%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWW252+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n018.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 18:18:57 EDT 2024

% Result   : Theorem 1.46s 1.63s
% Output   : Proof 1.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.28  % Problem    : SWW252+1 : TPTP v8.2.0. Released v5.2.0.
% 0.14/0.29  % Command    : do_cvc5 %s %d
% 0.30/0.51  % Computer : n018.cluster.edu
% 0.30/0.51  % Model    : x86_64 x86_64
% 0.30/0.51  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.30/0.51  % Memory   : 8042.1875MB
% 0.30/0.51  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.30/0.51  % CPULimit   : 300
% 0.30/0.51  % WCLimit    : 300
% 0.30/0.51  % DateTime   : Sun May 26 05:54:24 EDT 2024
% 0.30/0.51  % CPUTime    : 
% 0.65/0.98  %----Proving TF0_NAR, FOF, or CNF
% 1.46/1.63  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.46/1.63  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.nO8QCaxKt7/cvc5---1.0.5_22881.smt2
% 1.46/1.63  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.nO8QCaxKt7/cvc5---1.0.5_22881.smt2
% 1.46/1.63  (assume a0 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))))
% 1.46/1.63  (assume a1 (not (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.46/1.63  (assume a2 (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_p))))
% 1.46/1.63  (assume a3 (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____))))
% 1.46/1.63  (assume a4 (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____))))
% 1.46/1.63  (assume a5 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP tptp.c_Nat_OSuc V_n)))))
% 1.46/1.63  (assume a6 (forall ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) B_z) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) B_z)) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))
% 1.46/1.63  (assume a7 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.hAPP tptp.c_Nat_OSuc V_n)))))
% 1.46/1.63  (assume a8 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) (tptp.hAPP tptp.c_Nat_OSuc V_n))))))
% 1.46/1.63  (assume a9 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a10 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat V_P_2) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_Nat_Onat V_P_2) tptp.c_Nat_OSuc))))))))
% 1.46/1.63  (assume a11 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a12 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_p) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 1.46/1.63  (assume a13 (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))))
% 1.46/1.63  (assume a14 (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)))))
% 1.46/1.63  (assume a15 (forall ((V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2)) (exists ((B_m $$unsorted)) (= V_n_2 (tptp.hAPP tptp.c_Nat_OSuc B_m))))))
% 1.46/1.63  (assume a16 (forall ((V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a17 (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____))))
% 1.46/1.63  (assume a18 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 1.46/1.63  (assume a19 (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Polynomial_Osmult T_a V_b V_p)) (tptp.c_Polynomial_Osmult T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_p)))))
% 1.46/1.63  (assume a20 (forall ((V_f_2 $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant T_a T_b V_f_2) (forall ((B_x $$unsorted) (B_y $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_f_2 B_y))))))
% 1.46/1.63  (assume a21 (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))))))
% 1.46/1.63  (assume a22 (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))))))
% 1.46/1.63  (assume a23 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (= (tptp.hAPP tptp.c_Nat_OSuc V_x) (tptp.hAPP tptp.c_Nat_OSuc V_y)) (= V_x V_y))))
% 1.46/1.63  (assume a24 (forall ((V_nat_H_2 $$unsorted) (V_nat_2 $$unsorted)) (= (= (tptp.hAPP tptp.c_Nat_OSuc V_nat_2) (tptp.hAPP tptp.c_Nat_OSuc V_nat_H_2)) (= V_nat_2 V_nat_H_2))))
% 1.46/1.63  (assume a25 (forall ((V_n $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_n) V_n))))
% 1.46/1.63  (assume a26 (forall ((V_n $$unsorted)) (not (= V_n (tptp.hAPP tptp.c_Nat_OSuc V_n)))))
% 1.46/1.63  (assume a27 (forall ((V_P_2 $$unsorted) (V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (= V_m_2 V_n_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (=> (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_n_2) V_m_2)))))))
% 1.46/1.63  (assume a28 (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_s) V_t)) (not (= V_s V_t)))))
% 1.46/1.63  (assume a29 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_m)) (not (= V_m V_n)))))
% 1.46/1.63  (assume a30 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_n)))))
% 1.46/1.63  (assume a31 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_y) V_x))))))
% 1.46/1.63  (assume a32 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (= V_m_2 V_n_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2))))))
% 1.46/1.63  (assume a33 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_n)))))
% 1.46/1.63  (assume a34 (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pb_2) (tptp.c_Polynomial_Opoly T_a V_qa_2)) (= V_pb_2 V_qa_2)))))
% 1.46/1.63  (assume a35 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_Ocoeff T_a V_x_2) (tptp.c_Polynomial_Ocoeff T_a V_y_2)) (= V_x_2 V_y_2)))))
% 1.46/1.63  (assume a36 (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= V_pb_2 V_qa_2) (forall ((B_n $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_pb_2) B_n) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_qa_2) B_n)))))))
% 1.46/1.63  (assume a37 (forall ((V_m $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a38 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)))))
% 1.46/1.63  (assume a39 (forall ((V_nat_H_1 $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_nat_H_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a40 (forall ((V_m $$unsorted)) (not (= (tptp.hAPP tptp.c_Nat_OSuc V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a41 (forall ((V_nat_H $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_nat_H)))))
% 1.46/1.63  (assume a42 (forall ((V_m $$unsorted)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)))))
% 1.46/1.63  (assume a43 (forall ((V_n $$unsorted)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)))))
% 1.46/1.63  (assume a44 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a45 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a46 (forall ((V_n_2 $$unsorted)) (= (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2)))))
% 1.46/1.63  (assume a47 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a48 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) (tptp.hAPP tptp.c_Nat_OSuc V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a49 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a50 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= V_m V_n)))))
% 1.46/1.63  (assume a51 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_j) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_i)) V_k))))))
% 1.46/1.63  (assume a52 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (=> (not (= (tptp.hAPP tptp.c_Nat_OSuc V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n))))))
% 1.46/1.63  (assume a53 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n))))))
% 1.46/1.63  (assume a54 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_m))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.hAPP tptp.c_Nat_OSuc V_m))) (= V_m V_n)))))
% 1.46/1.63  (assume a55 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.hAPP tptp.c_Nat_OSuc V_m_2))) (= V_n_2 V_m_2)))))
% 1.46/1.63  (assume a56 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m_2)) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)))))
% 1.46/1.63  (assume a57 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (= V_m_2 V_n_2)))))
% 1.46/1.63  (assume a58 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.hAPP tptp.c_Nat_OSuc V_m_2))))))
% 1.46/1.63  (assume a59 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Oring__char__0 T_a) (tptp.class_Rings_Oidom T_a)) (= (= (tptp.c_Polynomial_Opoly T_a V_pb_2) (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.46/1.63  (assume a60 (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))))))
% 1.46/1.63  (assume a61 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (exists ((B_j $$unsorted)) (and (= V_m_2 (tptp.hAPP tptp.c_Nat_OSuc B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_j) V_n_2))))))))
% 1.46/1.63  (assume a62 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP 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.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.46/1.63  (assume a63 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))
% 1.46/1.63  (assume a64 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)))))))
% 1.46/1.63  (assume a65 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)))))))
% 1.46/1.63  (assume a66 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a67 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a68 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))
% 1.46/1.63  (assume a69 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a70 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)))))))
% 1.46/1.63  (assume a71 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))
% 1.46/1.63  (assume a72 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a73 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2))))))
% 1.46/1.63  (assume a74 (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____)))
% 1.46/1.63  (assume a75 (not (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) tptp.v_c____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.46/1.63  (assume a76 (forall ((V_n $$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))))
% 1.46/1.63  (assume a77 (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.46/1.63  (assume a78 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a79 (forall ((V_n_2 $$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))))))
% 1.46/1.63  (assume a80 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n_2) V_k_2)) (or (= V_m_2 V_n_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a81 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP 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.hAPP tptp.c_Nat_OSuc V_k_2)) V_n_2)) (= V_m_2 V_n_2))))
% 1.46/1.63  (assume a82 (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))))))
% 1.46/1.63  (assume a83 (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))))))
% 1.46/1.63  (assume a84 (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))))))
% 1.46/1.63  (assume a85 (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))))))
% 1.46/1.63  (assume a86 (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.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (and (= V_m_2 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.46/1.63  (assume a87 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2))))))
% 1.46/1.63  (assume a88 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2))))))
% 1.46/1.63  (assume a89 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2))))))
% 1.46/1.63  (assume a90 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_k)))))))
% 1.46/1.63  (assume a91 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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)))))))
% 1.46/1.63  (assume a92 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_k_2)) V_m_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_k_2)) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)))))
% 1.46/1.63  (assume a93 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))))
% 1.46/1.63  (assume a94 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m)))))))
% 1.46/1.63  (assume a95 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))))
% 1.46/1.63  (assume a96 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)))))))
% 1.46/1.63  (assume a97 (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))))
% 1.46/1.63  (assume a98 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b_2)) (= V_a_2 V_b_2)))))
% 1.46/1.63  (assume a99 (forall ((V_b $$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)))))
% 1.46/1.63  (assume a100 (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)))))
% 1.46/1.63  (assume a101 (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)))))
% 1.46/1.63  (assume a102 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a103 (forall ((V_b $$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))))))))
% 1.46/1.63  (assume a104 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a105 (forall ((T_a $$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)))))
% 1.46/1.63  (assume a106 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a107 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a108 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a109 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_a)))))
% 1.46/1.63  (assume a110 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a111 (forall ((V_b $$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)))))))
% 1.46/1.63  (assume a112 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))
% 1.46/1.63  (assume a113 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a114 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_ca_2))) (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_ca_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_ca_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b_2) V_a_2))))))))
% 1.46/1.63  (assume a115 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2))) (or (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_ca_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_ca_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b_2) V_a_2))))))))
% 1.46/1.63  (assume a116 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_ca_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) V_b_2)))))))
% 1.46/1.63  (assume a117 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a118 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a119 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a120 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)))))))
% 1.46/1.63  (assume a121 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)))))))
% 1.46/1.63  (assume a122 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_ca_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b_2) V_a_2)))))))
% 1.46/1.63  (assume a123 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a124 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a125 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a126 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a127 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a128 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a129 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a130 (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) tptp.v_c____) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.46/1.63  (assume a131 (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) tptp.v_c____) B_x)))))
% 1.46/1.63  (assume a132 (forall ((V_P_2 $$unsorted) (V_k_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_k_2) (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2))) (not (tptp.hBOOL (tptp.hAPP V_P_2 V_k_2)))))))
% 1.46/1.63  (assume a133 (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.46/1.63  (assume a134 (forall ((V_pb_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex V_pb_2)) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____))) (=> (not (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_pb_2))) (exists ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_pb_2) B_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))
% 1.46/1.63  (assume a135 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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)))))
% 1.46/1.63  (assume a136 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2))))))
% 1.46/1.63  (assume a137 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a138 (forall ((V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a139 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_m))))
% 1.46/1.63  (assume a140 (forall ((V_k $$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)))))
% 1.46/1.63  (assume a141 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_a)))))
% 1.46/1.63  (assume a142 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_d))))))
% 1.46/1.63  (assume a143 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) V_d)))))
% 1.46/1.63  (assume a144 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_c))))))
% 1.46/1.63  (assume a145 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) V_b)))))
% 1.46/1.63  (assume a146 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_d)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_d))))))
% 1.46/1.63  (assume a147 (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_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a148 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_b_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b_2) V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a149 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.46/1.63  (assume a150 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) V_a))))
% 1.46/1.63  (assume a151 (forall ((V_p $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Osmult T_a V_b V_p))))))
% 1.46/1.63  (assume a152 (forall ((V_n $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) V_n))))))
% 1.46/1.63  (assume a153 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_b_H)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 1.46/1.63  (assume a154 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_z))))))
% 1.46/1.63  (assume a155 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 1.46/1.63  (assume a156 (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_a_2 V_b_2)) (not (= V_ca_2 V_d_2))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_d_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_d_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_ca_2))))))))
% 1.46/1.63  (assume a157 (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a158 (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_a_H)) V_b) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a159 (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a160 (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_m)))))
% 1.46/1.63  (assume a161 (forall ((V_z_2 $$unsorted) (V_x_2 $$unsorted) (V_y_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_w_2) V_y_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_z_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_w_2) V_z_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_y_2))) (or (= V_w_2 V_x_2) (= V_y_2 V_z_2))))))
% 1.46/1.63  (assume a162 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 1.46/1.63  (assume a163 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_e)) V_c)))))
% 1.46/1.63  (assume a164 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a165 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_d)))))))))
% 1.46/1.63  (assume a166 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2)))) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a167 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y))) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a168 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c))))))))
% 1.46/1.63  (assume a169 (forall ((V_b $$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.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a170 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b))) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))))
% 1.46/1.63  (assume a171 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y))) (=> (not (= V_x V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)))))))
% 1.46/1.63  (assume a172 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)))))))
% 1.46/1.63  (assume a173 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_z) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_z) V_x)))))))
% 1.46/1.63  (assume a174 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_z)))))))
% 1.46/1.63  (assume a175 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_a)))))))
% 1.46/1.63  (assume a176 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_c)))))))
% 1.46/1.63  (assume a177 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_a)))))))
% 1.46/1.63  (assume a178 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_c)))))))
