.97/1.22  (assume a287 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) V_x_2) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) V_y_2) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (or (= V_x_2 V_y_2) (= V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_y_2)))))))
% 0.97/1.22  (assume a288 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_y_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_x_2))))))
% 0.97/1.22  (assume a289 (forall ((V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (and (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (tptp.c_Polynomial_Oorder T_a V_a V_p)) V_p) (not (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Oorder T_a V_a V_p))) V_p)))))))
% 0.97/1.22  (assume a290 (forall ((V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (=> (not (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (not (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Oorder T_a V_a V_p))) V_p))))))
% 0.97/1.22  (assume a291 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (tptp.c_Polynomial_Oorder T_a V_a V_p)) V_p))))
% 0.97/1.22  (assume a292 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (and (=> (and (= V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y)) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y))) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (and (= V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y)) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y))) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 0.97/1.22  (assume a293 (forall ((V_pa_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) (tptp.c_Polynomial_OpCons T_b V_ca_2 (tptp.c_Polynomial_OpCons T_b (tptp.c_Groups_Oone__class_Oone T_b) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))) V_pa_2) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_b V_pa_2) (tptp.c_Groups_Ouminus__class_Ouminus T_b V_ca_2)) (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a294 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (tptp.c_Rings_Odvd__class_Odvd T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a295 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y) V_x))))
% 0.97/1.22  (assume a296 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y) V_y))))
% 0.97/1.22  (assume a297 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 0.97/1.22  (assume a298 (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))
% 0.97/1.22  (assume a299 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z)) V_z)))
% 0.97/1.22  (assume a300 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 0.97/1.22  (assume a301 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_z) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))))
% 0.97/1.22  (assume a302 (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 0.97/1.22  (assume a303 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_x) V_y) (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y)))))
% 0.97/1.22  (assume a304 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_y)) (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y)))))
% 0.97/1.22  (assume a305 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_a))))
% 0.97/1.22  (assume a306 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_b V_c) (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_c))))))
% 0.97/1.22  (assume a307 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_a V_b) (tptp.c_Polynomial_Opoly__gcd T_a V_b V_a)))))
% 0.97/1.22  (assume a308 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_b (tptp.c_Polynomial_Opoly__gcd T_a V_a V_c)) (tptp.c_Polynomial_Opoly__gcd T_a V_a (tptp.c_Polynomial_Opoly__gcd T_a V_b V_c))))))
% 0.97/1.22  (assume a309 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_k_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (= (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) V_k_2 (tptp.c_Polynomial_Opoly__gcd T_b V_x_2 V_y_2)) (and (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) V_k_2 V_x_2) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) V_k_2 V_y_2))))))
% 0.97/1.22  (assume a310 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a (tptp.c_Polynomial_Opoly__gcd T_a V_a V_b) V_c) (tptp.c_Polynomial_Opoly__gcd T_a V_a (tptp.c_Polynomial_Opoly__gcd T_a V_b V_c))))))
% 0.97/1.22  (assume a311 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_k V_x) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_k V_y) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_k (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y)))))))
% 0.97/1.22  (assume a312 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)))
% 0.97/1.22  (assume a313 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)))
% 0.97/1.22  (assume a314 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))
% 0.97/1.22  (assume a315 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))))
% 0.97/1.22  (assume a316 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))))
% 0.97/1.22  (assume a317 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a318 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (tptp.c_Rings_Odvd__class_Odvd T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))
% 0.97/1.22  (assume a319 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (tptp.c_Rings_Odvd__class_Odvd T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)))))
% 0.97/1.22  (assume a320 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (tptp.c_Rings_Odvd__class_Odvd T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 0.97/1.22  (assume a321 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_c) (tptp.c_Rings_Odvd__class_Odvd T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 0.97/1.22  (assume a322 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_c V_d) (tptp.c_Rings_Odvd__class_Odvd T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))
% 0.97/1.22  (assume a323 (forall ((V_k $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odvd T_a) (=> (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_k)) (tptp.c_Rings_Odvd__class_Odvd T_a V_b V_a)))))
% 0.97/1.22  (assume a324 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_c)))))
% 0.97/1.22  (assume a325 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Rings_Odvd__class_Odvd T_a V_b V_c)))))
% 0.97/1.22  (assume a326 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_c) (tptp.c_Rings_Odvd__class_Odvd T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))))))
% 0.97/1.22  (assume a327 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (tptp.c_Rings_Odvd__class_Odvd T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a))))
% 0.97/1.22  (assume a328 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_b) (= (tptp.c_Rings_Odvd__class_Odvd T_b V_x_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_y_2)) (tptp.c_Rings_Odvd__class_Odvd T_b V_x_2 V_y_2)))))
% 0.97/1.22  (assume a329 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_b) (= (tptp.c_Rings_Odvd__class_Odvd T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_x_2) V_y_2) (tptp.c_Rings_Odvd__class_Odvd T_b V_x_2 V_y_2)))))
% 0.97/1.22  (assume a330 (forall ((V_n $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_x V_y) (tptp.c_Rings_Odvd__class_Odvd T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_n))))))
% 0.97/1.22  (assume a331 (forall ((V_a $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_p V_q) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Polynomial_Osmult T_a V_a V_q))))))
% 0.97/1.22  (assume a332 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p) V_q) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_p V_q)))))
% 0.97/1.22  (assume a333 (forall ((T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a334 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (= (= (tptp.c_Polynomial_Opoly__gcd T_b V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))))))))
% 0.97/1.22  (assume a335 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (tptp.c_Rings_Odvd__class_Odvd T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_ca_2)) (or (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Rings_Odvd__class_Odvd T_b V_a_2 V_b_2))))))
% 0.97/1.22  (assume a336 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (tptp.c_Rings_Odvd__class_Odvd T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_b_2)) (or (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Rings_Odvd__class_Odvd T_b V_a_2 V_b_2))))))
% 0.97/1.22  (assume a337 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a338 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)) V_y) (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a339 (forall ((V_q_2 $$unsorted) (V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (=> (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (= (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) V_pa_2 (tptp.c_Polynomial_Osmult T_b V_a_2 V_q_2)) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) V_pa_2 V_q_2))))))
% 0.97/1.22  (assume a340 (forall ((V_a $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_p V_q) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p) V_q))))))
% 0.97/1.22  (assume a341 (forall ((V_q $$unsorted) (V_a $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Polynomial_Osmult T_a V_a V_q)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_p V_q))))))
% 0.97/1.22  (assume a342 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (=> (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) (tptp.c_Polynomial_Odegree T_a V_q))) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_p V_q) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_q V_p) (= V_p V_q)))))))
% 0.97/1.22  (assume a343 (forall ((V_q_2 $$unsorted) (V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (= (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) (tptp.c_Polynomial_Osmult T_b V_a_2 V_pa_2) V_q_2) (and (=> (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_q_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))) (=> (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) V_pa_2 V_q_2)))))))
% 0.97/1.22  (assume a344 (forall ((V_ca_2 $$unsorted) (V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oidom T_b) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_b V_pa_2) V_ca_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_b) (tptp.c_Polynomial_OpCons T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_ca_2) (tptp.c_Polynomial_OpCons T_b (tptp.c_Groups_Oone__class_Oone T_b) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))) V_pa_2)))))
% 0.97/1.22  (assume a345 (forall ((V_l_2 $$unsorted) (V_P_2 $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Rings_Odvd T_b) (tptp.class_Rings_Osemiring__0 T_b)) (= (exists ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_l_2) B_x)))) (exists ((B_x $$unsorted)) (and (tptp.c_Rings_Odvd__class_Odvd T_b V_l_2 (tptp.c_Groups_Oplus__class_Oplus T_b B_x (tptp.c_Groups_Ozero__class_Ozero T_b))) (tptp.hBOOL (tptp.hAPP V_P_2 B_x))))))))
% 0.97/1.22  (assume a346 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_d $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_d V_x) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) V_d V_y) (=> (forall ((B_k $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) B_k V_x) (=> (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) B_k V_y) (tptp.c_Rings_Odvd__class_Odvd (tptp.tc_Polynomial_Opoly T_a) B_k V_d)))) (=> (and (=> (and (= V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_d) (tptp.c_Polynomial_Odegree T_a V_d)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (and (= V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_d) (tptp.c_Polynomial_Odegree T_a V_d)) (tptp.c_Groups_Oone__class_Oone T_a)))) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y) V_d))))))))
% 0.97/1.22  (assume a347 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_x) (tptp.c_Polynomial_Odegree T_a V_x))) V_x)))))
% 0.97/1.22  (assume a348 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y))))))
% 0.97/1.22  (assume a349 (forall ((V_p $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))))
% 0.97/1.22  (assume a350 (forall ((V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (tptp.c_Polynomial_Ocoeff T_b (tptp.c_Polynomial_OpCons T_b V_a_2 V_pa_2)) (tptp.c_Nat_Onat_Onat__case T_b V_a_2 (tptp.c_Polynomial_Ocoeff T_b V_pa_2))))))
% 0.97/1.22  (assume a351 (forall ((V_k $$unsorted)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k)))
% 0.97/1.22  (assume a352 (forall ((V_t_2 $$unsorted) (V_d_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_d_2 V_t_2) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_d_2 (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_t_2)))))
% 0.97/1.22  (assume a353 (forall ((V_t_2 $$unsorted) (V_d_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_d_2 V_t_2) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_d_2) V_t_2))))
% 0.97/1.22  (assume a354 (forall ((V_t_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (not (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_m_2 V_t_2) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_t_2))))))
% 0.97/1.22  (assume a355 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_k V_m) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_k V_n) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_k (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 0.97/1.22  (assume a356 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))))
% 0.97/1.22  (assume a357 (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_p) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p) (tptp.c_Polynomial_Osmult T_a V_b V_p))))))
% 0.97/1.22  (assume a358 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_k) V_j))))
% 0.97/1.22  (assume a359 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_x) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 0.97/1.22  (assume a360 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a V_p) (tptp.c_Polynomial_OpCons T_a V_b V_q)) (tptp.c_Polynomial_OpCons T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q))))))
% 0.97/1.22  (assume a361 (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_b) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_b V_ca_2 V_d_2)) (= (= V_a_2 V_b_2) (= V_ca_2 V_d_2))))))
% 0.97/1.22  (assume a362 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (= V_a V_b)))))
% 0.97/1.22  (assume a363 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_b) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_b V_a_2) (tptp.c_Rings_Oinverse__class_Oinverse T_b V_b_2)) (= V_a_2 V_b_2)))))
% 0.97/1.22  (assume a364 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a))))
% 0.97/1.22  (assume a365 (forall ((V_n $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_n) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) V_n))))))
% 0.97/1.22  (assume a366 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Omonom T_a V_a V_n) (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_n)))))
% 0.97/1.22  (assume a367 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= V_a V_b)))))))
% 0.97/1.22  (assume a368 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a369 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a)))))
% 0.97/1.22  (assume a370 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a371 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_b) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a372 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a373 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a374 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_b) (= (= (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 V_b_2)))))
% 0.97/1.22  (assume a375 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_b) (= (= V_a_2 V_b_2) (= (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a376 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a377 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 0.97/1.22  (assume a378 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))
% 0.97/1.22  (assume a379 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_n)))))
% 0.97/1.22  (assume a380 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 0.97/1.22  (assume a381 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 0.97/1.22  (assume a382 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 0.97/1.22  (assume a383 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_b_H)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 0.97/1.22  (assume a384 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) V_a))))
% 0.97/1.22  (assume a385 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))))