% 1.46/1.63  (assume a179 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a180 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)))))))
% 1.46/1.63  (assume a181 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (= V_y V_x))))))
% 1.46/1.63  (assume a182 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (= V_x V_y))))))
% 1.46/1.63  (assume a183 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)))))))
% 1.46/1.63  (assume a184 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)))))))
% 1.46/1.63  (assume a185 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (not (= V_x V_y))))))
% 1.46/1.63  (assume a186 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)))))))
% 1.46/1.63  (assume a187 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y_2) V_x_2))) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (= V_x_2 V_y_2))))))
% 1.46/1.63  (assume a188 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x))))))
% 1.46/1.63  (assume a189 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y_2) V_x_2)) (= V_x_2 V_y_2))))))
% 1.46/1.63  (assume a190 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y_2) V_x_2)))))))
% 1.46/1.63  (assume a191 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_x))))))
% 1.46/1.63  (assume a192 (forall ((V_b $$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)))))
% 1.46/1.63  (assume a193 (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))))))
% 1.46/1.63  (assume a194 (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)))))
% 1.46/1.63  (assume a195 (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))))))
% 1.46/1.63  (assume a196 (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)))))
% 1.46/1.63  (assume a197 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)))))))
% 1.46/1.63  (assume a198 (forall ((V_ry $$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))))))
% 1.46/1.63  (assume a199 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_ry))))))
% 1.46/1.63  (assume a200 (forall ((V_n_2 $$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)))))
% 1.46/1.63  (assume a201 (forall ((V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x1))) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2)))))))
% 1.46/1.63  (assume a202 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize T_a V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.46/1.63  (assume a203 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_k_2)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2)))))))
% 1.46/1.63  (assume a204 (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)))))
% 1.46/1.63  (assume a205 (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)))))
% 1.46/1.63  (assume a206 (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)))))
% 1.46/1.63  (assume a207 (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)))))
% 1.46/1.63  (assume a208 (exists ((B_q $$unsorted)) (and (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex B_q) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____)) (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex B_q) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) tptp.v_c____) B_x)))))))
% 1.46/1.63  (assume a209 (=> (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) tptp.v_c____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (exists ((B_z $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) B_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))
% 1.46/1.63  (assume a210 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a211 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))))
% 1.46/1.63  (assume a212 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a213 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a214 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2))))))
% 1.46/1.63  (assume a215 (not (forall ((B_q $$unsorted)) (=> (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex B_q) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex tptp.v_pa____)) (not (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex B_q) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) tptp.v_c____) B_x)))))))))
% 1.46/1.63  (assume a216 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b))))))
% 1.46/1.63  (assume a217 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n) V_n)))
% 1.46/1.63  (assume a218 (forall ((V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 1.46/1.63  (assume a219 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a220 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a221 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a222 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a223 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n)))))
% 1.46/1.63  (assume a224 (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_j)) V_i)))))
% 1.46/1.63  (assume a225 (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_i)) V_i)))))
% 1.46/1.63  (assume a226 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_m_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)))))
% 1.46/1.63  (assume a227 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_m))))))
% 1.46/1.63  (assume a228 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_j))))))
% 1.46/1.63  (assume a229 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_k))))))
% 1.46/1.63  (assume a230 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_k) V_l)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_l)))))))
% 1.46/1.63  (assume a231 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_k) V_l)) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_l) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))))))
% 1.46/1.63  (assume a232 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_j)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) V_k)))))
% 1.46/1.63  (assume a233 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_j)) V_u)) V_k))))
% 1.46/1.63  (assume a234 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.46/1.63  (assume a235 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (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)))))
% 1.46/1.63  (assume a236 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.63  (assume a237 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.63  (assume a238 (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a239 (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_r) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a240 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2)) (or (and (= V_m_2 (tptp.hAPP 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.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.46/1.63  (assume a241 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (and (= V_m_2 (tptp.hAPP 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.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.46/1.63  (assume a242 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_n_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2))))))
% 1.46/1.63  (assume a243 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_m))))))
% 1.46/1.63  (assume a244 (forall ((V_m $$unsorted) (V_i $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_i))))))
% 1.46/1.63  (assume a245 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) B_k)))))))
% 1.46/1.63  (assume a246 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a247 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a248 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a249 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 1.46/1.63  (assume a250 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_a)) (= V_b V_c)))))
% 1.46/1.63  (assume a251 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (= V_b V_c)))))
% 1.46/1.63  (assume a252 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (= V_b V_c)))))
% 1.46/1.63  (assume a253 (forall ((V_ca_2 $$unsorted) (V_a_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_ca_2) V_a_2)) (= V_b_2 V_ca_2)))))
% 1.46/1.63  (assume a254 (forall ((V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_ca_2)) (= V_b_2 V_ca_2)))))
% 1.46/1.63  (assume a255 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_c))))))
% 1.46/1.63  (assume a256 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) V_a))))
% 1.46/1.63  (assume a257 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a) V_a))))
% 1.46/1.63  (assume a258 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a259 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.46/1.63  (assume a260 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.46/1.63  (assume a261 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a262 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b_2) V_ca_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) V_b_2))))))
% 1.46/1.63  (assume a263 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_ca_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_ca_2) V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) V_b_2))))))
% 1.46/1.63  (assume a264 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_c)))))))
% 1.46/1.63  (assume a265 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_b)))))))
% 1.46/1.63  (assume a266 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_d))))))))
% 1.46/1.63  (assume a267 (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_c))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b))))))
% 1.46/1.63  (assume a268 (forall ((B_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) tptp.v_c____))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) B_w))))))
% 1.46/1.63  (assume a269 (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_pb_2) V_qa_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.tc_Nat_Onat T_a T_a) (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus T_a)) (tptp.c_Polynomial_Ocoeff T_a V_pb_2))) (tptp.c_Polynomial_Ocoeff T_a V_qa_2)))))))
% 1.46/1.63  (assume a270 (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.hAPP (tptp.c_COMBB T_a T_a tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2)) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)))))))
% 1.46/1.63  (assume a271 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.46/1.63  (assume a272 (forall ((V_a $$unsorted) (V_p $$unsorted)) (exists ((B_q $$unsorted)) (and (= (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex B_q) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Opsize tptp.tc_Complex_Ocomplex V_p)) (forall ((B_x $$unsorted)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex B_q) B_x) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) V_a) B_x))))))))
% 1.46/1.63  (assume a273 (forall ((B_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) B_w))))))
% 1.46/1.63  (assume a274 (forall ((V_m_2 $$unsorted) (V_Q_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (=> (tptp.hBOOL (tptp.hAPP V_Q_2 V_m_2)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (forall ((B_k $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP tptp.c_Nat_OSuc B_k))) (tptp.hBOOL (tptp.hAPP V_Q_2 B_k)))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat V_P_2) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat V_Q_2)))))))))
% 1.46/1.63  (assume a275 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_x)))))
% 1.46/1.63  (assume a276 (forall ((V_z $$unsorted) (V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) V_w) V_z))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z))))))
% 1.46/1.63  (assume a277 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)))))))
% 1.46/1.63  (assume a278 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n_2) V_k_2)) (= V_m_2 V_n_2))))
% 1.46/1.63  (assume a279 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_n_2)) (= V_m_2 V_n_2))))
% 1.46/1.63  (assume a280 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.46/1.63  (assume a281 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_x) V_z)))))
% 1.46/1.63  (assume a282 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_m))))
% 1.46/1.63  (assume a283 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x))))))
% 1.46/1.63  (assume a284 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a285 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))))))
% 1.46/1.63  (assume a286 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2)))))))
% 1.46/1.63  (assume a287 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z) V_x)))))))
% 1.46/1.63  (assume a288 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (= V_x V_y))))))
% 1.46/1.63  (assume a289 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_z)))))))
% 1.46/1.63  (assume a290 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (= V_x V_y))))))
% 1.46/1.63  (assume a291 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_a)))))))
% 1.46/1.63  (assume a292 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (= V_b V_c) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_c)))))))
% 1.46/1.63  (assume a293 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_a)))))))
% 1.46/1.63  (assume a294 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_c)))))))
% 1.46/1.63  (assume a295 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (= V_x_2 V_y_2))))))
% 1.46/1.63  (assume a296 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2)))))))
% 1.46/1.63  (assume a297 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))))))
% 1.46/1.63  (assume a298 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2)))))))
% 1.46/1.63  (assume a299 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))))))
% 1.46/1.63  (assume a300 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_g_2 B_x))))))))
% 1.46/1.63  (assume a301 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)))))))
% 1.46/1.63  (assume a302 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))))
% 1.46/1.63  (assume a303 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (= (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a304 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 1.46/1.63  (assume a305 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x_2))) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a306 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))))
% 1.46/1.63  (assume a307 (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)) V_s)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm 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 tptp.tc_RealDef_Oreal) V_r) V_s))))))))
% 1.46/1.63  (assume a308 (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)) V_s)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_r) V_s))))))))
% 1.46/1.63  (assume a309 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_z) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_z) V_x)))))))
% 1.46/1.63  (assume a310 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_z)))))))
% 1.46/1.63  (assume a311 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_z) V_x)))))))
% 1.46/1.63  (assume a312 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_z)))))))
% 1.46/1.63  (assume a313 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (not (= V_a V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)))))))
% 1.46/1.63  (assume a314 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (not (= V_a V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a315 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (= V_x V_y))))))
% 1.46/1.63  (assume a316 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (= V_x_2 V_y_2))))))
% 1.46/1.63  (assume a317 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))))))
% 1.46/1.63  (assume a318 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y)))))))
% 1.46/1.63  (assume a319 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_a)))))))
% 1.46/1.63  (assume a320 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a321 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (= V_x_2 V_y_2))))))
% 1.46/1.63  (assume a322 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y))))))
% 1.46/1.63  (assume a323 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_y))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))))))
% 1.46/1.63  (assume a324 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2)) (= V_x_2 V_y_2))))))
% 1.46/1.63  (assume a325 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2))))))))
% 1.46/1.63  (assume a326 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (not (= V_x_2 V_y_2)))))))
% 1.46/1.63  (assume a327 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_x))))))
% 1.46/1.63  (assume a328 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y_2) V_x_2))))))
% 1.46/1.63  (assume a329 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2))))))
% 1.46/1.63  (assume a330 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (tptp.class_Rings_Odivision__ring__inverse__zero T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a))))))
% 1.46/1.63  (assume a331 (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.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_b))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b))))))
% 1.46/1.63  (assume a332 (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.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_c))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b))))))
% 1.46/1.63  (assume a333 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_d))))))))
% 1.46/1.63  (assume a334 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) V_b)))))))
% 1.46/1.63  (assume a335 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_c)))))))
% 1.46/1.63  (assume a336 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_ca_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_ca_2) V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2))))))
% 1.46/1.63  (assume a337 (forall ((V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b_2) V_ca_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2))))))
% 1.46/1.63  (assume a338 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Owellorder T_a) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Orderings_Oord__class_OLeast T_a V_P_2)) V_k_2))))))
% 1.46/1.63  (assume a339 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_OAbs__poly T_a (tptp.c_Polynomial_Ocoeff T_a V_x_2)) V_x_2))))
% 1.46/1.63  (assume a340 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a341 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)))))))
% 1.46/1.63  (assume a342 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))))
% 1.46/1.63  (assume a343 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2))) (or (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.46/1.63  (assume a344 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_b_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (or (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b_2))))))))
% 1.46/1.63  (assume a345 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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))))))))
% 1.46/1.63  (assume a346 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a347 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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))))))))
% 1.46/1.63  (assume a348 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a349 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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))))))))
% 1.46/1.63  (assume a350 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a351 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a352 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__comm__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a353 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a354 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a355 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d))))))))))
% 1.46/1.63  (assume a356 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (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_d))))))))))
% 1.46/1.63  (assume a357 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (or (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a358 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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)))))))
% 1.46/1.63  (assume a359 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a360 (forall ((V_a $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c))))))))
% 1.46/1.63  (assume a361 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c))))))))
% 1.46/1.63  (assume a362 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y_2)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x_2) V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.46/1.63  (assume a363 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))))
% 1.46/1.63  (assume a364 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a365 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_2) V_a_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2))))))
% 1.46/1.63  (assume a366 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_d))))))))
% 1.46/1.63  (assume a367 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_b) V_d))))))))
% 1.46/1.63  (assume a368 (forall ((V_q $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_q)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))) V_n)))))))
% 1.46/1.63  (assume a369 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) (tptp.c_Polynomial_Odegree T_a V_q))))))
% 1.46/1.63  (assume a370 (forall ((V_p $$unsorted) (V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_q)) (tptp.c_Polynomial_Odegree T_a V_p))) (= (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) (tptp.c_Polynomial_Odegree T_a V_p))))))
% 1.46/1.63  (assume a371 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a372 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2))))))
% 1.46/1.63  (assume a373 (forall ((V_q $$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.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a374 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))))
% 1.46/1.63  (assume a375 (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.63  (assume a376 (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)))))))
% 1.46/1.63  (assume a377 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_pb_2) (tptp.c_Polynomial_Odegree T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.46/1.63  (assume a378 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))))
% 1.46/1.63  (assume a379 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))))
% 1.46/1.63  (assume a380 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a381 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a382 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a383 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a384 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d))))))))))
% 1.46/1.63  (assume a385 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))))
% 1.46/1.63  (assume a386 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d))))))))))
% 1.46/1.63  (assume a387 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))))
% 1.46/1.63  (assume a388 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_ca_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b_2) V_a_2)))))))
% 1.46/1.63  (assume a389 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_ca_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ca_2) V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2)))))))
% 1.46/1.63  (assume a390 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a391 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.46/1.63  (assume a392 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c))))))))
% 1.46/1.63  (assume a393 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c))))))))
% 1.46/1.63  (assume a394 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))))
% 1.46/1.63  (assume a395 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b))))))))
% 1.46/1.63  (assume a396 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y)))))))
% 1.46/1.63  (assume a397 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2))) (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a398 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Polynomial_Odegree T_a V_q))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) (tptp.c_Polynomial_Odegree T_a V_p))) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_q) (tptp.c_Polynomial_Odegree T_a V_q)))))))
% 1.46/1.63  (assume a399 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)))))))
% 1.46/1.63  (assume a400 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_a)))))))
% 1.46/1.63  (assume a401 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))
% 1.46/1.63  (assume a402 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))
% 1.46/1.63  (assume a403 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_OAbs__poly T_a (tptp.c_COMBK T_a tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a404 (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.hAPP tptp.c_Nat_OSuc (tptp.c_Polynomial_Odegree T_a V_p))))))))
% 1.46/1.63  (assume a405 (forall ((V_x $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_r) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x))) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_r))))))))
% 1.46/1.63  (assume a406 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)))) (= V_x (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a407 (forall ((V_r_2 $$unsorted) (V_qa_2 $$unsorted) (V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opdivmod__rel T_a V_x_2 V_y_2 V_qa_2 V_r_2) (and (= V_x_2 (tptp.hAPP (tptp.hAPP (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_qa_2) V_y_2)) V_r_2)) (=> (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_qa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (=> (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (= V_r_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_r_2)) (tptp.c_Polynomial_Odegree T_a V_y_2))))))))))
% 1.46/1.63  (assume a408 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z))))))
% 1.46/1.63  (assume a409 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z))))))
% 1.46/1.63  (assume a410 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Polynomial_Opos__poly T_a V_pb_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_pb_2) (tptp.c_Polynomial_Odegree T_a V_pb_2))))))))
% 1.46/1.63  (assume a411 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n))))
% 1.46/1.63  (assume a412 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_l_2)) (exists ((B_n $$unsorted)) (= V_l_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) B_n))))))
% 1.46/1.63  (assume a413 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z))))))
% 1.46/1.63  (assume a414 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z))))))
% 1.46/1.63  (assume a415 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) V_y)))))
% 1.46/1.63  (assume a416 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a T_b)) V_f_2) V_g_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_g_2) V_f_2))))))))
% 1.46/1.63  (assume a417 (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (= V_q1 V_q2))))))
% 1.46/1.63  (assume a418 (forall ((V_r2 $$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))))))
% 1.46/1.63  (assume a419 (forall ((V_r2 $$unsorted) (V_q2 $$unsorted) (V_r1 $$unsorted) (V_q1 $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q1 V_r1) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q2 V_r2) (and (= V_q1 V_q2) (= V_r1 V_r2)))))))
% 1.46/1.63  (assume a420 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n))))
% 1.46/1.63  (assume a421 (forall ((V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a422 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n)) V_n)))))
% 1.46/1.63  (assume a423 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)) V_m_2)))))
% 1.46/1.63  (assume a424 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (= V_m_2 (tptp.hAPP tptp.c_Nat_OSuc V_n_2))))))
% 1.46/1.63  (assume a425 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)) (tptp.hAPP tptp.c_Nat_OSuc V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) V_m_2)))))
% 1.46/1.63  (assume a426 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n))))))
% 1.46/1.63  (assume a427 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n))) (= V_m (tptp.hAPP tptp.c_Nat_OSuc V_n))))))
% 1.46/1.63  (assume a428 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.46/1.63  (assume a429 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (not (= V_m_2 V_n_2))))))
% 1.46/1.63  (assume a430 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)) (= V_m_2 V_n_2)))))
% 1.46/1.63  (assume a431 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.46/1.63  (assume a432 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (=> (not (= V_m V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))))))
% 1.46/1.63  (assume a433 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (= V_m V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.46/1.63  (assume a434 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a435 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_m)))))
% 1.46/1.63  (assume a436 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (exists ((B_k $$unsorted)) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m_2) B_k))))))
% 1.46/1.63  (assume a437 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_m_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))))
% 1.46/1.63  (assume a438 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_m))))))
% 1.46/1.63  (assume a439 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_j))))))
% 1.46/1.63  (assume a440 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_k))))))
% 1.46/1.63  (assume a441 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_l)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_l)))))))
% 1.46/1.63  (assume a442 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_k)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n)))))
% 1.46/1.63  (assume a443 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_k)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.46/1.63  (assume a444 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_k)) V_n)) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n))))))))
% 1.46/1.63  (assume a445 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_l)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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_l)))))))
% 1.46/1.63  (assume a446 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j))))))
% 1.46/1.63  (assume a447 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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))))))
% 1.46/1.63  (assume a448 (forall ((V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m))))))
% 1.46/1.63  (assume a449 (forall ((V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m)))))
% 1.46/1.63  (assume a450 (forall ((V_r_2 $$unsorted) (V_qa_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$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_2 V_qa_2 V_r_2) (and (= V_qa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_r_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))))
% 1.46/1.63  (assume a451 (forall ((V_r_2 $$unsorted) (V_qa_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opdivmod__rel T_a V_x_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_qa_2 V_r_2) (and (= V_qa_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_r_2 V_x_2))))))
% 1.46/1.63  (assume a452 (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))))))
% 1.46/1.63  (assume a453 (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))))
% 1.46/1.63  (assume a454 (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))))))
% 1.46/1.63  (assume a455 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Polynomial_Opos__poly T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))
% 1.46/1.63  (assume a456 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)) V_m_2)))))
% 1.46/1.63  (assume a457 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) (tptp.hAPP tptp.c_Nat_OSuc V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))))
% 1.46/1.63  (assume a458 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m_2)) V_n_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)))))
% 1.46/1.63  (assume a459 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc V_n))))))
% 1.46/1.63  (assume a460 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)))))
% 1.46/1.63  (assume a461 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.hAPP tptp.c_Nat_OSuc V_m_2))) (= V_n_2 V_m_2)))))
% 1.46/1.63  (assume a462 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a463 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP 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.hAPP tptp.c_Nat_OSuc V_k_2)) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))))
% 1.46/1.63  (assume a464 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Polynomial_Opos__poly T_a V_p) (=> (tptp.c_Polynomial_Opos__poly T_a V_q) (tptp.c_Polynomial_Opos__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)))))))
% 1.46/1.63  (assume a465 (forall ((V_q $$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)))))))
% 1.46/1.63  (assume a466 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p))) (tptp.c_Polynomial_Odegree T_a V_p))))))
% 1.46/1.63  (assume a467 (forall ((V_q $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_q)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))) V_n)))))))
% 1.46/1.63  (assume a468 (forall ((V_n_2 $$unsorted)) (= (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n_2)))))
% 1.46/1.63  (assume a469 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP 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_2) V_n_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n_2))))))
% 1.46/1.63  (assume a470 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2))))))
% 1.46/1.63  (assume a471 (forall ((V_n_2 $$unsorted) (V_k_2 $$unsorted) (V_m_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2))))))
% 1.46/1.63  (assume a472 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_m_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2))))))
% 1.46/1.63  (assume a473 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_z $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y V_q V_r) (=> (tptp.c_Polynomial_Opdivmod__rel T_a V_q V_z V_q_H V_r_H) (tptp.c_Polynomial_Opdivmod__rel T_a V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_z) V_q_H (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_r_H)) V_r)))))))
% 1.46/1.63  (assume a474 (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (not (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.c_Polynomial_Odegree T_a V_p)))))))
% 1.46/1.63  (assume a475 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Polynomial_Odegree T_a V_q)))))))
% 1.46/1.63  (assume a476 (forall ((V_a $$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)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Oorder T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))))
% 1.46/1.63  (assume a477 (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))))))
% 1.46/1.63  (assume a478 (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p)) V_n)) (=> (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_p (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) V_n))))))))
% 1.46/1.63  (assume a479 (forall ((V_u $$unsorted) (V_y $$unsorted) (V_x1 $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x1) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_u))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_u) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x1)))))))))
% 1.46/1.63  (assume a480 (forall ((V_u $$unsorted) (V_y $$unsorted) (V_x1 $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x1) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_u))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x1)) V_u))))))))
% 1.46/1.63  (assume a481 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_z_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_z_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2))))))
% 1.46/1.63  (assume a482 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2))))))
% 1.46/1.63  (assume a483 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.46/1.63  (assume a484 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= V_m V_n)))))
% 1.46/1.63  (assume a485 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_k))))))
% 1.46/1.63  (assume a486 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.46/1.63  (assume a487 (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)))))
% 1.46/1.63  (assume a488 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_n))))
% 1.46/1.63  (assume a489 (forall ((V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w) V_w))))
% 1.46/1.63  (assume a490 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z) V_w)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w) V_z)))))
% 1.46/1.63  (assume a491 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_j) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_i) V_k))))))
% 1.46/1.63  (assume a492 (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_z) V_w)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w) V_z)) (= V_z V_w)))))
% 1.46/1.63  (assume a493 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z2) V_z3)))))
% 1.46/1.63  (assume a494 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_w) V_z))))
% 1.46/1.63  (assume a495 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x_2) V_y_2)) (= V_x_2 V_y_2)))))
% 1.46/1.63  (assume a496 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x_2) V_y_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)) (not (= V_x_2 V_y_2))))))
% 1.46/1.63  (assume a497 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted)) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_ca_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_ca_2) V_b_2)) (= V_a_2 V_b_2)))))
% 1.46/1.63  (assume a498 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (V_ca_2 $$unsorted)) (=> (not (= V_ca_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_a_2) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_b_2) V_ca_2)) (= V_a_2 V_b_2)))))
% 1.46/1.63  (assume a499 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_z) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_z) V_y))))))
% 1.46/1.63  (assume a500 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_z1) V_z2)) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z2) V_w)))))
% 1.46/1.63  (assume a501 (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 1.46/1.63  (assume a502 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_y)))))))
% 1.46/1.63  (assume a503 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)))))))
% 1.46/1.63  (assume a504 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_z_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_z_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_z_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x_2) V_y_2))))))
% 1.46/1.63  (assume a505 (forall ((V_x_2 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_x_2)))) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 1.46/1.63  (assume a506 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))))
% 1.46/1.63  (assume a507 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))))
% 1.46/1.63  (assume a508 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K)))))))))
% 1.46/1.63  (assume a509 (forall ((V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Opcompose T_a V_p V_q))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) (tptp.c_Polynomial_Odegree T_a V_q)))))))
% 1.46/1.63  (assume a510 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Odecseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n)) (tptp.hAPP V_X_2 B_m)))))))))
% 1.46/1.63  (assume a511 (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)))))
% 1.46/1.63  (assume a512 (forall ((V_p $$unsorted) (V_r $$unsorted)) (exists ((B_m $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_m)) (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex B_z)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex V_p) B_z))) B_m))))))))
% 1.46/1.63  (assume a513 (forall ((T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 1.46/1.63  (assume a514 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (= (tptp.c_Polynomial_Opoly__gcd T_a V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))))
% 1.46/1.63  (assume a515 (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))))))
% 1.46/1.63  (assume a516 (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))))))
% 1.46/1.63  (assume a517 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Polynomial_Opoly__gcd T_a V_a V_b) (tptp.c_Polynomial_Opoly__gcd T_a V_b V_a)))))
% 1.46/1.63  (assume a518 (forall ((V_q $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.c_Polynomial_Opcompose T_a (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) V_q) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))
% 1.46/1.63  (assume a519 (forall ((V_x $$unsorted) (V_q $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Opcompose T_a V_p V_q)) V_x) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_q) V_x))))))