% 0.97/1.22  (assume a386 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a)))))
% 0.97/1.22  (assume a387 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_x V_y) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_x V_z) (tptp.c_Rings_Odvd__class_Odvd T_a V_x (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_z)))))))
% 0.97/1.22  (assume a388 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_n)) (=> (not (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_m V_n)))))
% 0.97/1.22  (assume a389 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m V_n)))))
% 0.97/1.22  (assume a390 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a391 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 0.97/1.22  (assume a392 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a393 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_k))))
% 0.97/1.22  (assume a394 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 0.97/1.22  (assume a395 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_k_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n_2 V_k_2)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_k_2 V_n_2))))
% 0.97/1.22  (assume a396 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 0.97/1.22  (assume a397 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 0.97/1.22  (assume a398 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 0.97/1.22  (assume a399 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_n) V_m)))
% 0.97/1.22  (assume a400 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n) V_m)))
% 0.97/1.22  (assume a401 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 0.97/1.22  (assume a402 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 0.97/1.22  (assume a403 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 0.97/1.22  (assume a404 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 0.97/1.22  (assume a405 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_p))))
% 0.97/1.22  (assume a406 (forall ((V_m_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a407 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_p) (tptp.c_Polynomial_Osmult T_a V_a V_q))))))
% 0.97/1.22  (assume a408 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))
% 0.97/1.22  (assume a409 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))
% 0.97/1.22  (assume a410 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Oone__class_Oone T_a)) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) V_b)))))
% 0.97/1.22  (assume a411 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_n))))))
% 0.97/1.22  (assume a412 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oring T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_e_2) V_d_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_b_2)) V_e_2) V_ca_2) V_d_2)))))
% 0.97/1.22  (assume a413 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oring T_b) (= (= (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_e_2) V_d_2)) (= V_ca_2 (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Groups_Ominus__class_Ominus T_b V_b_2 V_a_2)) V_e_2) V_d_2))))))
% 0.97/1.22  (assume a414 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)))))))
% 0.97/1.22  (assume a415 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b))))))
% 0.97/1.22  (assume a416 (forall ((V_t_2 $$unsorted) (V_D_2 $$unsorted) (V_d_2 $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Rings_Ocomm__ring T_b) (tptp.class_Rings_Odvd T_b)) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_d_2 V_D_2) (forall ((B_x $$unsorted) (B_k $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd T_b V_d_2 (tptp.c_Groups_Oplus__class_Oplus T_b B_x V_t_2)) (tptp.c_Rings_Odvd__class_Odvd T_b V_d_2 (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Ominus__class_Ominus T_b B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) B_k) V_D_2)) V_t_2))))))))
% 0.97/1.22  (assume a417 (forall ((V_t_2 $$unsorted) (V_D_2 $$unsorted) (V_d_2 $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Rings_Ocomm__ring T_b) (tptp.class_Rings_Odvd T_b)) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_d_2 V_D_2) (forall ((B_x $$unsorted) (B_k $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd T_b V_d_2 (tptp.c_Groups_Oplus__class_Oplus T_b B_x V_t_2)) (tptp.c_Rings_Odvd__class_Odvd T_b V_d_2 (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.c_Groups_Ominus__class_Ominus T_b B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) B_k) V_D_2)) V_t_2))))))))
% 0.97/1.22  (assume a418 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)))))
% 0.97/1.22  (assume a419 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y) (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y))))))
% 0.97/1.22  (assume a420 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))
% 0.97/1.22  (assume a421 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 0.97/1.22  (assume a422 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 0.97/1.22  (assume a423 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_m_2))) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k_2 V_n_2))))
% 0.97/1.22  (assume a424 (forall ((V_ca_2 $$unsorted) (V_t_2 $$unsorted) (V_x_2 $$unsorted) (V_d_2 $$unsorted) (V_a_2 $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_a_2 V_d_2) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 V_t_2)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_ca_2) V_d_2)) V_t_2))))))
% 0.97/1.22  (assume a425 (forall ((V_m_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_m_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a426 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a427 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 0.97/1.22  (assume a428 (forall ((V_f2_2 $$unsorted) (V_f1_2 $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Nat_Onat_Onat__case T_b V_f1_2 V_f2_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_f1_2)))
% 0.97/1.22  (assume a429 (forall ((V_nat_2 $$unsorted) (V_f2_2 $$unsorted) (V_f1_2 $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_Nat_Onat_Onat__case T_b V_f1_2 V_f2_2) (tptp.c_Nat_OSuc V_nat_2)) (tptp.hAPP V_f2_2 V_nat_2))))
% 0.97/1.22  (assume a430 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))
% 0.97/1.22  (assume a431 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))))
% 0.97/1.22  (assume a432 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)))))
% 0.97/1.22  (assume a433 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_w)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z V_w))))
% 0.97/1.22  (assume a434 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_q) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_q)))))
% 0.97/1.22  (assume a435 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))))
% 0.97/1.22  (assume a436 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a437 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a438 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 0.97/1.22  (assume a439 (forall ((V_c $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osynthetic__div T_a V_p V_c)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a440 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n)) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))))))
% 0.97/1.22  (assume a441 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n)))))))
% 0.97/1.22  (assume a442 (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 0.97/1.22  (assume a443 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)))))))))
% 0.97/1.22  (assume a444 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a445 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))))
% 0.97/1.22  (assume a446 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_b) V_n)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b)))))
% 0.97/1.22  (assume a447 (forall ((V_x $$unsorted)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_x)))
% 0.97/1.22  (assume a448 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= V_x_2 V_y_2) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x_2 V_y_2) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y_2 V_x_2)))))
% 0.97/1.22  (assume a449 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x_2 V_y_2) (or (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x_2 V_y_2) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y_2 V_x_2))) (= V_x_2 V_y_2)))))
% 0.97/1.22  (assume a450 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x_2 V_y_2) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y_2 V_x_2))) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x_2 V_y_2) (not (= V_x_2 V_y_2))))))
% 0.97/1.22  (assume a451 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (not (= V_a V_b)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_b V_a)))))))
% 0.97/1.22  (assume a452 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= V_x V_y) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y))))
% 0.97/1.22  (assume a453 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y_2 V_x_2) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x_2 V_y_2) (= V_x_2 V_y_2)))))
% 0.97/1.22  (assume a454 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (or (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (= V_x V_y)))))
% 0.97/1.22  (assume a455 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b) (=> (not (= V_a V_b)) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_b V_a)))))))
% 0.97/1.22  (assume a456 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (= V_a V_b) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_b V_c) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_c)))))
% 0.97/1.22  (assume a457 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b) (=> (= V_b V_c) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_c)))))
% 0.97/1.22  (assume a458 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_n V_m) (= V_m V_n)))))
% 0.97/1.22  (assume a459 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x) (= V_x V_y)))))
% 0.97/1.22  (assume a460 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_z) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_z)))))
% 0.97/1.22  (assume a461 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (= V_a V_b) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_b V_c) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_c V_b))) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_c) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_c V_a)))))))
% 0.97/1.22  (assume a462 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_z) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_z V_y))) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_z) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_z V_x)))))))
% 0.97/1.22  (assume a463 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (not (= V_x V_y)))))
% 0.97/1.22  (assume a464 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (not (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y)))))))
% 0.97/1.22  (assume a465 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y))))
% 0.97/1.22  (assume a466 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (not (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y)))))))
% 0.97/1.22  (assume a467 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (not (= V_x V_y)))))
% 0.97/1.22  (assume a468 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (not (= V_y V_x)))))
% 0.97/1.22  (assume a469 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_b V_a))) (=> (= V_b V_c) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_c) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_c V_a)))))))
% 0.97/1.22  (assume a470 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_z) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_z) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_z V_x)))))))
% 0.97/1.22  (assume a471 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_b V_a))) (not (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_b V_a) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a V_b)))))))
% 0.97/1.22  (assume a472 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_z) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_z V_y))) (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_z) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_z V_x)))))))
% 0.97/1.22  (assume a473 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x))) (not (and (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_y V_x) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x V_y)))))))
% 0.97/1.22  (assume a474 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_m V_n)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k V_n) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k V_m)))))
% 0.97/1.22  (assume a475 (forall ((V_x $$unsorted)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a476 (forall ((V_x $$unsorted)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_x)))
% 0.97/1.22  (assume a477 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus T_a V_c V_d))))))
% 0.97/1.22  (assume a478 (forall ((T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a479 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))
% 0.97/1.22  (assume a480 (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_b) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_b V_x_2) (tptp.c_Groups_Oone__class_Oone T_b)) (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_b))))))
% 0.97/1.22  (assume a481 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_b) V_n)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_a V_b)))))
% 0.97/1.22  (assume a482 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_a_2) V_n_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_b_2) V_n_2)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_a_2 V_b_2)))))
% 0.97/1.22  (assume a483 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_a_2) V_n_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_b_2) V_n_2)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_a_2 V_b_2)))))
% 0.97/1.22  (assume a484 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 0.97/1.22  (assume a485 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (and (=> (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y) (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_x) (tptp.c_Polynomial_Odegree T_a V_x))) V_x))) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y) (tptp.c_Polynomial_Opoly__gcd T_a V_y (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))))
% 0.97/1.22  (assume a486 (forall ((V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (tptp.c_Polynomial_OpCons T_b V_a_2 V_pa_2) (tptp.c_Polynomial_OAbs__poly T_b (tptp.c_Nat_Onat_Onat__case T_b V_a_2 (tptp.c_Polynomial_Ocoeff T_b V_pa_2)))))))
% 0.97/1.22  (assume a487 (forall ((V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 0.97/1.22  (assume a488 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a489 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)))))
% 0.97/1.22  (assume a490 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_n))))
% 0.97/1.22  (assume a491 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_n))))
% 0.97/1.22  (assume a492 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_b V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2)))))
% 0.97/1.22  (assume a493 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_ca_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_b V_ca_2 V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2)))))
% 0.97/1.22  (assume a494 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 0.97/1.22  (assume a495 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 0.97/1.22  (assume a496 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 0.97/1.22  (assume a497 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 0.97/1.22  (assume a498 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 0.97/1.22  (assume a499 (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_b) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_b_2) (tptp.c_Groups_Ominus__class_Ominus T_b V_ca_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 V_d_2))))))
% 0.97/1.22  (assume a500 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2))))))
% 0.97/1.22  (assume a501 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) V_b_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2) V_a_2)))))
% 0.97/1.22  (assume a502 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_b_2) (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2)))))
% 0.97/1.22  (assume a503 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y) (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 0.97/1.22  (assume a504 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a505 (forall ((V_n_2 $$unsorted)) (= (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2))))
% 0.97/1.22  (assume a506 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a507 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a508 (forall ((V_n $$unsorted)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n))))
% 0.97/1.22  (assume a509 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)))))
% 0.97/1.22  (assume a510 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (= V_m_2 V_n_2)))))
% 0.97/1.22  (assume a511 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m_2) (tptp.c_Nat_OSuc V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 0.97/1.22  (assume a512 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc V_m_2)) (= V_n_2 V_m_2)))))
% 0.97/1.22  (assume a513 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_m)) (= V_m V_n)))))
% 0.97/1.22  (assume a514 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)))))
% 0.97/1.22  (assume a515 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (not (= (tptp.c_Nat_OSuc V_m) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n)))))
% 0.97/1.22  (assume a516 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_i) V_k)))))
% 0.97/1.22  (assume a517 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc V_n)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= V_m V_n)))))
% 0.97/1.22  (assume a518 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 0.97/1.22  (assume a519 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) (tptp.c_Nat_OSuc V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))
% 0.97/1.22  (assume a520 (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_i))))
% 0.97/1.22  (assume a521 (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_i))))
% 0.97/1.22  (assume a522 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_m_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 0.97/1.22  (assume a523 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))))
% 0.97/1.22  (assume a524 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 0.97/1.22  (assume a525 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 0.97/1.22  (assume a526 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))))
% 0.97/1.22  (assume a527 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a528 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))))
% 0.97/1.22  (assume a529 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_n) V_k))))
% 0.97/1.22  (assume a530 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))))
% 0.97/1.22  (assume a531 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 0.97/1.22  (assume a532 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_y)) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y)))))
% 0.97/1.22  (assume a533 (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (= V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2)))))))
% 0.97/1.22  (assume a534 (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_s V_t) (not (= V_s V_t)))))
% 0.97/1.22  (assume a535 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m) (not (= V_m V_n)))))
% 0.97/1.22  (assume a536 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 0.97/1.22  (assume a537 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))))
% 0.97/1.22  (assume a538 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 V_m_2)))))
% 0.97/1.22  (assume a539 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 0.97/1.22  (assume a540 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_x) (tptp.c_Polynomial_Odegree T_a V_y)) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_x)))))
% 0.97/1.22  (assume a541 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 0.97/1.22  (assume a542 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y)) (tptp.c_Polynomial_Odegree T_a V_y)))))))
% 0.97/1.22  (assume a543 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 0.97/1.22  (assume a544 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))))
% 0.97/1.22  (assume a545 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oone__class_Oone T_b) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) V_b_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) V_b_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2))))))
% 0.97/1.22  (assume a546 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))))
% 0.97/1.22  (assume a547 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 0.97/1.22  (assume a548 (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Ozero T_b) (= (tptp.c_Polynomial_OAbs__poly T_b (tptp.c_Polynomial_Ocoeff T_b V_x_2)) V_x_2))))
% 0.97/1.22  (assume a549 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.c_Polynomial_Osmult T_a V_a V_y)) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 0.97/1.22  (assume a550 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 0.97/1.22  (assume a551 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 0.97/1.22  (assume a552 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 0.97/1.22  (assume a553 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 0.97/1.22  (assume a554 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 0.97/1.22  (assume a555 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 0.97/1.22  (assume a556 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a557 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 V_a_2))))))
% 0.97/1.22  (assume a558 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 0.97/1.22  (assume a559 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 0.97/1.22  (assume a560 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a561 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a562 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 0.97/1.22  (assume a563 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2))))))
% 0.97/1.22  (assume a564 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 V_a_2)))))))
% 0.97/1.22  (assume a565 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_ca_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 V_a_2)))))))
% 0.97/1.22  (assume a566 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a567 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a568 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 0.97/1.22  (assume a569 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 0.97/1.22  (assume a570 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a571 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))
% 0.97/1.22  (assume a572 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a573 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a574 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a575 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a576 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a577 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a578 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))
% 0.97/1.22  (assume a579 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))
% 0.97/1.22  (assume a580 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) V_n)))))))
% 0.97/1.22  (assume a581 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 0.97/1.22  (assume a582 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a583 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oone__class_Oone T_b) V_a_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) V_a_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) V_a_2) V_n_2)) (= V_m_2 V_n_2))))))
% 0.97/1.22  (assume a584 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 0.97/1.22  (assume a585 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 0.97/1.22  (assume a586 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a587 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))
% 0.97/1.22  (assume a588 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))
% 0.97/1.22  (assume a589 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a590 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a))))))
% 0.97/1.22  (assume a591 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))
% 0.97/1.22  (assume a592 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Rings_Oinverse__class_Oinverse T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a593 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Rings_Oinverse__class_Oinverse T_b V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))
% 0.97/1.22  (assume a594 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 (tptp.c_Nat_OSuc V_n_2)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.c_Nat_OSuc B_j)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_n_2)))))))
% 0.97/1.22  (assume a595 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a596 (forall ((V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2) (exists ((B_m $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc B_m))))))
% 0.97/1.22  (assume a597 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_n V_m))))))
% 0.97/1.22  (assume a598 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m)))))
% 0.97/1.22  (assume a599 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)))))
% 0.97/1.22  (assume a600 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m_2 B_k)))))))
% 0.97/1.22  (assume a601 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_i)))))
% 0.97/1.22  (assume a602 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_m)))))
% 0.97/1.22  (assume a603 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Polynomial_Opoly__gcd T_a V_x V_y) (tptp.c_Polynomial_Opoly__gcd T_a V_y (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y)))))))
% 0.97/1.22  (assume a604 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n_2)))))
% 0.97/1.22  (assume a605 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 0.97/1.22  (assume a606 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 0.97/1.22  (assume a607 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_k))))))
% 0.97/1.22  (assume a608 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j))))))
% 0.97/1.22  (assume a609 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (= V_m_2 V_n_2)))))
% 0.97/1.22  (assume a610 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 0.97/1.22  (assume a611 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n_2 V_m_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 0.97/1.22  (assume a612 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m)))))
% 0.97/1.22  (assume a613 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc V_k_2)) V_n_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m_2 V_n_2))))
% 0.97/1.22  (assume a614 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc V_m))))
% 0.97/1.22  (assume a615 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 0.97/1.22  (assume a616 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2))))
% 0.97/1.22  (assume a617 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_i) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a618 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a619 (forall ((V_q $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_q) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_n))))))
% 0.97/1.22  (assume a620 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p) (tptp.c_Polynomial_Odegree T_a V_q)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) (tptp.c_Polynomial_Odegree T_a V_q))))))
% 0.97/1.22  (assume a621 (forall ((V_p $$unsorted) (V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_q) (tptp.c_Polynomial_Odegree T_a V_p)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) (tptp.c_Polynomial_Odegree T_a V_p))))))
% 0.97/1.22  (assume a622 (forall ((V_q $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_q) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)) V_n))))))
% 0.97/1.22  (assume a623 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_y_2) V_y_2))) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))))
% 0.97/1.22  (assume a624 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a625 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a626 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_e_2) V_d_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Groups_Ominus__class_Ominus T_b V_b_2 V_a_2)) V_e_2) V_d_2))))))
% 0.97/1.22  (assume a627 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_e_2) V_ca_2) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_e_2) V_d_2)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_b_2)) V_e_2) V_ca_2) V_d_2)))))
% 0.97/1.22  (assume a628 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 0.97/1.22  (assume a629 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 0.97/1.22  (assume a630 (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oone__class_Oone T_b) (tptp.c_Rings_Oinverse__class_Oinverse T_b V_x_2)) (and (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_b V_x_2 (tptp.c_Groups_Oone__class_Oone T_b)))))))
% 0.97/1.22  (assume a631 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))
% 0.97/1.22  (assume a632 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)))))))
% 0.97/1.22  (assume a633 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n))))))
% 0.97/1.22  (assume a634 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m))))))
% 0.97/1.22  (assume a635 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n))))))
% 0.97/1.22  (assume a636 (forall ((V_i $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc V_i)) V_n))))
% 0.97/1.22  (assume a637 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) V_n))))
% 0.97/1.22  (assume a638 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a639 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat V_m_2 V_n_2)))))
% 0.97/1.22  (assume a640 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))
% 0.97/1.22  (assume a641 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_b_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_b_2) (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$unsorted)) (and (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_b_2 B_d)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))))
% 0.97/1.22  (assume a642 (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p) V_n) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a643 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 0.97/1.22  (assume a644 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 0.97/1.22  (assume a645 (forall ((V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_x (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Rings_Odvd__class_Odvd T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 0.97/1.22  (assume a646 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= V_n (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 0.97/1.22  (assume a647 (forall ((V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n))))
% 0.97/1.22  (assume a648 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) V_m_2) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a649 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m_2) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_m_2) V_m_2) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a650 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2)) (or (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2)))))
% 0.97/1.22  (assume a651 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Nat_OSuc (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (or (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_x (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 0.97/1.22  (assume a652 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_b) (= (tptp.c_Rings_Odvd__class_Odvd T_b V_a_2 V_b_2) (= (tptp.c_Divides_Odiv__class_Omod T_b V_b_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a653 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a654 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k V_n) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_k V_m)))))
% 0.97/1.22  (assume a655 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_f $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_f V_m) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_f V_n) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_f (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n))))))
% 0.97/1.22  (assume a656 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_m)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n))))))
% 0.97/1.22  (assume a657 (forall ((V_m $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_y V_m)) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y) V_m))))