% 1.46/1.63  (assume a520 (forall ((V_p $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (forall ((B_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) B_i)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) B_i) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a V_p)) V_n))))))
% 1.46/1.63  (assume a521 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))))
% 1.46/1.63  (assume a522 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))))
% 1.46/1.63  (assume a523 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K)))))))))
% 1.46/1.63  (assume a524 (forall ((V_x $$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))))))))
% 1.46/1.63  (assume a525 (forall ((V_ca_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_a) (= (= (tptp.c_Polynomial_Osynthetic__div T_a V_pb_2 V_ca_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a526 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) B_K)))))))))
% 1.46/1.63  (assume a527 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Oincseq T_a V_X_2) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m)) (tptp.hAPP V_X_2 B_n)))))))))
% 1.46/1.63  (assume a528 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y) (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 1.46/1.63  (assume a529 (forall ((V_r $$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)))))
% 1.46/1.63  (assume a530 (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))))))
% 1.46/1.63  (assume a531 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_x)) (tptp.c_Polynomial_Odegree T_a V_y))) (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_x)))))
% 1.46/1.63  (assume a532 (forall ((V_x $$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)))))))
% 1.46/1.63  (assume a533 (forall ((V_k_2 $$unsorted) (V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_SEQ_OBseq T_a V_X_2) (tptp.c_SEQ_OBseq T_a (tptp.hAPP (tptp.c_COMBB tptp.tc_Nat_Onat T_a tptp.tc_Nat_Onat V_X_2) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Nat_Onat tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2)))))))
% 1.46/1.63  (assume a534 (forall ((V_k_2 $$unsorted) (V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_SEQ_OBseq T_a (tptp.hAPP (tptp.c_COMBB tptp.tc_Nat_Onat T_a tptp.tc_Nat_Onat V_X_2) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Nat_Onat tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2))) (tptp.c_SEQ_OBseq T_a V_X_2)))))
% 1.46/1.63  (assume a535 (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))))))
% 1.46/1.63  (assume a536 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (=> (not (= V_y (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (= (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y))) (tptp.c_Polynomial_Odegree T_a V_y))))))))
% 1.46/1.63  (assume a537 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.46/1.63  (assume a538 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.46/1.63  (assume a539 (forall ((V_a $$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)))))
% 1.46/1.63  (assume a540 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a541 (forall ((V_n $$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)))))
% 1.46/1.63  (assume a542 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.46/1.63  (assume a543 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n))))
% 1.46/1.63  (assume a544 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.63  (assume a545 (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 $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_d_2) B_q))))))
% 1.46/1.63  (assume a546 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n)))))
% 1.46/1.63  (assume a547 (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.46/1.63  (assume a548 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= (tptp.hAPP 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.hAPP tptp.c_Nat_OSuc V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= (tptp.hAPP 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.hAPP tptp.c_Nat_OSuc V_m) V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)))))))
% 1.46/1.63  (assume a549 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.63  (assume a550 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 1.46/1.63  (assume a551 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n)) V_n)))))
% 1.46/1.63  (assume a552 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) V_m)) V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_m) V_n))))
% 1.46/1.63  (assume a553 (forall ((V_k_2 $$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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_j) V_k_2)) (=> (= V_n_2 (tptp.hAPP (tptp.hAPP (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))))))))))
% 1.46/1.63  (assume a554 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_r) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (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)))))))
% 1.46/1.63  (assume a555 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.46/1.63  (assume a556 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a557 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.46/1.63  (assume a558 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a559 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b_H) V_c)))))))
% 1.46/1.63  (assume a560 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c)))))
% 1.46/1.63  (assume a561 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_c)))))
% 1.46/1.63  (assume a562 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))))))
% 1.46/1.63  (assume a563 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.46/1.63  (assume a564 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c)))))
% 1.46/1.63  (assume a565 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.46/1.63  (assume a566 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a_H) V_b_H) V_c)))))))
% 1.46/1.63  (assume a567 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_c)))))
% 1.46/1.63  (assume a568 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_c)))))
% 1.46/1.63  (assume a569 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.46/1.63  (assume a570 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c)))))
% 1.46/1.63  (assume a571 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.46/1.63  (assume a572 (forall ((V_a $$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_Oplus__class_Oplus T_a) V_b) V_a) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.46/1.63  (assume a573 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_b) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)))))
% 1.46/1.63  (assume a574 (forall ((V_X_2 $$unsorted) (V_K_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_K_2)) (=> (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) V_K_2))) (tptp.c_SEQ_OBseq T_a V_X_2))))))
% 1.46/1.63  (assume a575 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) B_K)))))))))
% 1.46/1.63  (assume a576 (forall ((V_y $$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)))))))
% 1.46/1.63  (assume a577 (forall ((V_K_2 $$unsorted) (V_X_2 $$unsorted) (V_N_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (forall ((B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_N_2) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) V_K_2)))) (tptp.c_SEQ_OBseq T_a V_X_2)))))
% 1.46/1.63  (assume a578 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a579 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.46/1.63  (assume a580 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.63  (assume a581 (forall ((T_a $$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))))))
% 1.46/1.63  (assume a582 (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))))
% 1.46/1.63  (assume a583 (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))))
% 1.46/1.63  (assume a584 (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))))
% 1.46/1.63  (assume a585 (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))))
% 1.46/1.63  (assume a586 (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))))
% 1.46/1.63  (assume a587 (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))))
% 1.46/1.63  (assume a588 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.46/1.63  (assume a589 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield__inverse__zero T_a) (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a)) (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.46/1.63  (assume a590 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oone T_a) (= (= (tptp.c_Groups_Oone__class_Oone T_a) V_x_2) (= V_x_2 (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.46/1.63  (assume a591 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) V_x) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.46/1.63  (assume a592 (forall ((V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Polynomial_Osmult T_a (tptp.c_Groups_Oone__class_Oone T_a) V_p) V_p))))
% 1.46/1.63  (assume a593 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (and (= V_m_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_n_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a594 (forall ((V_n $$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)))
% 1.46/1.63  (assume a595 (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))))))
% 1.46/1.63  (assume a596 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) V_n)))
% 1.46/1.63  (assume a597 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.46/1.63  (assume a598 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_z) V_z)))
% 1.46/1.63  (assume a599 (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))))))
% 1.46/1.63  (assume a600 (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))))))
% 1.46/1.63  (assume a601 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a602 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.46/1.63  (assume a603 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.46/1.63  (assume a604 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a605 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_m)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) V_n))))))))
% 1.46/1.63  (assume a606 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.46/1.63  (assume a607 (forall ((V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.46/1.63  (assume a608 (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.46/1.63  (assume a609 (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m)) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.46/1.63  (assume a610 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a611 (forall ((V_b $$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)))))
% 1.46/1.63  (assume a612 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.46/1.63  (assume a613 (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a614 (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))))
% 1.46/1.63  (assume a615 (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))))))
% 1.46/1.63  (assume a616 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Groups_Oone__class_Oone (tptp.tc_Polynomial_Opoly T_a))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a617 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) V_x))))))))
% 1.46/1.63  (assume a618 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x)) V_x))))))))
% 1.46/1.63  (assume a619 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.46/1.63  (assume a620 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2)) (tptp.c_Groups_Oone__class_Oone T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_x_2)))))))
% 1.46/1.63  (assume a621 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a622 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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_x_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x_2) (tptp.c_Groups_Oone__class_Oone T_a))))))))
% 1.46/1.63  (assume a623 (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))))))
% 1.46/1.63  (assume a624 (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))))))
% 1.46/1.63  (assume a625 (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))))))
% 1.46/1.63  (assume a626 (forall ((V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hAPP 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)))))
% 1.46/1.63  (assume a627 (forall ((V_x $$unsorted)) (=> (not (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal V_x)) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.46/1.63  (assume a628 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1 T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_u)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_v)) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_u) V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y))) V_a))))))))))
% 1.46/1.63  (assume a629 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))))
% 1.46/1.63  (assume a630 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2)) (tptp.c_Groups_Oone__class_Oone T_a))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_x_2)))))))
% 1.46/1.63  (assume a631 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_x_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) (tptp.c_Groups_Oone__class_Oone T_a))))))))
% 1.46/1.63  (assume a632 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_x) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_y) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_u)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_v)) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_u) V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y))) V_a))))))))))
% 1.46/1.63  (assume a633 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Olinordered__field__inverse__zero T_a) (=> (forall ((B_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) B_z)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) B_z) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_z) V_x)) V_y))))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y))))))
% 1.46/1.63  (assume a634 (forall ((V_p $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) (tptp.c_Polynomial_Odegree T_a V_p))) (exists ((B_i $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) B_i)) (not (= (tptp.hAPP (tptp.c_Polynomial_Ocoeff T_a V_p) B_i) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.46/1.63  (assume a635 (forall ((V_y $$unsorted) (V_n $$unsorted) (V_x $$unsorted)) (=> (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_x V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_y V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_y) V_x)) (exists ((B_q $$unsorted)) (= V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) B_q))))))))
% 1.46/1.63  (assume a636 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2)) (exists ((B_k $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_k) V_n_2)) (forall ((B_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i) B_k)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) B_k) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 1.46/1.63  (assume a637 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatceiling (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a638 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a639 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 1.46/1.63  (assume a640 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 1.46/1.63  (assume a641 (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatfloor V_x)))))
% 1.46/1.63  (assume a642 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_RComplete_Onatfloor V_y))))))
% 1.46/1.63  (assume a643 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.46/1.63  (assume a644 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)) (tptp.c_RComplete_Onatceiling V_y))))))
% 1.46/1.63  (assume a645 (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatceiling V_x)))))
% 1.46/1.63  (assume a646 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.46/1.63  (assume a647 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a648 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a649 (forall ((V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatfloor V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x_2)))))
% 1.46/1.63  (assume a650 (forall ((V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.46/1.63  (assume a651 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_a)) (tptp.c_RComplete_Onatfloor V_b))) (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_a) V_b))))))))
% 1.46/1.63  (assume a652 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 1.46/1.63  (assume a653 (forall ((V_i_2 $$unsorted) (V_P_2 $$unsorted) (V_pb_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) B_i) V_pb_2)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_i)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_i) V_pb_2)))))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_i_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i_2) V_pb_2)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.46/1.63  (assume a654 (not (forall ((B_c $$unsorted)) (not (forall ((B_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) B_c))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_pa____) B_w)))))))))
% 1.46/1.63  (assume a655 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 1.46/1.63  (assume a656 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 1.46/1.63  (assume a657 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_n)))
% 1.46/1.63  (assume a658 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (= V_n_2 V_m_2))))
% 1.46/1.63  (assume a659 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 1.46/1.63  (assume a660 (forall ((V_n_2 $$unsorted)) (= (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a661 (forall ((V_n $$unsorted)) (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.46/1.63  (assume a662 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2)))))
% 1.46/1.63  (assume a663 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) V_m_2)))))
% 1.46/1.63  (assume a664 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (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_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 1.46/1.63  (assume a665 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)))))
% 1.46/1.63  (assume a666 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.46/1.63  (assume a667 (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x))))))
% 1.46/1.63  (assume a668 (forall ((V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a669 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n))))))
% 1.46/1.63  (assume a670 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.46/1.63  (assume a671 (forall ((V_n $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.46/1.63  (assume a672 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x))) V_x)))))
% 1.46/1.63  (assume a673 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_x)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) (tptp.c_RComplete_Onatfloor V_a))))))
% 1.46/1.63  (assume a674 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)) V_a)))))
% 1.46/1.63  (assume a675 (forall ((V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n_2)))))
% 1.46/1.63  (assume a676 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n_2) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2))))))
% 1.46/1.63  (assume a677 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n_2) V_m_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m_2)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 1.46/1.63  (assume a678 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_a_2) (tptp.c_RComplete_Onatfloor V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2)) V_x_2))))))
% 1.46/1.63  (assume a679 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))))
% 1.46/1.63  (assume a680 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_SEQ_OBseq T_a V_X_2) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))))
% 1.46/1.63  (assume a681 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2)) V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a_2)))))))
% 1.46/1.63  (assume a682 (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.46/1.63  (assume a683 (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) B_K))))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))))