% 0.97/1.22  (assume a658 (forall ((V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m) V_y) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y) V_m))))
% 0.97/1.22  (assume a659 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))
% 0.97/1.22  (assume a660 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j V_k)))))
% 0.97/1.22  (assume a661 (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 0.97/1.22  (assume a662 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))))))
% 0.97/1.22  (assume a663 (forall ((V_d_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m_2 V_d_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_q $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_d_2) B_q))))))
% 0.97/1.22  (assume a664 (forall ((V_d_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m_2 V_d_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (exists ((B_q $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_d_2) B_q))))))
% 0.97/1.22  (assume a665 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n) V_m) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n))))
% 0.97/1.22  (assume a666 (forall ((V_l $$unsorted) (V_k $$unsorted)) (=> (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_k (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_l)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_k V_l) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 0.97/1.22  (assume a667 (forall ((V_l $$unsorted) (V_k $$unsorted)) (=> (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_k) V_l) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_k V_l) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 0.97/1.22  (assume a668 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) V_b)))))
% 0.97/1.22  (assume a669 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 0.97/1.22  (assume a670 (forall ((V_m $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m)) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_x) V_m))))
% 0.97/1.22  (assume a671 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_m))))
% 0.97/1.22  (assume a672 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n))))
% 0.97/1.22  (assume a673 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c))))
% 0.97/1.22  (assume a674 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c))))
% 0.97/1.22  (assume a675 (forall ((V_y $$unsorted) (V_m $$unsorted) (V_x $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_m)) V_y) V_m) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y) V_m))))
% 0.97/1.22  (assume a676 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 0.97/1.22  (assume a677 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 0.97/1.22  (assume a678 (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 0.97/1.22  (assume a679 (forall ((V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 0.97/1.22  (assume a680 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b))))
% 0.97/1.22  (assume a681 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_n))))
% 0.97/1.22  (assume a682 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 0.97/1.22  (assume a683 (forall ((V_y_2 $$unsorted) (V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x_2 V_n_2) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_y_2 V_n_2)) (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_n_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x_2 V_y_2)))))
% 0.97/1.22  (assume a684 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n) V_m)) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_m) V_n))))
% 0.97/1.22  (assume a685 (forall ((V_b $$unsorted) (V_a $$unsorted)) (and (=> (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b))))))
% 0.97/1.22  (assume a686 (forall ((V_b $$unsorted) (V_a $$unsorted)) (and (=> (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) V_b) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_b (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))))
% 0.97/1.22  (assume a687 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 0.97/1.22  (assume a688 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_j))))))
% 0.97/1.22  (assume a689 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_z_2) (= V_w_2 V_z_2)))))
% 0.97/1.22  (assume a690 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 0.97/1.22  (assume a691 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_m V_n) (not (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_n V_m))))))
% 0.97/1.22  (assume a692 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_c) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_r V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_q V_c)) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c))))))
% 0.97/1.22  (assume a693 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2))) (=> (not (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_k_2) (=> (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) B_i) B_j)) (tptp.hBOOL (tptp.hAPP V_P_2 B_j))))))))))
% 0.97/1.22  (assume a694 (forall ((V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_k) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m)) V_k) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a695 (forall ((V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z_2) V_z_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 0.97/1.22  (assume a696 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_m_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 0.97/1.22  (assume a697 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 0.97/1.22  (assume a698 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a699 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 0.97/1.22  (assume a700 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a701 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 0.97/1.22  (assume a702 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c)))))
% 0.97/1.22  (assume a703 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 0.97/1.22  (assume a704 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))))))
% 0.97/1.22  (assume a705 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c)))))
% 0.97/1.22  (assume a706 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c)))))
% 0.97/1.22  (assume a707 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b_H) V_c)))))))
% 0.97/1.22  (assume a708 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 0.97/1.22  (assume a709 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 0.97/1.22  (assume a710 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 0.97/1.22  (assume a711 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c)))))
% 0.97/1.22  (assume a712 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 0.97/1.22  (assume a713 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c)))))
% 0.97/1.22  (assume a714 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c)))))
% 0.97/1.22  (assume a715 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_H V_b_H) V_c)))))))
% 0.97/1.22  (assume a716 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_H V_b_H) V_c)))))))
% 0.97/1.22  (assume a717 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 0.97/1.22  (assume a718 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) V_b) V_c)))))
% 0.97/1.22  (assume a719 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 0.97/1.22  (assume a720 (forall ((V_a_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_b)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a_H) V_b))))))
% 0.97/1.22  (assume a721 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_b)))))
% 0.97/1.22  (assume a722 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted) (V_k_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_b) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_k_2 V_n_2) (= (tptp.c_Rings_Odvd__class_Odvd T_b V_k_2 (tptp.c_Divides_Odiv__class_Omod T_b V_m_2 V_n_2)) (tptp.c_Rings_Odvd__class_Odvd T_b V_k_2 V_m_2))))))
% 0.97/1.22  (assume a723 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_c V_b) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c))))))
% 0.97/1.22  (assume a724 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_k V_m) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_k V_n) (tptp.c_Rings_Odvd__class_Odvd T_a V_k (tptp.c_Divides_Odiv__class_Omod T_a V_m V_n)))))))
% 0.97/1.22  (assume a725 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_k (tptp.c_Divides_Odiv__class_Omod T_a V_m V_n)) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_k V_n) (tptp.c_Rings_Odvd__class_Odvd T_a V_k V_m))))))
% 0.97/1.22  (assume a726 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a727 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a728 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a729 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 0.97/1.22  (assume a730 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 0.97/1.22  (assume a731 (forall ((V_x $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a V_x) V_y) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y)) (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_OpCons T_a V_a (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))) (tptp.c_Polynomial_Odegree T_a V_y)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_y) (tptp.c_Polynomial_Odegree T_a V_y))) V_y)))))))
% 0.97/1.22  (assume a732 (forall ((V_r_2 $$unsorted) (V_q_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (= (tptp.c_Polynomial_Opdivmod__rel T_b V_x_2 V_y_2 V_q_2 V_r_2) (and (= V_x_2 (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_b)) V_q_2) V_y_2) V_r_2)) (=> (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (= V_q_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))) (=> (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)))) (or (= V_r_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_b V_r_2) (tptp.c_Polynomial_Odegree T_b V_y_2)))))))))
% 0.97/1.22  (assume a733 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 0.97/1.22  (assume a734 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))))
% 0.97/1.22  (assume a735 (forall ((V_r_2 $$unsorted) (V_q_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (= (tptp.c_Polynomial_Opdivmod__rel T_b (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)) V_y_2 V_q_2 V_r_2) (and (= V_q_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (= V_r_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))))))))
% 0.97/1.22  (assume a736 (forall ((V_r_2 $$unsorted) (V_q_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (= (tptp.c_Polynomial_Opdivmod__rel T_b V_x_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b)) V_q_2 V_r_2) (and (= V_q_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (= V_r_2 V_x_2))))))
% 0.97/1.22  (assume a737 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Polynomial_Opdivmod__rel T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 0.97/1.22  (assume a738 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Polynomial_Opdivmod__rel T_a V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_x))))
% 0.97/1.22  (assume a739 (forall ((V_a $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (tptp.c_Polynomial_Opdivmod__rel T_a (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y (tptp.c_Polynomial_Osmult T_a V_a V_q) (tptp.c_Polynomial_Osmult T_a V_a V_r))))))
% 0.97/1.22  (assume a740 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_r)))))
% 0.97/1.22  (assume a741 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Rings_Oinverse__class_Odivide T_b V_a_2 V_b_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_b_2)) (and (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))))
% 0.97/1.22  (assume a742 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Rings_Oinverse__class_Odivide T_b V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (or (and (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (and (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_b_2)))))))
% 0.97/1.22  (assume a743 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))))
% 0.97/1.22  (assume a744 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a745 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a746 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))))
% 0.97/1.22  (assume a747 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))))
% 0.97/1.22  (assume a748 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))))
% 0.97/1.22  (assume a749 (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_b) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2)) (and (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) V_b_2)) (=> (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))))
% 0.97/1.22  (assume a750 (forall ((V_a_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_b) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2) V_a_2) (and (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2))) (=> (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))))
% 0.97/1.22  (assume a751 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))))
% 0.97/1.22  (assume a752 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))))
% 0.97/1.22  (assume a753 (forall ((V_w_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted) (V_y_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Ofield T_b) (=> (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (=> (not (= V_z_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_b V_x_2 V_y_2) (tptp.c_Rings_Oinverse__class_Odivide T_b V_w_2 V_z_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_x_2) V_z_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_w_2) V_y_2))))))))
% 0.97/1.22  (assume a754 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_b) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (= (= V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) V_b_2))))))
% 0.97/1.22  (assume a755 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_b) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2) V_a_2) (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2)))))))
% 0.97/1.22  (assume a756 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= V_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c) V_a))))))
% 0.97/1.22  (assume a757 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) V_b) (= V_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)))))))
% 0.97/1.22  (assume a758 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_b) (=> (not (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (= (= (tptp.c_Rings_Oinverse__class_Odivide T_b V_a_2 V_b_2) (tptp.c_Groups_Oone__class_Oone T_b)) (= V_a_2 V_b_2))))))
% 0.97/1.22  (assume a759 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a760 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 0.97/1.22  (assume a761 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b))))))
% 0.97/1.22  (assume a762 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)))))))
% 0.97/1.22  (assume a763 (forall ((V_n $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) V_n) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n)))))))
% 0.97/1.22  (assume a764 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a)) V_n)))))
% 0.97/1.22  (assume a765 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_a)))))
% 0.97/1.22  (assume a766 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_ya) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_ya))))))
% 0.97/1.22  (assume a767 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_c) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c))))))
% 0.97/1.22  (assume a768 (forall ((V_w $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_z V_w)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_w))))))
% 0.97/1.22  (assume a769 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)))))
% 0.97/1.22  (assume a770 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_b))))))
% 0.97/1.22  (assume a771 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 0.97/1.22  (assume a772 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))))
% 0.97/1.22  (assume a773 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y))))))
% 0.97/1.22  (assume a774 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) V_n) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))
% 0.97/1.22  (assume a775 (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (and (= V_q1 V_q2) (= V_r1 V_r2)))))))
% 0.97/1.22  (assume a776 (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (= V_r1 V_r2))))))
% 0.97/1.22  (assume a777 (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (= V_q1 V_q2))))))
% 0.97/1.22  (assume a778 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_c) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c))))))
% 0.97/1.22  (assume a779 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_ya) (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_ya))))))
% 0.97/1.22  (assume a780 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_b V_c)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c)))))
% 0.97/1.22  (assume a781 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a782 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a783 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a784 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))
% 0.97/1.22  (assume a785 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))
% 0.97/1.22  (assume a786 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a)))))
% 0.97/1.22  (assume a787 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a)))))
% 0.97/1.22  (assume a788 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b))))))))
% 0.97/1.22  (assume a789 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a V_c V_b))))))))
% 0.97/1.22  (assume a790 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) V_b_2))))))
% 0.97/1.22  (assume a791 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2)))))))
% 0.97/1.22  (assume a792 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y) V_x) (tptp.c_Orderings_Oord__class_Oless T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))))
% 0.97/1.22  (assume a793 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z))))))
% 0.97/1.22  (assume a794 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2) V_a_2) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2)))))))
% 0.97/1.22  (assume a795 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) V_b_2))))))
% 0.97/1.22  (assume a796 (forall ((V_a_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2) V_a_2) (and (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2))) (=> (not (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2)) (and (=> (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) V_b_2)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))))))
% 0.97/1.22  (assume a797 (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Rings_Oinverse__class_Odivide T_b V_b_2 V_ca_2)) (and (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2) V_b_2)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2)) (and (=> (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_ca_2))) (=> (not (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))))))
% 0.97/1.22  (assume a798 (forall ((V_w $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a V_w V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_w) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_z))))))))
% 0.97/1.22  (assume a799 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) V_z))))))
% 0.97/1.22  (assume a800 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) V_z) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) V_y))))))
% 0.97/1.22  (assume a801 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_x) V_y) V_z))))))
% 0.97/1.22  (assume a802 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_z (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) V_y))))))
% 0.97/1.22  (assume a803 (forall ((V_w $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a V_w V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_w) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_z))))))))
% 0.97/1.22  (assume a804 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_z) V_y) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_y)) V_z))))))
% 0.97/1.22  (assume a805 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_z (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.c_Rings_Oinverse__class_Odivide T_a V_y V_z)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) V_x) V_y) V_z))))))
% 0.97/1.22  (assume a806 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))))
% 0.97/1.22  (assume a807 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_b)))))
% 0.97/1.22  (assume a808 (forall ((V_h $$unsorted) (V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__field T_a) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_d)) V_h) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d) V_h)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c) V_h)) V_d))))))
% 0.97/1.22  (assume a809 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a))))))
% 0.97/1.22  (assume a810 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_z $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_q V_z V_q_H V_r_H) (tptp.c_Polynomial_Opdivmod__rel T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_z) V_q_H (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_r_H) V_r)))))))
% 0.97/1.22  (assume a811 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (= V_b (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Polynomial_OpCons T_a V_a V_r)) (tptp.c_Polynomial_Odegree T_a V_y)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_y) (tptp.c_Polynomial_Odegree T_a V_y)))) (tptp.c_Polynomial_Opdivmod__rel T_a (tptp.c_Polynomial_OpCons T_a V_a V_x) V_y (tptp.c_Polynomial_OpCons T_a V_b V_q) (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_OpCons T_a V_a V_r) (tptp.c_Polynomial_Osmult T_a V_b V_y)))))))))
% 0.97/1.22  (assume a812 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (tptp.c_Polynomial_Opdivmod__rel T_a V_x (tptp.c_Polynomial_Osmult T_a V_a V_y) (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) V_q) V_r))))))
% 0.97/1.22  (assume a813 (forall ((V_h $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__field T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) V_h) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_h))) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)))))))))
% 0.97/1.22  (assume a814 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 0.97/1.22  (assume a815 (forall ((V_pa_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Polynomial_Opos__poly T_b V_pa_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_b V_pa_2) (tptp.c_Polynomial_Odegree T_b V_pa_2)))))))
% 0.97/1.22  (assume a816 (forall ((V_pa_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Polynomial_Opos__poly T_b (tptp.c_Polynomial_OpCons T_b V_a_2 V_pa_2)) (or (tptp.c_Polynomial_Opos__poly T_b V_pa_2) (and (= V_pa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_b))) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))))
% 0.97/1.22  (assume a817 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 0.97/1.22  (assume a818 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Polynomial_Opos__poly T_a V_p) (=> (tptp.c_Polynomial_Opos__poly T_a V_q) (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) V_p V_q)))))))
% 0.97/1.22  (assume a819 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Polynomial_Opos__poly T_a V_p) (=> (tptp.c_Polynomial_Opos__poly T_a V_q) (tptp.c_Polynomial_Opos__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)))))))
% 0.97/1.22  (assume a820 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_Polynomial_Opoly T_b) V_x_2 V_y_2) (tptp.c_Polynomial_Opos__poly T_b (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_b) V_y_2 V_x_2))))))
% 0.97/1.22  (assume a821 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (or (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Polynomial_Opos__poly T_a V_p) (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_p))))))
% 0.97/1.22  (assume a822 (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))))
% 0.97/1.22  (assume a823 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d)) V_z))))
% 0.97/1.22  (assume a824 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a825 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a826 (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 0.97/1.22  (assume a827 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))))
% 0.97/1.22  (assume a828 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) V_b))))
% 0.97/1.22  (assume a829 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 0.97/1.22  (assume a830 (forall ((V_a $$unsorted)) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 0.97/1.22  (assume a831 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_y V_x) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_y)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_y))))))
% 0.97/1.22  (assume a832 (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_b) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_a_2 V_b_2) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_a_2 V_ca_2) (= (tptp.c_Rings_Odvd__class_Odvd T_b (tptp.c_Divides_Odiv__class_Odiv T_b V_b_2 V_a_2) (tptp.c_Divides_Odiv__class_Odiv T_b V_ca_2 V_a_2)) (tptp.c_Rings_Odvd__class_Odvd T_b V_b_2 V_ca_2)))))))
% 0.97/1.22  (assume a833 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))))
% 0.97/1.22  (assume a834 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) V_n)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 0.97/1.22  (assume a835 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_a V_b) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_b V_a) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_a) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_b))))))
% 0.97/1.22  (assume a836 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))))
% 0.97/1.22  (assume a837 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 0.97/1.22  (assume a838 (forall ((V_k $$unsorted) (V_l $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (= (tptp.c_Groups_Oabs__class_Oabs T_a V_l) (tptp.c_Groups_Oabs__class_Oabs T_a V_k)) (tptp.c_Rings_Odvd__class_Odvd T_a V_l V_k)))))
% 0.97/1.22  (assume a839 (forall ((V_k_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Rings_Odvd__class_Odvd T_b (tptp.c_Groups_Oabs__class_Oabs T_b V_m_2) V_k_2) (tptp.c_Rings_Odvd__class_Odvd T_b V_m_2 V_k_2)))))
% 0.97/1.22  (assume a840 (forall ((V_k_2 $$unsorted) (V_m_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Rings_Odvd__class_Odvd T_b V_m_2 (tptp.c_Groups_Oabs__class_Oabs T_b V_k_2)) (tptp.c_Rings_Odvd__class_Odvd T_b V_m_2 V_k_2)))))
% 0.97/1.22  (assume a841 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 0.97/1.22  (assume a842 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) V_n)))))
% 0.97/1.22  (assume a843 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 0.97/1.22  (assume a844 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a845 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 0.97/1.22  (assume a846 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 0.97/1.22  (assume a847 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 0.97/1.22  (assume a848 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a849 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_b) (= (= (tptp.c_Groups_Oabs__class_Oabs T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a850 (forall ((V_n $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_y V_x) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_x V_y)) V_n) (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_n)))))))
% 0.97/1.22  (assume a851 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_y V_x) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_x V_y)))))))
% 0.97/1.22  (assume a852 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_y V_x) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_x (tptp.c_Groups_Ouminus__class_Ouminus T_a V_y)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_x V_y)))))))
% 0.97/1.22  (assume a853 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a854 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_z V_x) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_z V_y) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y) V_z) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_x V_z) (tptp.c_Divides_Odiv__class_Odiv T_a V_y V_z))))))))
% 0.97/1.22  (assume a855 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_b V_a)) V_b)))))
% 0.97/1.22  (assume a856 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_c V_b) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c))))))
% 0.97/1.22  (assume a857 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_b V_a)) V_a) V_b)))))
% 0.97/1.22  (assume a858 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_a V_b) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_b V_a)) V_c) (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c) V_a))))))
% 0.97/1.22  (assume a859 (forall ((V_w $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_y V_x) (=> (tptp.c_Rings_Odvd__class_Odvd T_a V_z V_w) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_x V_y)) (tptp.c_Divides_Odiv__class_Odiv T_a V_w V_z)) (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_z))))))))
% 0.97/1.22  (assume a860 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a861 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 0.97/1.22  (assume a862 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 0.97/1.22  (assume a863 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) V_b) V_a)))))
% 0.97/1.22  (assume a864 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) V_a)))))
% 0.97/1.22  (assume a865 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (and (=> (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 0.97/1.22  (assume a866 (forall ((V_x_2 $$unsorted)) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 0.97/1.22  (assume a867 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint V_n V_m) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_m V_n)) V_m))))
% 0.97/1.22  (assume a868 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m) V_n)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_m) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 0.97/1.22  (assume a869 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 0.97/1.22  (assume a870 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_a V_b)) (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))))))
% 0.97/1.22  (assume a871 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oabs__class_Oabs T_b V_a_2) V_b_2) (and (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) V_b_2))))))
% 0.97/1.22  (assume a872 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_b) V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_d)))))))
% 0.97/1.22  (assume a873 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 0.97/1.22  (assume a874 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Groups_Oabs__class_Oabs T_b V_a_2)) (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b)))))))
% 0.97/1.22  (assume a875 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 0.97/1.22  (assume a876 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 0.97/1.22  (assume a877 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a_2)))))
% 0.97/1.22  (assume a878 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_a_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 0.97/1.22  (assume a879 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 0.97/1.22  (assume a880 (forall ((V_a $$unsorted)) (and (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a))))
% 0.97/1.22  (assume a881 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c)))))
% 0.97/1.22  (assume a882 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oabs__if T_a) (and (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a))))))
% 0.97/1.22  (assume a883 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a))))))
% 0.97/1.22  (assume a884 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_y) (= (tptp.c_Rings_Oinverse__class_Odivide T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_x) V_y) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Rings_Oinverse__class_Odivide T_a V_x V_y)))))))
% 0.97/1.22  (assume a885 (forall ((V_k $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_k) V_x)))))
% 0.97/1.22  (assume a886 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)))))
% 0.97/1.22  (assume a887 (forall ((V_z_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_z_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_z_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 0.97/1.22  (assume a888 (forall ((V_i $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_i) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_i))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_i) V_i)))))
% 0.97/1.22  (assume a889 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))
% 0.97/1.22  (assume a890 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c)))))
% 0.97/1.22  (assume a891 (forall ((V_k $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_k))))
% 0.97/1.22  (assume a892 (forall ((V_k $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_a V_k))))