% 1.46/1.63  (assume a684 (forall ((V_X_2 $$unsorted) (T_b $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_b) (= (exists ((B_K $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_K)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) B_K))))) (exists ((B_N $$unsorted)) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 B_n))) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_N))))))))))
% 1.46/1.63  (assume a685 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) V_n))))))
% 1.46/1.63  (assume a686 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) V_a)))))
% 1.46/1.63  (assume a687 (forall ((V_n $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_z) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n))))))
% 1.46/1.63  (assume a688 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (= (tptp.c_RComplete_Onatfloor V_x) V_n)))))
% 1.46/1.63  (assume a689 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatceiling (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x)) V_a)))))
% 1.46/1.63  (assume a690 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (exists ((B_n $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_y)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_n))) V_y)))))))))
% 1.46/1.63  (assume a691 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (exists ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_n)))) V_x))))))
% 1.46/1.63  (assume a692 (forall ((V_r $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_r)) (exists ((B_n $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_r) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc B_n)))))))))
% 1.46/1.63  (assume a693 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) V_n))))))
% 1.46/1.63  (assume a694 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (forall ((B_y $$unsorted)) (exists ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) B_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat B_n)) V_x))))))))
% 1.46/1.63  (assume a695 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K))))))))
% 1.46/1.63  (assume a696 (forall ((V_q $$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.hAPP 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))))))
% 1.46/1.63  (assume a697 (forall ((V_q $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.hAPP tptp.c_Nat_OSuc V_q))))))
% 1.46/1.63  (assume a698 (forall ((V_q $$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.hAPP tptp.c_Nat_OSuc V_q))))))
% 1.46/1.63  (assume a699 (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)))))
% 1.46/1.63  (assume a700 (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_p) V_q))))))
% 1.46/1.63  (assume a701 (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n))))))
% 1.46/1.63  (assume a702 (forall ((V_x $$unsorted) (V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) V_p) V_n)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x)) V_n)))))
% 1.46/1.63  (assume a703 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_p)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) V_q))))))
% 1.46/1.63  (assume a704 (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_q))))))
% 1.46/1.63  (assume a705 (forall ((V_n $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm 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 tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) V_n)))))
% 1.46/1.63  (assume a706 (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))))
% 1.46/1.63  (assume a707 (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_SEQ_OBseq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x_2))))))
% 1.46/1.63  (assume a708 (forall ((V_n $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_r) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_r) (tptp.hAPP tptp.c_Nat_OSuc V_n))) V_r)))))))
% 1.46/1.63  (assume a709 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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_b) V_n)))))))))
% 1.46/1.63  (assume a710 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))))
% 1.46/1.63  (assume a711 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))))
% 1.46/1.63  (assume a712 (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_i)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n))))))
% 1.46/1.63  (assume a713 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2))) (or (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_x_2))))))
% 1.46/1.63  (assume a714 (forall ((V_m_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_m_2) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (= V_m_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_x_2 (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.46/1.63  (assume a715 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.63  (assume a716 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_i)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))))))
% 1.46/1.63  (assume a717 (forall ((V_n_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_n_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_x_2)) (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.46/1.63  (assume a718 (forall ((V_z $$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)))))
% 1.46/1.63  (assume a719 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_z)))))
% 1.46/1.63  (assume a720 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.46/1.63  (assume a721 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_m)) V_n))))
% 1.46/1.63  (assume a722 (forall ((V_n $$unsorted) (V_p $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower (tptp.tc_Polynomial_Opoly T_a)) V_p) V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a V_p)) V_n))))))
% 1.46/1.63  (assume a723 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (= V_x (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x))) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) V_n)))))
% 1.46/1.63  (assume a724 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.63  (assume a725 (forall ((V_n $$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))))))
% 1.46/1.63  (assume a726 (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))))))
% 1.46/1.63  (assume a727 (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)))))
% 1.46/1.63  (assume a728 (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)))))
% 1.46/1.63  (assume a729 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Odivision__ring__inverse__zero T_a) (= (tptp.c_Rings_Oinverse__class_Oinverse T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)) V_n)))))
% 1.46/1.63  (assume a730 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_a))))
% 1.46/1.63  (assume a731 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))))
% 1.46/1.63  (assume a732 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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)))))))
% 1.46/1.63  (assume a733 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.46/1.63  (assume a734 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq 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)))))))
% 1.46/1.63  (assume a735 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= V_n_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.46/1.63  (assume a736 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a_2)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_m_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_n_2)) (= V_m_2 V_n_2))))))
% 1.46/1.63  (assume a737 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.63  (assume a738 (forall ((V_n $$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.hAPP 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)))))
% 1.46/1.63  (assume a739 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.46/1.63  (assume a740 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.46/1.63  (assume a741 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.46/1.63  (assume a742 (forall ((V_n $$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))))))
% 1.46/1.63  (assume a743 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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_b) V_n))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) V_b)))))))
% 1.46/1.63  (assume a744 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) (tptp.hAPP tptp.c_Nat_OSuc V_n))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (= V_a V_b)))))))
% 1.46/1.63  (assume a745 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Nat_OSuc V_n))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) (tptp.hAPP tptp.c_Nat_OSuc V_n)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))))
% 1.46/1.63  (assume a746 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))))
% 1.46/1.63  (assume a747 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a748 (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)))))))
% 1.46/1.63  (assume a749 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Nat_OSuc V_n))))))))
% 1.46/1.63  (assume a750 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N))))))))
% 1.46/1.63  (assume a751 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)))))))
% 1.46/1.63  (assume a752 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_b_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_x_2) V_y_2)))))))
% 1.46/1.63  (assume a753 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N))))))))
% 1.46/1.63  (assume a754 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))))
% 1.46/1.63  (assume a755 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP tptp.c_Nat_OSuc V_n))) (tptp.c_Groups_Oone__class_Oone T_a))))))))
% 1.46/1.63  (assume a756 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))))
% 1.46/1.63  (assume a757 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (= V_a V_b))))))))
% 1.46/1.63  (assume a758 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_N)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))))
% 1.46/1.63  (assume a759 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_b_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_b_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x_2) V_y_2)))))))
% 1.46/1.63  (assume a760 (forall ((V_n $$unsorted) (V_b $$unsorted)) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (exists ((B_z $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) V_n))))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))))
% 1.46/1.63  (assume a761 (forall ((T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Power_Opower_Opower T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Otimes__class_Otimes T_a))))))
% 1.46/1.63  (assume a762 (forall ((V_x $$unsorted) (V_p $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a (tptp.c_Groups_Oone__class_Oone T_a) V_n)) V_p)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_p) V_x))))))
% 1.46/1.63  (assume a763 (forall ((V_y $$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))))
% 1.46/1.63  (assume a764 (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 $$unsorted)) (= V_m_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_d_2) B_q))))))
% 1.46/1.63  (assume a765 (forall ((V_c $$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))))
% 1.46/1.63  (assume a766 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_b V_c)) V_c) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_b) V_c))))
% 1.46/1.63  (assume a767 (forall ((V_y $$unsorted) (V_q_1 $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (=> (= V_a_1 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_1) V_q_1)) V_y)) (=> (and (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_1)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_y) V_b_1)))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_1))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b_1) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))) (=> (not (= V_b_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a_1 V_b_1) V_y))))))
% 1.46/1.63  (assume a768 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))))
% 1.46/1.63  (assume a769 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_b $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r))))))))
% 1.46/1.63  (assume a770 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c))))))))
% 1.46/1.63  (assume a771 (forall ((V_q $$unsorted) (V_b $$unsorted) (V_r $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_q V_c))) V_r))))))))
% 1.46/1.63  (assume a772 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hBOOL (tptp.hAPP V_P_2 V_n_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k_2)) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) B_j) V_k_2)) (= V_n_2 (tptp.hAPP (tptp.hAPP (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 V_P_2 B_j))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) B_j)) (tptp.hBOOL (tptp.hAPP (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.hAPP (tptp.hAPP (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 V_P_2 B_j)))))))))
% 1.46/1.63  (assume a773 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_i)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_j)))))))
% 1.46/1.63  (assume a774 (forall ((V_b_2 $$unsorted) (V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_Omonom T_a V_a_2 V_n_2) (tptp.c_Polynomial_Omonom T_a V_b_2 V_n_2)) (= V_a_2 V_b_2)))))
% 1.46/1.63  (assume a775 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z))))
% 1.46/1.63  (assume a776 (forall ((V_z3 $$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)))))
% 1.46/1.63  (assume a777 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z1) V_z2)) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 1.46/1.63  (assume a778 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z1) V_z2)) (tptp.hAPP (tptp.hAPP (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)))))
% 1.46/1.63  (assume a779 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (tptp.hAPP (tptp.hAPP (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) V_q)) V_r) (tptp.hAPP (tptp.hAPP (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_H) V_q_H)) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (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_H) V_q_H)) V_r_H)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) V_q))))))))))
% 1.46/1.63  (assume a780 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q_H)) V_r_H)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q)) V_r))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_r_H)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q) V_q_H))))))))
% 1.46/1.64  (assume a781 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q)) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H)) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H)) V_r_H))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r_H) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q) V_q_H))))))))))
% 1.46/1.64  (assume a782 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (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) V_q_H)) V_r_H)) (tptp.hAPP (tptp.hAPP (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) V_q)) V_r))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r_H) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) V_q))))))))
% 1.46/1.64  (assume a783 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H)) V_r_H)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_H)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))))
% 1.46/1.64  (assume a784 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (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_H) V_q_H)) V_r_H))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r_H) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_H)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_q_H)))))))
% 1.46/1.64  (assume a785 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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)))))))
% 1.46/1.64  (assume a786 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z) V_z)))
% 1.46/1.64  (assume a787 (forall ((V_z $$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)))
% 1.46/1.64  (assume a788 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_q)))))))
% 1.46/1.64  (assume a789 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (= V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_r) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))))
% 1.46/1.64  (assume a790 (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))))))
% 1.46/1.64  (assume a791 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (= (tptp.c_Polynomial_Omonom T_a V_a_2 V_n_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.46/1.64  (assume a792 (forall ((V_n $$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)))))
% 1.46/1.64  (assume a793 (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)))))))
% 1.46/1.64  (assume a794 (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)))))
% 1.46/1.64  (assume a795 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Omonom T_a V_a V_n))) V_n)))))
% 1.46/1.64  (assume a796 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Omonom T_a V_a V_n)) (tptp.c_Polynomial_Omonom T_a V_b V_n)) (tptp.c_Polynomial_Omonom T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_n)))))
% 1.46/1.64  (assume a797 (forall ((V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_one_2)))
% 1.46/1.64  (assume a798 (forall ((V_n_2 $$unsorted) (V_a_2 $$unsorted) (V_times_2 $$unsorted) (V_one_2 $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower_Opower T_a V_one_2 V_times_2) V_a_2) (tptp.hAPP 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_a V_one_2 V_times_2) V_a_2) V_n_2)))))
% 1.46/1.64  (assume a799 (forall ((V_m_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Omonom T_a V_a_2 V_m_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.c_COMBC tptp.tc_Nat_Onat T_a T_a (tptp.c_COMBC tptp.tc_Nat_Onat T_a (tptp.tc_fun T_a T_a) (tptp.hAPP (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun T_a (tptp.tc_fun T_a T_a)) tptp.tc_Nat_Onat (tptp.c_If T_a)) (tptp.hAPP tptp.c_fequal V_m_2)) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.64  (assume a800 (forall ((V_x $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a (tptp.c_Polynomial_Omonom T_a V_a V_n)) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 1.46/1.64  (assume a801 (forall ((V_n $$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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_m) V_n))))))
% 1.46/1.64  (assume a802 (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.c_SEQ_Omonoseq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x_2))))))
% 1.46/1.64  (assume a803 (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_a)) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_x)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_x) V_n) V_a) (forall ((B_y $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_y)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_y) V_n) V_a)) (= B_y B_x)))))))))
% 1.46/1.64  (assume a804 (forall ((V_z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_z_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.46/1.64  (assume a805 (forall ((V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z))))))
% 1.46/1.64  (assume a806 (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_z)))))
% 1.46/1.64  (assume a807 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_w_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_z_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_2) V_z_2)))))
% 1.46/1.64  (assume a808 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_2) V_z_2)) (= V_w_2 V_z_2)))))
% 1.46/1.64  (assume a809 (forall ((V_z_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2) V_z_2)))))
% 1.46/1.64  (assume a810 (forall ((V_z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z_2)))))
% 1.46/1.64  (assume a811 (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.64  (assume a812 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 1.46/1.64  (assume a813 (forall ((V_z $$unsorted)) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z)) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.46/1.64  (assume a814 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_w) V_z))))
% 1.46/1.64  (assume a815 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_y) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_x) V_z)))))
% 1.46/1.64  (assume a816 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z2) V_z3)))))
% 1.46/1.64  (assume a817 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)))
% 1.46/1.64  (assume a818 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z) V_z)))
% 1.46/1.64  (assume a819 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_x) V_y)) (= V_x V_y) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_y) V_x)))))