% 0.97/1.22  (assume a893 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_m (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n)))))
% 0.97/1.22  (assume a894 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_m V_n)) V_n)))))
% 0.97/1.22  (assume a895 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 0.97/1.22  (assume a896 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 0.97/1.22  (assume a897 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 0.97/1.22  (assume a898 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 0.97/1.22  (assume a899 (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_b) (=> (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_a_2 V_b_2) (= (= (tptp.c_Divides_Odiv__class_Odiv T_b V_b_2 V_a_2) V_ca_2) (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_a_2))))))))
% 0.97/1.22  (assume a900 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_b) (=> (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b))) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_a_2 V_b_2) (=> (tptp.c_Rings_Odvd__class_Odvd T_b V_ca_2 V_d_2) (= (= (tptp.c_Divides_Odiv__class_Odiv T_b V_b_2 V_a_2) (tptp.c_Divides_Odiv__class_Odiv T_b V_d_2 V_ca_2)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a_2) V_d_2))))))))))
% 0.97/1.22  (assume a901 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) V_a))))
% 0.97/1.22  (assume a902 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))))
% 0.97/1.22  (assume a903 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))))
% 0.97/1.22  (assume a904 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))
% 0.97/1.22  (assume a905 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))
% 0.97/1.22  (assume a906 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (not (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Rings_Odvd__class_Odvd tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m_2) V_n_2) V_m_2) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))
% 0.97/1.22  (assume a907 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x_2)) V_n_2)) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 0.97/1.22  (assume a908 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_c) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 0.97/1.22  (assume a909 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (and (=> (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) V_b) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)))) (=> (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_a) V_b) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))))
% 0.97/1.22  (assume a910 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (and (=> (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)))) (=> (not (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint V_b)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Groups_Ouminus__class_Ouminus tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))))
% 0.97/1.22  (assume a911 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d))))))
% 0.97/1.22  (assume a912 (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Oabs__class_Oabs T_b (tptp.c_Groups_Ominus__class_Ominus T_b V_x_2 V_a_2)) V_r_2) (and (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ominus__class_Ominus T_b V_a_2 V_r_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_b V_x_2 (tptp.c_Groups_Oplus__class_Oplus T_b V_a_2 V_r_2)))))))
% 0.97/1.22  (assume a913 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (and (=> (= V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= (tptp.c_Groups_Osgn__class_Osgn (tptp.tc_Polynomial_Opoly T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (and (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_x) (= (tptp.c_Groups_Osgn__class_Osgn (tptp.tc_Polynomial_Opoly T_a) V_x) (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)))) (=> (not (tptp.c_Orderings_Oord__class_Oless (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_x)) (= (tptp.c_Groups_Osgn__class_Osgn (tptp.tc_Polynomial_Opoly T_a) V_x) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a)))))))))))
% 0.97/1.22  (assume a914 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) (tptp.c_Groups_Osgn__class_Osgn T_b V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))
% 0.97/1.22  (assume a915 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Osgn__class_Osgn T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a916 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y)))))
% 0.97/1.22  (assume a917 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_b) V_c))))
% 0.97/1.22  (assume a918 (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)))
% 0.97/1.22  (assume a919 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (and (=> (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n))))))
% 0.97/1.22  (assume a920 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y) (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 0.97/1.22  (assume a921 (forall ((V_k $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_k) (tptp.c_Groups_Osgn__class_Osgn T_a V_k))))))
% 0.97/1.22  (assume a922 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) V_x))))
% 0.97/1.22  (assume a923 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_x) V_y) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 0.97/1.22  (assume a924 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_y)) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 0.97/1.22  (assume a925 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_z)) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_z)))))
% 0.97/1.22  (assume a926 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_q)))))
% 0.97/1.22  (assume a927 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 0.97/1.22  (assume a928 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_b V_c)) V_c)))))
% 0.97/1.22  (assume a929 (forall ((V_x_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (= (tptp.c_Groups_Osgn__class_Osgn T_b V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a930 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (= (tptp.c_Groups_Osgn__class_Osgn T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a931 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a932 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Osgn__if T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 0.97/1.22  (assume a933 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_x)) (tptp.c_Groups_Osgn__class_Osgn T_a V_y))))))
% 0.97/1.22  (assume a934 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_b))))))
% 0.97/1.22  (assume a935 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 0.97/1.22  (assume a936 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_x)) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_x))))))
% 0.97/1.22  (assume a937 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a (tptp.c_Groups_Osgn__class_Osgn T_a V_a)) (tptp.c_Groups_Osgn__class_Osgn T_a V_a)))))
% 0.97/1.22  (assume a938 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m) V_n) V_m))))
% 0.97/1.22  (assume a939 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) V_n) V_m))))
% 0.97/1.22  (assume a940 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a941 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) V_m)))))
% 0.97/1.22  (assume a942 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_a) V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_a) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_b V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_b V_c)) V_c)))))
% 0.97/1.22  (assume a943 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_b) V_c)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_b)))))
% 0.97/1.22  (assume a944 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_n)))))
% 0.97/1.22  (assume a945 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a946 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))))
% 0.97/1.22  (assume a947 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.c_Polynomial_Osmult T_a V_a V_y)) (tptp.c_Polynomial_Osmult T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y)))))))
% 0.97/1.22  (assume a948 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_x) (tptp.c_Polynomial_Odegree T_a V_y)) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 0.97/1.22  (assume a949 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (= (tptp.c_Groups_Osgn__class_Osgn T_b V_a_2) (tptp.c_Groups_Oone__class_Oone T_b)) (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_a_2)))))
% 0.97/1.22  (assume a950 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 0.97/1.22  (assume a951 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_z)) (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_z)) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 0.97/1.22  (assume a952 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n)))))))
% 0.97/1.22  (assume a953 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n))))))))
% 0.97/1.22  (assume a954 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_j V_k_2) (=> (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) B_i) B_j)) (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))))))))
% 0.97/1.22  (assume a955 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (and (=> (tptp.c_Orderings_Oord__class_Oless (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= (tptp.c_Groups_Oabs__class_Oabs (tptp.tc_Polynomial_Opoly T_a) V_x) (tptp.c_Groups_Ouminus__class_Ouminus (tptp.tc_Polynomial_Opoly T_a) V_x))) (=> (not (tptp.c_Orderings_Oord__class_Oless (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Oabs__class_Oabs (tptp.tc_Polynomial_Opoly T_a) V_x) V_x))))))
% 0.97/1.22  (assume a956 (forall ((V_c $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Nat_OSuc V_a) V_c) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_a V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) V_c)))))
% 0.97/1.22  (assume a957 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Osgn__if T_a) (and (=> (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x)) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_x) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a))))))))))
% 0.97/1.22  (assume a958 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_b) (= (= (tptp.c_Groups_Osgn__class_Osgn T_b V_a_2) (tptp.c_Groups_Ouminus__class_Ouminus T_b (tptp.c_Groups_Oone__class_Oone T_b))) (tptp.c_Orderings_Oord__class_Oless T_b V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a959 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Osgn__class_Osgn T_a V_a) (tptp.c_Groups_Ouminus__class_Ouminus T_a (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 0.97/1.22  (assume a960 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k_2) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) B_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint B_j V_k_2) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))))
% 0.97/1.22  (assume a961 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 B_j) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint B_j (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_n_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))))
% 0.97/1.22  (assume a962 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_x) (=> (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_y) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_y))))))
% 0.97/1.22  (assume a963 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 0.97/1.22  (assume a964 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 0.97/1.22  (assume a965 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))))))
% 0.97/1.22  (assume a966 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b)))))
% 0.97/1.22  (assume a967 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b))))))
% 0.97/1.22  (assume a968 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.c_Groups_Oabs__class_Oabs T_b V_a_2) V_b_2) (and (tptp.c_Orderings_Oord__class_Oless__eq T_b V_a_2 V_b_2) (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.c_Groups_Ouminus__class_Ouminus T_b V_a_2) V_b_2))))))
% 0.97/1.22  (assume a969 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ouminus__class_Ouminus T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 0.97/1.22  (assume a970 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 0.97/1.22  (assume a971 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_b) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b)))))
% 0.97/1.22  (assume a972 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 0.97/1.22  (assume a973 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 0.97/1.22  (assume a974 (forall ((V_a_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_b) (= (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.c_Groups_Oabs__class_Oabs T_b V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_b)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_b))))))
% 0.97/1.22  (assume a975 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 0.97/1.22  (assume a976 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b (tptp.c_Groups_Ozero__class_Ozero T_b) V_ca_2) (= (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_b V_a_2 V_b_2))))))
% 0.97/1.22  (assume a977 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_b) (=> (tptp.c_Orderings_Oord__class_Oless T_b V_ca_2 (tptp.c_Groups_Ozero__class_Ozero T_b)) (= (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_ca_2) V_b_2)) (tptp.c_Orderings_Oord__class_Oless__eq T_b V_b_2 V_a_2))))))
% 0.97/1.22  (assume a978 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 0.97/1.22  (assume a979 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 0.97/1.22  (assume a980 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 0.97/1.22  (assume a981 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 0.97/1.22  (assume a982 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 0.97/1.22  (assume a983 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 0.97/1.22  (assume a984 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 0.97/1.22  (assume a985 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 0.97/1.22  (assume a986 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 0.97/1.22  (assume a987 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a V_b))))))
% 0.97/1.22  (assume a988 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 0.97/1.22  (assume a989 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 0.97/1.22  (assume a990 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 0.97/1.22  (assume a991 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 0.97/1.22  (assume a992 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a993 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 0.97/1.22  (assume a994 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y))))))
% 0.97/1.22  (assume a995 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T))))
% 0.97/1.22  (assume a996 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Ocancel__ab__semigroup__add T))))
% 0.97/1.22  (assume a997 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Oring__1__no__zero__divisors T))))
% 0.97/1.22  (assume a998 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Oring__no__zero__divisors T))))
% 0.97/1.22  (assume a999 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Ocancel__semigroup__add T))))
% 0.97/1.22  (assume a1000 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Oab__semigroup__mult T))))
% 0.97/1.22  (assume a1001 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Ocomm__monoid__mult T))))
% 0.97/1.22  (assume a1002 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Oab__semigroup__add T))))
% 0.97/1.22  (assume a1003 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Ono__zero__divisors T))))
% 0.97/1.22  (assume a1004 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Ocomm__monoid__add T))))
% 0.97/1.22  (assume a1005 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Ocomm__semiring__1 T))))
% 0.97/1.22  (assume a1006 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Ocomm__semiring__0 T))))
% 0.97/1.22  (assume a1007 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Ocomm__semiring T))))
% 0.97/1.22  (assume a1008 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Oab__group__add T))))
% 0.97/1.22  (assume a1009 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Ozero__neq__one T))))
% 0.97/1.22  (assume a1010 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Omonoid__mult T))))
% 0.97/1.22  (assume a1011 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Ocomm__ring__1 T))))
% 0.97/1.22  (assume a1012 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Omonoid__add T))))
% 0.97/1.22  (assume a1013 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Osemiring__0 T))))
% 0.97/1.22  (assume a1014 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Ogroup__add T))))
% 0.97/1.22  (assume a1015 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Omult__zero T))))
% 0.97/1.22  (assume a1016 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Ocomm__ring T))))
% 0.97/1.22  (assume a1017 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Osemiring T))))
% 0.97/1.22  (assume a1018 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Oring__1 T))))
% 0.97/1.22  (assume a1019 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Power_Opower T))))
% 0.97/1.22  (assume a1020 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Ozero T))))
% 0.97/1.22  (assume a1021 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Oring T))))
% 0.97/1.22  (assume a1022 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Oone T))))
% 0.97/1.22  (assume a1023 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Rings_Odvd T))))
% 0.97/1.22  (assume a1024 (forall ((T $$unsorted)) (=> (tptp.class_Rings_Oidom T) (tptp.class_Groups_Ocancel__comm__monoid__add T))))
% 0.97/1.22  (assume a1025 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1026 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1027 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1028 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1029 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1030 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1031 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1032 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1033 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1034 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1035 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1036 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1037 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1038 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1039 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1040 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1041 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1042 (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1043 (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1044 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1045 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1046 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1047 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1048 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1049 (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1050 (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1051 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1052 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1053 (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1054 (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1055 (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1056 (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1057 (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1058 (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1059 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1060 (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1061 (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1062 (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1063 (tptp.class_Divides_Oring__div tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1064 (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1065 (tptp.class_Rings_Ocomm__ring tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1066 (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1067 (tptp.class_Rings_Osemiring tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1068 (tptp.class_Groups_Osgn__if tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1069 (tptp.class_Groups_Oabs__if tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1070 (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1071 (tptp.class_Power_Opower tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1072 (tptp.class_Groups_Ozero tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1073 (tptp.class_Rings_Oring tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1074 (tptp.class_Rings_Oidom tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1075 (tptp.class_Groups_Oone tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1076 (tptp.class_Rings_Odvd tptp.tc_Int_Oint))
% 0.97/1.22  (assume a1077 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1078 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1079 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1080 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1081 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1082 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1083 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1084 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1085 (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1086 (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1087 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1088 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1089 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1090 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1091 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1092 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1093 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1094 (tptp.class_Divides_Osemiring__div tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1095 (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1096 (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1097 (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1098 (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1099 (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1100 (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1101 (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1102 (tptp.class_Power_Opower tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1103 (tptp.class_Groups_Ozero tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1104 (tptp.class_Groups_Oone tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1105 (tptp.class_Rings_Odvd tptp.tc_Nat_Onat))
% 0.97/1.22  (assume a1106 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1107 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1108 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1109 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1110 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1111 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add__abs (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1112 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1113 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Olinordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1114 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1115 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1116 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1117 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1118 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1119 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1120 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1121 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semidom (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1122 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Groups_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1123 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1124 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1125 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1126 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1127 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1128 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__idom (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1129 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1130 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1131 (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Osemiring__div (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1132 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1133 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1134 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1135 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1136 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1137 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1138 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1139 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1140 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Ogroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1141 (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Oring__div (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1142 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Omult__zero (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1143 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1144 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1145 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1146 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Osgn__if (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1147 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oabs__if (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1148 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Oring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1149 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Power_Opower (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1150 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ozero T_1) (tptp.class_Groups_Ozero (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1151 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Oring (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1152 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oidom (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1153 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Oone (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1154 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Odvd (tptp.tc_Polynomial_Opoly T_1)))))
% 0.97/1.22  (assume a1155 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.c_fequal V_x_2 V_y_2))) (= V_x_2 V_y_2))))
% 0.97/1.22  (assume a1156 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.c_fequal V_x_2 V_y_2)))))
% 0.97/1.22  (assume a1157 (not (tptp.hBOOL tptp.c_fFalse)))
% 0.97/1.22  (assume a1158 (tptp.hBOOL tptp.c_fTrue))
% 0.97/1.22  (assume a1159 (not (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))
% 0.97/1.22  (assume a1160 (tptp.class_Rings_Oidom tptp.t_a))
% 0.97/1.22  (assume a1161 true)
% 0.97/1.22  (step t1 (cl (not (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))) (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))) :rule implies_pos)
% 0.97/1.22  (step t2 (cl (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))) (not (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))))) :rule reordering :premises (t1))
% 0.97/1.22  (step t3 (cl (not (= (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))))) (not (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule equiv_pos2)
% 0.97/1.22  (step t4 (cl (= (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))))) :rule refl)
% 0.97/1.22  (step t5 (cl (= (= (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) true) (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))))) :rule equiv_simplify)
% 0.97/1.22  (step t6 (cl (not (= (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) true)) (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) :rule equiv1 :premises (t5))
% 0.97/1.22  (step t7 (cl (= (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (= (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))))))) :rule all_simplify)
% 0.97/1.22  (step t8 (cl (= (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) :rule refl)
% 0.97/1.22  (step t9 (cl (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) :rule all_simplify)
% 0.97/1.22  (step t10 (cl (= (= (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))))) (= (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))))) :rule cong :premises (t8 t9))
% 0.97/1.22  (step t11 (cl (= (= (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) true)) :rule all_simplify)
% 0.97/1.22  (step t12 (cl (= (= (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))))) true)) :rule trans :premises (t10 t11))
% 0.97/1.22  (step t13 (cl (= (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) true)) :rule trans :premises (t7 t12))
% 0.97/1.22  (step t14 (cl (= (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) :rule resolution :premises (t6 t13))
% 0.97/1.22  (step t15 (cl (= (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule refl)
% 0.97/1.22  (step t16 (cl (= (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))))) :rule cong :premises (t4 t14 t15))
% 0.97/1.22  (step t17 (cl (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) :rule implies_pos)
% 0.97/1.22  (step t18 (cl (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (not (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))))) :rule or_neg)
% 0.97/1.22  (step t19 (cl (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (not (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))))) :rule or_neg)
% 0.97/1.22  (step t20 (cl (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (not (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule or_neg)
% 0.97/1.22  (step t21 (cl (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule resolution :premises (t17 t18 t19 t20))
% 0.97/1.22  (step t22 (cl (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (not (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule contraction :premises (t21))
% 0.97/1.22  (step t23 (cl (or (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule resolution :premises (t3 t16 t22))
% 0.97/1.22  (step t24 (cl (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) :rule or :premises (t23))
% 0.97/1.22  (step t25 (cl (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) (not (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))))) :rule reordering :premises (t24))
% 0.97/1.22  (step t26 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) :rule hole :args ((forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) (= B_a B_a) (= B_z B_z) (= B_k B_k) (= BOUND_VARIABLE_14989 BOUND_VARIABLE_21473)))
% 0.97/1.22  (step t27 (cl (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) :rule equiv2 :premises (t26))
% 0.97/1.22  (step t28 (cl (not (= (not (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) (not (not (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))) :rule equiv_pos2)
% 0.97/1.22  (anchor :step t29 :args ((B_k $$unsorted) (:= B_k B_k) (B_a $$unsorted) (:= B_a B_a)))
% 0.97/1.22  (step t29.t1 (cl (= B_k B_k)) :rule refl)
% 0.97/1.22  (step t29.t2 (cl (= B_a B_a)) :rule refl)
% 0.97/1.22  (step t29.t3 (cl (= (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a))) :rule all_simplify)
% 0.97/1.22  (step t29.t4 (cl (= (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)))) :rule cong :premises (t29.t3))
% 0.97/1.22  (anchor :step t29.t5 :args ((B_q $$unsorted) (:= B_q B_q)))
% 0.97/1.22  (step t29.t5.t1 (cl (= B_q B_q)) :rule refl)
% 0.97/1.22  (step t29.t5.t2 (cl (= (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))))) :rule refl)
% 0.97/1.22  (step t29.t5.t3 (cl (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) :rule all_simplify)
% 0.97/1.22  (step t29.t5.t4 (cl (= (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))))) :rule cong :premises (t29.t5.t2 t29.t5.t3))
% 0.97/1.22  (step t29.t5.t5 (cl (= (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))))) :rule refl)
% 0.97/1.22  (step t29.t5.t6 (cl (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) :rule all_simplify)
% 0.97/1.22  (step t29.t5.t7 (cl (= (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))))) :rule cong :premises (t29.t5.t5 t29.t5.t6))
% 0.97/1.22  (step t29.t5.t8 (cl (= (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) :rule refl)
% 0.97/1.22  (step t29.t5.t9 (cl (= (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) :rule cong :premises (t29.t5.t4 t29.t5.t7 t29.t5.t8))
% 0.97/1.22  (step t29.t5 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) :rule bind)
% 0.97/1.22  (step t29.t6 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule all_simplify)