% 1.46/1.64  (assume a820 (forall ((V_w_2 $$unsorted) (V_z_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_z_2) V_w_2)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_2) V_w_2)) (not (= V_z_2 V_w_2))))))
% 1.46/1.64  (assume a821 (forall ((V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w) V_w))))
% 1.46/1.64  (assume a822 (forall ((V_w $$unsorted) (V_z $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z) V_w)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w) V_z)))))
% 1.46/1.64  (assume a823 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i) V_k))))))
% 1.46/1.64  (assume a824 (forall ((V_w $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z) V_w)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w) V_z)) (= V_z V_w)))))
% 1.46/1.64  (assume a825 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_k) V_i)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_k) V_j))))))
% 1.46/1.64  (assume a826 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_i) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_j) V_k))))))
% 1.46/1.64  (assume a827 (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_w_H) V_w)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_w_H) V_z_H)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_w) V_z)))))))
% 1.46/1.64  (assume a828 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_a) V_b))))))
% 1.46/1.64  (assume a829 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 1.46/1.64  (assume a830 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_b))))))
% 1.46/1.64  (assume a831 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_a) V_b)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))))
% 1.46/1.64  (assume a832 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.46/1.64  (assume a833 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)))))))
% 1.46/1.64  (assume a834 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_a)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b) V_a)))))
% 1.46/1.64  (assume a835 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_x V_y)))))))
% 1.46/1.64  (assume a836 (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_m V_k)) V_m)))))
% 1.46/1.64  (assume a837 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 1.46/1.64  (assume a838 (forall ((V_a $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b)) V_b)))))
% 1.46/1.64  (assume a839 (forall ((V_a $$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))))
% 1.46/1.64  (assume a840 (forall ((V_b $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.46/1.64  (assume a841 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Oincseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))))
% 1.46/1.64  (assume a842 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_SEQ_Odecseq T_a V_X_2) (tptp.c_SEQ_Omonoseq T_a V_X_2)))))
% 1.46/1.64  (assume a843 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n)) (tptp.hAPP V_X_2 (tptp.hAPP tptp.c_Nat_OSuc B_n))))) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 (tptp.hAPP tptp.c_Nat_OSuc B_n))) (tptp.hAPP V_X_2 B_n)))))))))
% 1.46/1.64  (assume a844 (forall ((V_X_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_SEQ_Omonoseq T_a V_X_2) (or (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m)) (tptp.hAPP V_X_2 B_n))))) (forall ((B_m $$unsorted) (B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_n)) (tptp.hAPP V_X_2 B_m))))))))))
% 1.46/1.64  (assume a845 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n))))))
% 1.46/1.64  (assume a846 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)))))))
% 1.46/1.64  (assume a847 (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.46/1.64  (assume a848 (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 1.46/1.64  (assume a849 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_x) V_y)))))))
% 1.46/1.64  (assume a850 (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_a)) (exists ((B_r $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_r)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_r) V_n) V_a)))))))
% 1.46/1.64  (assume a851 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat V_n)) (tptp.c_Transcendental_Oln V_x))))))
% 1.46/1.64  (assume a852 (= (tptp.c_Transcendental_Oln (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 1.46/1.64  (assume a853 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_y_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Transcendental_Oln V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x_2) V_y_2)))))))
% 1.46/1.64  (assume a854 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_y_2)) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Transcendental_Oln V_y_2)) (= V_x_2 V_y_2))))))
% 1.46/1.64  (assume a855 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) V_x)))))
% 1.46/1.64  (assume a856 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_y_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Transcendental_Oln V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)))))))
% 1.46/1.64  (assume a857 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x))))))
% 1.46/1.64  (assume a858 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x))))))
% 1.46/1.64  (assume a859 (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x_2))))))
% 1.46/1.64  (assume a860 (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (= (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.46/1.64  (assume a861 (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 1.46/1.64  (assume a862 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))))
% 1.46/1.64  (assume a863 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))))
% 1.46/1.64  (assume a864 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))))
% 1.46/1.64  (assume a865 (forall ((V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x_2))))))
% 1.46/1.64  (assume a866 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_y)) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (tptp.c_Transcendental_Oln V_y)))))))
% 1.46/1.64  (assume a867 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))) V_x)))))
% 1.46/1.64  (assume a868 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) B_j)) (tptp.hBOOL (tptp.hAPP (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.hAPP (tptp.hAPP (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))))))))
% 1.46/1.64  (assume a869 (forall ((V_n_2 $$unsorted) (V_P_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2)) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_n_2 V_k_2))) (forall ((B_i $$unsorted) (B_j $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) B_j) V_k_2)) (= V_n_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) B_i)) B_j))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 B_i) B_j))))))))
% 1.46/1.64  (assume a870 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 1.46/1.64  (assume a871 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))))))
% 1.46/1.64  (assume a872 (forall ((V_a $$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)))))
% 1.46/1.64  (assume a873 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) V_b) V_a)))))
% 1.46/1.64  (assume a874 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (and (=> (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (= V_c (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 1.46/1.64  (assume a875 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.46/1.64  (assume a876 (forall ((V_a $$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)))))
% 1.46/1.64  (assume a877 (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))))
% 1.46/1.64  (assume a878 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.46/1.64  (assume a879 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_x V_y)))))))
% 1.46/1.64  (assume a880 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 1.46/1.64  (assume a881 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a_2))))))
% 1.46/1.64  (assume a882 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_a_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 1.46/1.64  (assume a883 (forall ((V_b $$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))))
% 1.46/1.64  (assume a884 (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)))))
% 1.46/1.64  (assume a885 (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)))))
% 1.46/1.64  (assume a886 (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))))
% 1.46/1.64  (assume a887 (forall ((V_a $$unsorted)) (and (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a))))
% 1.46/1.64  (assume a888 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_a) V_b) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a889 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) V_a_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)))))))
% 1.46/1.64  (assume a890 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) V_a_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_H V_b)))))))
% 1.46/1.64  (assume a891 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) V_a)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.46/1.64  (assume a892 (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))))))))
% 1.46/1.64  (assume a893 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 1.46/1.64  (assume a894 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_2 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_a_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 1.46/1.64  (assume a895 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_a) V_b)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.46/1.64  (assume a896 (forall ((V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))))
% 1.46/1.64  (assume a897 (forall ((V_b $$unsorted) (V_b_H $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b_H))))))))
% 1.46/1.64  (assume a898 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless 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_a_2 V_b_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_2) V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_2)))))))
% 1.46/1.64  (assume a899 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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 (tptp.c_Orderings_Oord__class_Oless 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_i_2 V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) V_i_2))))))
% 1.46/1.64  (assume a900 (forall ((V_a_2 $$unsorted) (V_b_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_2)) (= (tptp.hBOOL (tptp.hAPP (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_a_2 V_b_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_a_2))))))
% 1.46/1.64  (assume a901 (forall ((V_k_2 $$unsorted) (V_i_2 $$unsorted)) (= (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_i_2 V_k_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_i_2) V_k_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) V_i_2)))))))
% 1.46/1.64  (assume a902 (forall ((V_k $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a903 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c)))))
% 1.46/1.64  (assume a904 (forall ((V_k $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_a) V_k))))
% 1.46/1.64  (assume a905 (forall ((V_k $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b))) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) V_a) V_k))))
% 1.46/1.64  (assume a906 (forall ((V_c $$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.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a907 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= V_a (tptp.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a908 (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.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 1.46/1.64  (assume a909 (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.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_c) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)))))))
% 1.46/1.64  (assume a910 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (=> (not (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Divides_Odiv__class_Odiv T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_b) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.46/1.64  (assume a911 (forall ((V_a $$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_Oplus__class_Oplus T_a) V_b) V_a) V_b) (tptp.hAPP (tptp.hAPP (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)))))))
% 1.46/1.64  (assume a912 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) V_a))))
% 1.46/1.64  (assume a913 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.64  (assume a914 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b)) V_a))))
% 1.46/1.64  (assume a915 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b))) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)))))
% 1.46/1.64  (assume a916 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Osemiring__div T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Divides_Odiv__class_Odiv T_a V_a V_b)) V_b)) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_b))) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_a) V_c)))))
% 1.46/1.64  (assume a917 (forall ((V_k_2 $$unsorted) (V_n_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_n_2 V_k_2))) (and (=> (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k_2)) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_j)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) B_j) V_k_2)) (= V_n_2 (tptp.hAPP (tptp.hAPP (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 V_P_2 B_i))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (forall ((B_i $$unsorted)) (=> (exists ((B_j $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_k_2) B_j)) (tptp.hBOOL (tptp.hAPP (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.hAPP (tptp.hAPP (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 V_P_2 B_i)))))))))
% 1.46/1.64  (assume a918 (forall ((V_r_1 $$unsorted) (V_y $$unsorted) (V_b_1 $$unsorted) (V_a_1 $$unsorted)) (=> (= V_a_1 (tptp.hAPP (tptp.hAPP (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_1) V_y)) V_r_1)) (=> (and (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_1)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r_1)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_r_1) V_b_1)))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_b_1))) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) V_b_1) V_r_1)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_r_1) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))) (=> (not (= V_b_1 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a_1 V_b_1) V_y))))))
% 1.46/1.64  (assume a919 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_c)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint V_a V_b) V_c))) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Int_Oint V_a V_b))))))
% 1.46/1.64  (assume a920 (forall ((V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))))
% 1.46/1.64  (assume a921 (forall ((V_n $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_a)) (exists ((B_r $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) B_r)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_r) (tptp.hAPP tptp.c_Nat_OSuc V_n)) V_a))))))
% 1.46/1.64  (assume a922 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a923 (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.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a924 (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.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a925 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (and (=> (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_k (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n))))))
% 1.46/1.64  (assume a926 (forall ((V_m $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_m)))
% 1.46/1.64  (assume a927 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a928 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n)))))))
% 1.46/1.64  (assume a929 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 1.46/1.64  (assume a930 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_k)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_n V_k))))))
% 1.46/1.64  (assume a931 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n))))))))
% 1.46/1.64  (assume a932 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n)))))))
% 1.46/1.64  (assume a933 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_a) V_b) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a934 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (tptp.c_Polynomial_Opdivmod__rel T_a V_x V_y (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) (tptp.c_Divides_Odiv__class_Omod (tptp.tc_Polynomial_Opoly T_a) V_x V_y)))))
% 1.46/1.64  (assume a935 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Polynomial_Osmult T_a V_a V_x) V_y) (tptp.c_Polynomial_Osmult T_a V_a (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y))))))
% 1.46/1.64  (assume a936 (forall ((V_r $$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)))))
% 1.46/1.64  (assume a937 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_b) V_c)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_a V_b) V_c))))
% 1.46/1.64  (assume a938 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Fields_Ofield T_a) (= (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes (tptp.tc_Polynomial_Opoly T_a)) V_y) V_z)) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) (tptp.c_Divides_Odiv__class_Odiv (tptp.tc_Polynomial_Opoly T_a) V_x V_y) V_z)))))
% 1.46/1.64  (assume a939 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) V_e_2)) V_ca_2)) V_d_2))))))
% 1.46/1.64  (assume a940 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_b_2) V_a_2)) V_e_2)) V_d_2)))))))
% 1.46/1.64  (assume a941 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) V_e_2)) V_ca_2)) V_d_2))))))
% 1.46/1.64  (assume a942 (forall ((V_d_2 $$unsorted) (V_b_2 $$unsorted) (V_ca_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2)) V_ca_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b_2) V_e_2)) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_ca_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_b_2) V_a_2)) V_e_2)) V_d_2)))))))
% 1.46/1.64  (assume a943 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_k V_m)))))))
% 1.46/1.64  (assume a944 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus T_a) V_x) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_x) (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.46/1.64  (assume a945 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.64  (assume a946 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (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))))
% 1.46/1.64  (assume a947 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_k)) (= (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)))))
% 1.46/1.64  (assume a948 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Divides_Odiv__class_Odiv tptp.tc_Nat_Onat V_m V_n)) V_m))))))
% 1.46/1.64  (assume a949 (forall ((V_b $$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.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_b) V_a))) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_b))))))))
% 1.46/1.64  (assume a950 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.hAPP (tptp.hAPP (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_n)))))
% 1.46/1.64  (assume a951 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 1.46/1.64  (assume a952 (forall ((V_k $$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_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_k) (tptp.hAPP (tptp.hAPP (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)))))
% 1.46/1.64  (assume a953 (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_b) V_b_H)) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a954 (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a955 (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_a_H)) V_b) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a956 (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_x) V_y)) V_ya) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a957 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_b) V_a))))))
% 1.46/1.64  (assume a958 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) (tptp.hAPP tptp.c_Nat_OSuc V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n))))
% 1.46/1.64  (assume a959 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n)) (tptp.hAPP tptp.c_Nat_OSuc V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_k))))
% 1.46/1.64  (assume a960 (forall ((V_d_2 $$unsorted) (V_ca_2 $$unsorted) (V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_ca_2) V_d_2)) (= (= V_a_2 V_b_2) (= V_ca_2 V_d_2))))))
% 1.46/1.64  (assume a961 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_i) V_j)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_i) V_k)) V_j))))
% 1.46/1.64  (assume a962 (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_n) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a963 (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_p) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a964 (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.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) V_p) V_q)) V_x) (tptp.hAPP (tptp.hAPP (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))))))
% 1.46/1.64  (assume a965 (forall ((V_qa_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus (tptp.tc_Polynomial_Opoly T_a)) V_pb_2) V_qa_2) (tptp.c_Polynomial_OAbs__poly T_a (tptp.hAPP (tptp.hAPP (tptp.c_COMBS tptp.tc_Nat_Onat T_a T_a) (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a T_a) tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus T_a)) (tptp.c_Polynomial_Ocoeff T_a V_pb_2))) (tptp.c_Polynomial_Ocoeff T_a V_qa_2)))))))
% 1.46/1.64  (assume a966 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n)))))
% 1.46/1.64  (assume a967 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) V_m)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n))))))
% 1.46/1.64  (assume a968 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat V_m V_n) (tptp.c_Divides_Odiv__class_Omod tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) V_n)))))
% 1.46/1.64  (assume a969 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_m))))))
% 1.46/1.64  (assume a970 (forall ((V_m_2 $$unsorted) (V_n_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_n_2) V_m_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)))))
% 1.46/1.64  (assume a971 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP tptp.c_Nat_OSuc V_m)))))
% 1.46/1.64  (assume a972 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.46/1.64  (assume a973 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.46/1.64  (assume a974 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m_2) V_n_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m_2) V_n_2)))))
% 1.46/1.64  (assume a975 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc V_m)) V_n) (tptp.hAPP tptp.c_Nat_OSuc (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n))))))
% 1.46/1.64  (assume a976 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_i_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i_2) V_k_2)) V_j_2)))))
% 1.46/1.64  (assume a977 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m) V_n))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_m))))
% 1.46/1.64  (assume a978 (forall ((V_n_2 $$unsorted) (V_m_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_m_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_n_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m_2) V_k_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_n_2) V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_m_2) V_n_2)))))))
% 1.46/1.64  (assume a979 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_c) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_b) V_c)))))))
% 1.46/1.64  (assume a980 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_i)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j) V_k)) V_i)))))
% 1.46/1.64  (assume a981 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j) V_k)) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_j) V_i)) V_k)))))
% 1.46/1.64  (assume a982 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_j)) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j) V_k))))))
% 1.46/1.64  (assume a983 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) V_j_2)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_i_2) V_k_2) (= V_j_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_k_2) V_i_2))))))
% 1.46/1.64  (assume a984 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_n) V_m))))
% 1.46/1.64  (assume a985 (forall ((V_i_2 $$unsorted) (V_j_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_j_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i_2) V_k_2)) V_j_2))))))
% 1.46/1.64  (assume a986 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_j)) V_k)))))
% 1.46/1.64  (assume a987 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_m) V_n)) V_m))))
% 1.46/1.64  (assume a988 (forall ((V_m $$unsorted) (V_n $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_n) V_m)) V_k))))))
% 1.46/1.64  (assume a989 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j_2) V_k_2)) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i_2) V_k_2))))))
% 1.46/1.64  (assume a990 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) V_j) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) V_i) V_k)) V_j)))))
% 1.46/1.64  (assume a991 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.64  (assume a992 (forall ((V_b_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) V_a_2) V_b_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_2) V_b_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.46/1.64  (assume a993 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.46/1.64  (assume a994 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) V_b) V_c)))))
% 1.46/1.64  (assume a995 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c)) (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c)) V_c)))))
% 1.46/1.64  (assume a996 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a_H $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Divides_Oring__div T_a) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_a V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_a_H V_c)) (=> (= (tptp.c_Divides_Odiv__class_Omod T_a V_b V_c) (tptp.c_Divides_Odiv__class_Omod T_a V_b_H V_c)) (= (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a) V_b) V_c) (tptp.c_Divides_Odiv__class_Omod T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Ominus__class_Ominus T_a) V_a_H) V_b_H) V_c)))))))
% 1.46/1.64  (assume a997 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a998 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a999 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1000 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1001 (tptp.class_Groups_Ocancel__comm__monoid__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1002 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))))
% 1.46/1.64  (assume a1003 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))))
% 1.46/1.64  (assume a1004 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))))
% 1.46/1.64  (assume a1005 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1006 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1007 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1008 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1009 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1010 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1011 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1012 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1013 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1014 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1015 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1016 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1017 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1018 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1019 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1020 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1021 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1022 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1023 (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1024 (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1025 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1026 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1027 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1028 (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1029 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1030 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1031 (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1032 (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1033 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1034 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1035 (tptp.class_Divides_Osemiring__div tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1036 (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1037 (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1038 (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1039 (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1040 (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1041 (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1042 (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1043 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1044 (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1045 (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1046 (tptp.class_Divides_Oring__div tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1047 (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1048 (tptp.class_Rings_Ocomm__ring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1049 (tptp.class_Orderings_Oorder tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1050 (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1051 (tptp.class_Rings_Osemiring tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1052 (tptp.class_Orderings_Oord tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1053 (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1054 (tptp.class_Power_Opower tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1055 (tptp.class_Groups_Ozero tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1056 (tptp.class_Rings_Oidom tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1057 (tptp.class_Groups_Oone tptp.tc_Int_Oint))
% 1.46/1.64  (assume a1058 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1059 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1060 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1061 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1062 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1063 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1064 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1065 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1066 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1067 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1068 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1069 (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1070 (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1071 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1072 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1073 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1074 (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1075 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1076 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1077 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1078 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1079 (tptp.class_Divides_Osemiring__div tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1080 (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1081 (tptp.class_Orderings_Owellorder tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1082 (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1083 (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1084 (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1085 (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1086 (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1087 (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1088 (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1089 (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1090 (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1091 (tptp.class_Orderings_Oord tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1092 (tptp.class_Power_Opower tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1093 (tptp.class_Groups_Ozero tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1094 (tptp.class_Groups_Oone tptp.tc_Nat_Onat))
% 1.46/1.64  (assume a1095 (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool))
% 1.46/1.64  (assume a1096 (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool))
% 1.46/1.64  (assume a1097 (tptp.class_Orderings_Oord tptp.tc_HOL_Obool))
% 1.46/1.64  (assume a1098 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1099 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1100 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1101 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1102 (tptp.class_Fields_Olinordered__field__inverse__zero tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1103 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1104 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1105 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1106 (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1107 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1108 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1109 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1110 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1111 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1112 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1113 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1114 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1115 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1116 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1117 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1118 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1119 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1120 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1121 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1122 (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1123 (tptp.class_Fields_Ofield__inverse__zero tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1124 (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1125 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1126 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1127 (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1128 (tptp.class_Fields_Olinordered__field tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1129 (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1130 (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1131 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1132 (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1133 (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1134 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1135 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1136 (tptp.class_Rings_Odivision__ring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1137 (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1138 (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1139 (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1140 (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1141 (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1142 (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1143 (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1144 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1145 (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1146 (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1147 (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1148 (tptp.class_Rings_Ocomm__ring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1149 (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1150 (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1151 (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1152 (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1153 (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1154 (tptp.class_Fields_Ofield tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1155 (tptp.class_Power_Opower tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1156 (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1157 (tptp.class_Rings_Oidom tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1158 (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal))
% 1.46/1.64  (assume a1159 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1160 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1161 (tptp.class_Rings_Odivision__ring__inverse__zero tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1162 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1163 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1164 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1165 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1166 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1167 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1168 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1169 (tptp.class_Fields_Ofield__inverse__zero tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1170 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1171 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1172 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1173 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1174 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1175 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1176 (tptp.class_Rings_Ocomm__semiring__0 tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1177 (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1178 (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1179 (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1180 (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1181 (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1182 (tptp.class_Rings_Ocomm__ring__1 tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1183 (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1184 (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1185 (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1186 (tptp.class_Rings_Ocomm__ring tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1187 (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1188 (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1189 (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1190 (tptp.class_Fields_Ofield tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1191 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1192 (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1193 (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1194 (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex))