% 0.97/1.22  (step t29.t7 (cl (= (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) :rule all_simplify)
% 0.97/1.22  (step t29.t8 (cl (= (not (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule cong :premises (t29.t7))
% 0.97/1.22  (step t29.t9 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule trans :premises (t29.t6 t29.t8))
% 0.97/1.22  (step t29.t10 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule trans :premises (t29.t5 t29.t9))
% 0.97/1.22  (step t29.t11 (cl (= (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) :rule cong :premises (t29.t4 t29.t10))
% 0.97/1.22  (step t29 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))) :rule bind)
% 0.97/1.22  (step t30 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))))) :rule all_simplify)
% 0.97/1.22  (step t31 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) :rule all_simplify)
% 0.97/1.22  (step t32 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))))) :rule all_simplify)
% 0.97/1.22  (anchor :step t33 :args ((B_k $$unsorted) (:= B_k B_k) (B_a $$unsorted) (:= B_a B_a) (BOUND_VARIABLE_21473 $$unsorted) (:= BOUND_VARIABLE_21473 BOUND_VARIABLE_21473)))
% 0.97/1.22  (step t33.t1 (cl (= B_k B_k)) :rule refl)
% 0.97/1.22  (step t33.t2 (cl (= B_a B_a)) :rule refl)
% 0.97/1.22  (step t33.t3 (cl (= BOUND_VARIABLE_21473 BOUND_VARIABLE_21473)) :rule refl)
% 0.97/1.22  (step t33.t4 (cl (= (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))) :rule all_simplify)
% 0.97/1.22  (step t33 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) :rule bind)
% 0.97/1.22  (step t34 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) :rule trans :premises (t32 t33))
% 0.97/1.22  (step t35 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) :rule trans :premises (t31 t34))
% 0.97/1.22  (step t36 (cl (= (not (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))))) :rule cong :premises (t35))
% 0.97/1.22  (step t37 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))))) :rule trans :premises (t30 t36))
% 0.97/1.22  (step t38 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))))) :rule trans :premises (t29 t37))
% 0.97/1.22  (step t39 (cl (= (not (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (not (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))))) :rule cong :premises (t38))
% 0.97/1.22  (step t40 (cl (= (not (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) :rule all_simplify)
% 0.97/1.22  (step t41 (cl (= (not (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z))))))))) :rule trans :premises (t39 t40))
% 0.97/1.22  (step t42 (cl (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_21473 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_21473 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_21473))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_21473)) B_z)))))))) :rule resolution :premises (t28 t41 a1159))
% 0.97/1.22  (step t43 (cl (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) :rule resolution :premises (t27 t42))
% 0.97/1.22  (step t44 (cl (not (= (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))))) (not (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))))) :rule equiv_pos2)
% 0.97/1.22  (step t45 (cl (= (tptp.class_Rings_Oidom tptp.t_a) (tptp.class_Rings_Oidom tptp.t_a))) :rule refl)
% 0.97/1.22  (step t46 (cl (= (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))))) :rule refl)
% 0.97/1.22  (anchor :step t47 :args ((B_k $$unsorted) (:= B_k B_k) (B_a $$unsorted) (:= B_a B_a)))
% 0.97/1.22  (step t47.t1 (cl (= B_k B_k)) :rule refl)
% 0.97/1.22  (step t47.t2 (cl (= B_a B_a)) :rule refl)
% 0.97/1.22  (step t47.t3 (cl (= (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a))) :rule all_simplify)
% 0.97/1.22  (step t47.t4 (cl (= (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)))) :rule cong :premises (t47.t3))
% 0.97/1.22  (anchor :step t47.t5 :args ((B_q $$unsorted) (:= B_q B_q)))
% 0.97/1.22  (step t47.t5.t1 (cl (= B_q B_q)) :rule refl)
% 0.97/1.22  (step t47.t5.t2 (cl (= (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))))) :rule refl)
% 0.97/1.22  (step t47.t5.t3 (cl (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) :rule all_simplify)
% 0.97/1.22  (step t47.t5.t4 (cl (= (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))))) :rule cong :premises (t47.t5.t2 t47.t5.t3))
% 0.97/1.22  (step t47.t5.t5 (cl (= (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))))) :rule refl)
% 0.97/1.22  (step t47.t5.t6 (cl (= (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) :rule refl)
% 0.97/1.22  (step t47.t5.t7 (cl (= (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) :rule cong :premises (t47.t5.t4 t47.t5.t5 t47.t5.t6))
% 0.97/1.22  (step t47.t5 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) :rule bind)
% 0.97/1.22  (step t47.t6 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule all_simplify)
% 0.97/1.22  (step t47.t7 (cl (= (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) :rule all_simplify)
% 0.97/1.22  (step t47.t8 (cl (= (not (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule cong :premises (t47.t7))
% 0.97/1.22  (step t47.t9 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule trans :premises (t47.t6 t47.t8))
% 0.97/1.22  (step t47.t10 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule trans :premises (t47.t5 t47.t9))
% 0.97/1.22  (step t47.t11 (cl (= (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) :rule cong :premises (t47.t4 t47.t10))
% 0.97/1.22  (step t47 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))) :rule bind)
% 0.97/1.22  (step t48 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))))) :rule all_simplify)
% 0.97/1.22  (step t49 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) :rule all_simplify)
% 0.97/1.22  (step t50 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule all_simplify)
% 0.97/1.22  (anchor :step t51 :args ((B_k $$unsorted) (:= B_k B_k) (B_a $$unsorted) (:= B_a B_a) (BOUND_VARIABLE_14989 $$unsorted) (:= BOUND_VARIABLE_14989 BOUND_VARIABLE_14989)))
% 0.97/1.22  (step t51.t1 (cl (= B_k B_k)) :rule refl)
% 0.97/1.22  (step t51.t2 (cl (= B_a B_a)) :rule refl)
% 0.97/1.22  (step t51.t3 (cl (= BOUND_VARIABLE_14989 BOUND_VARIABLE_14989)) :rule refl)
% 0.97/1.22  (step t51.t4 (cl (= (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) :rule all_simplify)
% 0.97/1.22  (step t51.t5 (cl (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a))) :rule refl)
% 0.97/1.22  (step t51.t6 (cl (= (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))))) :rule refl)
% 0.97/1.22  (step t51.t7 (cl (= (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))))) :rule refl)
% 0.97/1.22  (step t51.t8 (cl (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) :rule all_simplify)
% 0.97/1.22  (step t51.t9 (cl (= (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)))))) :rule cong :premises (t51.t8))
% 0.97/1.22  (step t51.t10 (cl (= (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))))) :rule cong :premises (t51.t7 t51.t9))
% 0.97/1.22  (step t51.t11 (cl (= (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) :rule refl)
% 0.97/1.22  (step t51.t12 (cl (= (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) :rule cong :premises (t51.t5 t51.t6 t51.t10 t51.t11))
% 0.97/1.22  (step t51.t13 (cl (= (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) :rule trans :premises (t51.t4 t51.t12))
% 0.97/1.22  (step t51 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) :rule bind)
% 0.97/1.22  (step t52 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) :rule trans :premises (t50 t51))
% 0.97/1.22  (step t53 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) :rule trans :premises (t49 t52))
% 0.97/1.22  (step t54 (cl (= (not (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule cong :premises (t53))
% 0.97/1.22  (step t55 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule trans :premises (t48 t54))
% 0.97/1.22  (step t56 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule trans :premises (t47 t55))
% 0.97/1.22  (step t57 (cl (= (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))))) :rule cong :premises (t46 t56))
% 0.97/1.22  (step t58 (cl (= (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))))) :rule cong :premises (t45 t57))
% 0.97/1.22  (step t59 (cl (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))))) :rule resolution :premises (t44 t58 a3))
% 0.97/1.22  (step t60 (cl (not (tptp.class_Rings_Oidom tptp.t_a)) (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule implies :premises (t59))
% 0.97/1.22  (step t61 (cl (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))))) (not (tptp.class_Rings_Oidom tptp.t_a))) :rule reordering :premises (t60))
% 0.97/1.22  (step t62 (cl (=> (not (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))))) :rule resolution :premises (t61 a1160))
% 0.97/1.22  (step t63 (cl (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) :rule resolution :premises (t25 t43 t62))
% 0.97/1.22  (step t64 (cl (not (= (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))))) (not (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))))) :rule equiv_pos2)
% 0.97/1.22  (anchor :step t65 :args ((B_k $$unsorted) (:= B_k B_k) (B_a $$unsorted) (:= B_a B_a)))
% 0.97/1.22  (step t65.t1 (cl (= B_k B_k)) :rule refl)
% 0.97/1.22  (step t65.t2 (cl (= B_a B_a)) :rule refl)
% 0.97/1.22  (step t65.t3 (cl (= (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a))) :rule all_simplify)
% 0.97/1.22  (step t65.t4 (cl (= (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)))) :rule cong :premises (t65.t3))
% 0.97/1.22  (anchor :step t65.t5 :args ((B_q $$unsorted) (:= B_q B_q)))
% 0.97/1.22  (step t65.t5.t1 (cl (= B_q B_q)) :rule refl)
% 0.97/1.22  (step t65.t5.t2 (cl (= (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))))) :rule refl)
% 0.97/1.22  (step t65.t5.t3 (cl (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) :rule all_simplify)
% 0.97/1.22  (step t65.t5.t4 (cl (= (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))))) :rule cong :premises (t65.t5.t2 t65.t5.t3))
% 0.97/1.22  (step t65.t5.t5 (cl (= (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))))) :rule refl)
% 0.97/1.22  (step t65.t5.t6 (cl (= (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) :rule all_simplify)
% 0.97/1.22  (step t65.t5.t7 (cl (= (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))))) :rule cong :premises (t65.t5.t5 t65.t5.t6))
% 0.97/1.22  (step t65.t5.t8 (cl (= (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) :rule refl)
% 0.97/1.22  (step t65.t5.t9 (cl (= (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) :rule cong :premises (t65.t5.t4 t65.t5.t7 t65.t5.t8))
% 0.97/1.22  (step t65.t5 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) :rule bind)
% 0.97/1.22  (step t65.t6 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule all_simplify)
% 0.97/1.22  (step t65.t7 (cl (= (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) :rule all_simplify)
% 0.97/1.22  (step t65.t8 (cl (= (not (forall ((B_q $$unsorted)) (not (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule cong :premises (t65.t7))
% 0.97/1.22  (step t65.t9 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule trans :premises (t65.t6 t65.t8))
% 0.97/1.22  (step t65.t10 (cl (= (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) :rule trans :premises (t65.t5 t65.t9))
% 0.97/1.22  (step t65.t11 (cl (= (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) :rule cong :premises (t65.t4 t65.t10))
% 0.97/1.22  (step t65 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))) :rule bind)
% 0.97/1.22  (step t66 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))))) :rule all_simplify)
% 0.97/1.22  (step t67 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) :rule all_simplify)
% 0.97/1.22  (step t68 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))) :rule all_simplify)
% 0.97/1.22  (anchor :step t69 :args ((B_k $$unsorted) (:= B_k B_k) (B_a $$unsorted) (:= B_a B_a) (BOUND_VARIABLE_15052 $$unsorted) (:= BOUND_VARIABLE_15052 BOUND_VARIABLE_15052)))
% 0.97/1.22  (step t69.t1 (cl (= B_k B_k)) :rule refl)
% 0.97/1.22  (step t69.t2 (cl (= B_a B_a)) :rule refl)
% 0.97/1.22  (step t69.t3 (cl (= BOUND_VARIABLE_15052 BOUND_VARIABLE_15052)) :rule refl)
% 0.97/1.22  (step t69.t4 (cl (= (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))) :rule all_simplify)
% 0.97/1.23  (step t69 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))) :rule bind)
% 0.97/1.23  (step t70 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))) :rule trans :premises (t68 t69))
% 0.97/1.23  (step t71 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))) :rule trans :premises (t67 t70))
% 0.97/1.23  (step t72 (cl (= (not (forall ((B_k $$unsorted) (B_a $$unsorted)) (not (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))) :rule cong :premises (t71))
% 0.97/1.23  (step t73 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a)) (not (forall ((B_q $$unsorted)) (or (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))) :rule trans :premises (t66 t72))
% 0.97/1.23  (step t74 (cl (= (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))) :rule trans :premises (t65 t73))
% 0.97/1.23  (step t75 (cl (= (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z))))))))) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))))) :rule cong :premises (t8 t74))
% 0.97/1.23  (step t76 (cl (= (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (exists ((B_k $$unsorted) (B_a $$unsorted)) (and (not (= B_a (tptp.c_Groups_Ozero__class_Ozero tptp.t_a))) (exists ((B_q $$unsorted)) (and (=> (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (= (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal B_q (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a B_q))) B_k)) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))))) (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a B_q)) B_z)))))))))) (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))))) :rule cong :premises (t45 t75))
% 0.97/1.23  (step t77 (cl (=> (tptp.class_Rings_Oidom tptp.t_a) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))))) :rule resolution :premises (t64 t76 a4))
% 0.97/1.23  (step t78 (cl (not (tptp.class_Rings_Oidom tptp.t_a)) (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))) :rule implies :premises (t77))
% 0.97/1.23  (step t79 (cl (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))) (not (tptp.class_Rings_Oidom tptp.t_a))) :rule reordering :premises (t78))
% 0.97/1.23  (step t80 (cl (=> (= tptp.v_c____ (tptp.c_Groups_Ozero__class_Ozero tptp.t_a)) (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))))) :rule resolution :premises (t79 a1160))
% 0.97/1.23  (step t81 (cl (= (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z))))))))) :rule hole :args ((forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z))))))) (= B_a B_a) (= B_z B_z) (= B_k B_k) (= BOUND_VARIABLE_14989 BOUND_VARIABLE_15052)))
% 0.97/1.23  (step t82 (cl (not (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_14989 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_14989 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_14989))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_14989)) B_z)))))))) (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))) :rule equiv1 :premises (t81))
% 0.97/1.23  (step t83 (cl (forall ((B_k $$unsorted) (B_a $$unsorted) (BOUND_VARIABLE_15052 $$unsorted)) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.t_a) B_a) (and (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (and (not (= (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a)))) (not (= (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____))) (tptp.c_Nat_OSuc (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_If tptp.tc_Nat_Onat (tptp.c_fequal BOUND_VARIABLE_15052 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.t_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree tptp.t_a BOUND_VARIABLE_15052))) B_k))))) (not (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a tptp.v_c____ tptp.v_cs____)) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.t_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.t_a) B_z) B_k)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.t_a (tptp.c_Polynomial_OpCons tptp.t_a B_a BOUND_VARIABLE_15052)) B_z)))))))) :rule resolution :premises (t82 t43))
% 0.97/1.23  (step t84 (cl) :rule resolution :premises (t2 t63 t80 t83))
% 0.97/1.23  
% 0.97/1.23  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.zIms5SNDm7/cvc5---1.0.5_29063.smt2
% 0.97/1.23  % cvc5---1.0.5 exiting
% 0.97/1.23  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------