% 1.46/1.64  (assume a1195 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1196 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__cancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1197 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1198 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__comm__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1199 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1200 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1201 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1202 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__comm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1203 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Olinordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1204 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__ab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1205 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__1__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1206 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__cancel__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1207 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring__strict (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1208 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oring__no__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1209 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__comm__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1210 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1211 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Groups_Oordered__ab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1212 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocancel__comm__monoid__add T_1) (tptp.class_Groups_Ocancel__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1213 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1214 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__semidom (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1215 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Groups_Oab__semigroup__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1216 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Ocomm__monoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1217 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Oab__semigroup__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1218 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1219 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Ono__zero__divisors (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1220 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Ocomm__monoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1221 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1222 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Olinordered__idom (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1223 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ocomm__semiring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1224 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1225 (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Osemiring__div (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1226 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Ocomm__semiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1227 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_1) (tptp.class_Groups_Oab__group__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1228 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Rings_Ozero__neq__one (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1229 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Rings_Oordered__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1230 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Opreorder (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1231 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Olinorder (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1232 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Omonoid__mult (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1233 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Ocomm__ring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1234 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_1) (tptp.class_Groups_Omonoid__add (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1235 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1236 (forall ((T_1 $$unsorted)) (=> (tptp.class_Fields_Ofield T_1) (tptp.class_Divides_Oring__div (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1237 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Omult__zero (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1238 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring T_1) (tptp.class_Rings_Ocomm__ring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1239 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oorder (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1240 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Int_Oring__char__0 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1241 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__0 T_1) (tptp.class_Rings_Osemiring (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1242 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_1) (tptp.class_Orderings_Oord (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1243 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__ring__1 T_1) (tptp.class_Rings_Oring__1 (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1244 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Power_Opower (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1245 (forall ((T_1 $$unsorted)) (=> (tptp.class_Groups_Ozero T_1) (tptp.class_Groups_Ozero (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1246 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Oidom T_1) (tptp.class_Rings_Oidom (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1247 (forall ((T_1 $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_1) (tptp.class_Groups_Oone (tptp.tc_Polynomial_Opoly T_1)))))
% 1.46/1.64  (assume a1248 (forall ((V_Q $$unsorted) (V_P $$unsorted) (T_b $$unsorted) (T_a $$unsorted)) (= (tptp.hAPP (tptp.c_COMBK T_a T_b V_P) V_Q) V_P)))
% 1.46/1.64  (assume a1249 (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_c $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_COMBB T_b T_a T_c V_P_2) V_Q_2) V_R_2) (tptp.hAPP V_P_2 (tptp.hAPP V_Q_2 V_R_2)))))
% 1.46/1.64  (assume a1250 (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.c_COMBC T_b T_c T_a V_P_2 V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_P_2 V_R_2) V_Q_2))))
% 1.46/1.64  (assume a1251 (forall ((V_R_2 $$unsorted) (V_Q_2 $$unsorted) (V_P_2 $$unsorted) (T_a $$unsorted) (T_c $$unsorted) (T_b $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.hAPP (tptp.c_COMBS T_b T_c T_a) V_P_2) V_Q_2) V_R_2) (tptp.hAPP (tptp.hAPP V_P_2 V_R_2) (tptp.hAPP V_Q_2 V_R_2)))))
% 1.46/1.64  (assume a1252 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2))) (= V_x_2 V_y_2))))
% 1.46/1.64  (assume a1253 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (or (not (= V_x_2 V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fequal V_x_2) V_y_2)))))
% 1.46/1.64  (assume a1254 (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted)) (or (tptp.hBOOL V_P_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fimplies V_P_2) V_Q_2)))))
% 1.46/1.64  (assume a1255 (forall ((V_P_2 $$unsorted) (V_Q_2 $$unsorted)) (or (not (tptp.hBOOL V_Q_2)) (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fimplies V_P_2) V_Q_2)))))
% 1.46/1.64  (assume a1256 (forall ((V_Q_2 $$unsorted) (V_P_2 $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP (tptp.hAPP tptp.c_fimplies V_P_2) V_Q_2))) (not (tptp.hBOOL V_P_2)) (tptp.hBOOL V_Q_2))))
% 1.46/1.64  (assume a1257 (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))))
% 1.46/1.64  (assume a1258 true)
% 1.46/1.64  (step t1 (cl (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule and_neg)
% 1.46/1.64  (step t2 (cl (=> (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t3)
% 1.46/1.64  (assume t3.a0 (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))
% 1.46/1.64  (assume t3.a1 (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))
% 1.46/1.64  (assume t3.a2 (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))
% 1.46/1.64  (assume t3.a3 (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))
% 1.46/1.64  (assume t3.a4 (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))
% 1.46/1.64  (step t3.t1 (cl (=> (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t3.t2)
% 1.46/1.64  (assume t3.t2.a0 (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))
% 1.46/1.64  (assume t3.t2.a1 (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))
% 1.46/1.64  (assume t3.t2.a2 (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))
% 1.46/1.64  (assume t3.t2.a3 (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))
% 1.46/1.64  (assume t3.t2.a4 (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))
% 1.46/1.64  (step t3.t2.t1 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule symm :premises (t3.t2.a4))
% 1.46/1.64  (step t3.t2.t2 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule symm :premises (t3.t2.t1))
% 1.46/1.64  (step t3.t2.t3 (cl (= (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) :rule refl)
% 1.46/1.64  (step t3.t2.t4 (cl (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule symm :premises (t3.t2.a3))
% 1.46/1.64  (step t3.t2.t5 (cl (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule symm :premises (t3.t2.t4))
% 1.46/1.64  (step t3.t2.t6 (cl (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) :rule symm :premises (t3.t2.a2))
% 1.46/1.64  (step t3.t2.t7 (cl (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule symm :premises (t3.t2.a1))
% 1.46/1.64  (step t3.t2.t8 (cl (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule trans :premises (t3.t2.t5 t3.t2.t6 t3.t2.t7))
% 1.46/1.64  (step t3.t2.t9 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule cong :premises (t3.t2.t3 t3.t2.t8))
% 1.46/1.64  (step t3.t2.t10 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule symm :premises (t3.t2.a0))
% 1.46/1.64  (step t3.t2.t11 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule trans :premises (t3.t2.t2 t3.t2.t9 t3.t2.t10))
% 1.46/1.64  (step t3.t2 (cl (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (not (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3 t3.t2.a4))
% 1.46/1.64  (step t3.t3 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule and_pos)
% 1.46/1.64  (step t3.t4 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) :rule and_pos)
% 1.46/1.64  (step t3.t5 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule and_pos)
% 1.46/1.64  (step t3.t6 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule and_pos)
% 1.46/1.64  (step t3.t7 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule and_pos)
% 1.46/1.64  (step t3.t8 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6 t3.t7))
% 1.46/1.64  (step t3.t9 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule reordering :premises (t3.t8))
% 1.46/1.64  (step t3.t10 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule contraction :premises (t3.t9))
% 1.46/1.64  (step t3.t11 (cl (=> (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t3.t1 t3.t10))
% 1.46/1.64  (step t3.t12 (cl (=> (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg2)
% 1.46/1.64  (step t3.t13 (cl (=> (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t3.t11 t3.t12))
% 1.46/1.64  (step t3.t14 (cl (=> (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule contraction :premises (t3.t13))
% 1.46/1.64  (step t3.t15 (cl (not (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule implies :premises (t3.t14))
% 1.46/1.64  (step t3.t16 (cl (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (not (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule and_neg)
% 1.46/1.64  (step t3.t17 (cl (and (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t3.t16 t3.a4 t3.a0 t3.a2 t3.a1 t3.a3))
% 1.46/1.64  (step t3.t18 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t3.t15 t3.t17))
% 1.46/1.64  (step t3 (cl (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3 t3.a4))
% 1.46/1.64  (step t4 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) :rule and_pos)
% 1.46/1.64  (step t5 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule and_pos)
% 1.46/1.64  (step t6 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule and_pos)
% 1.46/1.64  (step t7 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule and_pos)
% 1.46/1.64  (step t8 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule and_pos)
% 1.46/1.64  (step t9 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8))
% 1.46/1.64  (step t10 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule reordering :premises (t9))
% 1.46/1.64  (step t11 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule contraction :premises (t10))
% 1.46/1.64  (step t12 (cl (=> (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t2 t11))
% 1.46/1.64  (step t13 (cl (=> (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg2)
% 1.46/1.64  (step t14 (cl (=> (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t12 t13))
% 1.46/1.64  (step t15 (cl (=> (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule contraction :premises (t14))
% 1.46/1.64  (step t16 (cl (not (and (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule implies :premises (t15))
% 1.46/1.64  (step t17 (cl (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t1 t16))
% 1.46/1.64  (step t18 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (not (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule reordering :premises (t17))
% 1.46/1.64  (step t19 (cl (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg2)
% 1.46/1.64  (step t20 (cl (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule and_neg)
% 1.46/1.64  (step t21 (cl (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) (not (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))) :rule implies_neg2)
% 1.46/1.64  (step t22 (cl (not (= (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))) (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))))) (not (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))))) (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))))) :rule equiv_pos2)
% 1.46/1.64  (step t23 (cl (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) :rule refl)
% 1.46/1.64  (step t24 (cl (= (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule refl)
% 1.46/1.64  (step t25 (cl (= (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule all_simplify)
% 1.46/1.64  (step t26 (cl (= (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule cong :premises (t24 t25))
% 1.46/1.64  (step t27 (cl (= (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))) :rule cong :premises (t23 t26))
% 1.46/1.64  (step t28 (cl (= (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule refl)
% 1.46/1.64  (step t29 (cl (= (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule refl)
% 1.46/1.64  (step t30 (cl (= (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule all_simplify)
% 1.46/1.64  (step t31 (cl (= (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule cong :premises (t24 t30))
% 1.46/1.64  (step t32 (cl (= (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))) :rule cong :premises (t29 t31))
% 1.46/1.64  (step t33 (cl (= (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))) :rule cong :premises (t28 t32))
% 1.46/1.64  (step t34 (cl (= (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))) (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))))) :rule cong :premises (t27 t33))
% 1.46/1.64  (step t35 (cl (= (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))) (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))))) :rule cong :premises (t34))
% 1.46/1.64  (step t36 (cl (not (and (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))))) :rule resolution :premises (t22 t35 a1257))
% 1.46/1.64  (step t37 (cl (not (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) (not (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))) :rule not_and :premises (t36))
% 1.46/1.64  (step t38 (cl (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) :rule implies_neg1)
% 1.46/1.64  (step t39 (cl (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule reordering :premises (t38))
% 1.46/1.64  (step t40 (cl (not (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) :rule equiv_pos2)
% 1.46/1.64  (step t41 (cl (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (not (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))) :rule reordering :premises (t40))
% 1.46/1.64  (step t42 (cl (not (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) :rule or_pos)
% 1.46/1.64  (step t43 (cl (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (not (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule reordering :premises (t42))
% 1.46/1.64  (step t44 (cl (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))) (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) :rule or_neg)
% 1.46/1.64  (step t45 (cl (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))) :rule reordering :premises (t44))
% 1.46/1.64  (step t46 (cl (not (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))) :rule equiv_pos1)
% 1.46/1.64  (step t47 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))) (not (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule reordering :premises (t46))
% 1.46/1.64  (step t48 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) :rule not_symm :premises (a1))
% 1.46/1.64  (step t49 (cl (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))) :rule or_pos)
% 1.46/1.64  (step t50 (cl (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))) (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule reordering :premises (t49))
% 1.46/1.64  (step t51 (cl (not (= (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))))) (not (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule equiv_pos2)
% 1.46/1.64  (step t52 (cl (= (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))))) :rule refl)
% 1.46/1.64  (step t53 (cl (= (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)))) :rule refl)
% 1.46/1.64  (step t54 (cl (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) :rule all_simplify)
% 1.46/1.64  (step t55 (cl (= (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))) :rule refl)
% 1.46/1.64  (step t56 (cl (= (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule cong :premises (t54 t55))
% 1.46/1.64  (step t57 (cl (= (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule cong :premises (t53 t56))
% 1.46/1.64  (step t58 (cl (= (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))))) :rule cong :premises (t52 t57))
% 1.46/1.64  (step t59 (cl (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t60)
% 1.46/1.64  (assume t60.a0 (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))))
% 1.46/1.64  (step t60.t1 (cl (or (not (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule forall_inst :args ((:= V_a_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (:= V_pb_2 tptp.v_q____) (:= T_a tptp.tc_Complex_Ocomplex)))
% 1.46/1.64  (step t60.t2 (cl (not (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule or :premises (t60.t1))
% 1.46/1.64  (step t60.t3 (cl (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule resolution :premises (t60.t2 t60.a0))
% 1.46/1.64  (step t60 (cl (not (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule subproof :discharge (t60.a0))
% 1.46/1.64  (step t61 (cl (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule resolution :premises (t59 t60))
% 1.46/1.64  (step t62 (cl (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule implies_neg2)
% 1.46/1.64  (step t63 (cl (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule resolution :premises (t61 t62))
% 1.46/1.64  (step t64 (cl (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule contraction :premises (t63))
% 1.46/1.64  (step t65 (cl (=> (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))))) :rule resolution :premises (t51 t58 t64))
% 1.46/1.64  (step t66 (cl (not (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule implies :premises (t65))
% 1.46/1.64  (step t67 (cl (not (= (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))) (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))))) (not (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))) (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) :rule equiv_pos2)
% 1.46/1.64  (anchor :step t68 :args ((V_a_2 $$unsorted) (:= V_a_2 V_a_2) (V_pb_2 $$unsorted) (:= V_pb_2 V_pb_2) (T_a $$unsorted) (:= T_a T_a)))
% 1.46/1.64  (step t68.t1 (cl (= V_a_2 V_a_2)) :rule refl)
% 1.46/1.64  (step t68.t2 (cl (= V_pb_2 V_pb_2)) :rule refl)
% 1.46/1.64  (step t68.t3 (cl (= T_a T_a)) :rule refl)
% 1.46/1.64  (step t68.t4 (cl (= (tptp.class_Rings_Oidom T_a) (tptp.class_Rings_Oidom T_a))) :rule refl)
% 1.46/1.64  (step t68.t5 (cl (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))) :rule refl)
% 1.46/1.64  (step t68.t6 (cl (= (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) :rule refl)
% 1.46/1.64  (step t68.t7 (cl (= (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))) :rule all_simplify)
% 1.46/1.64  (step t68.t8 (cl (= (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))) :rule cong :premises (t68.t7))
% 1.46/1.64  (step t68.t9 (cl (= (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))) :rule cong :premises (t68.t6 t68.t8))
% 1.46/1.64  (step t68.t10 (cl (= (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) :rule cong :premises (t68.t5 t68.t9))
% 1.46/1.64  (step t68.t11 (cl (= (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) :rule cong :premises (t68.t4 t68.t10))
% 1.46/1.64  (step t68 (cl (= (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))) (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))))) :rule bind)
% 1.46/1.64  (step t69 (cl (= (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))) (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))))) :rule all_simplify)
% 1.46/1.64  (step t70 (cl (= (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))) (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2))))))))) :rule trans :premises (t68 t69))
% 1.46/1.64  (step t71 (cl (forall ((V_a_2 $$unsorted) (V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (= (tptp.hAPP (tptp.c_Polynomial_Opoly T_a V_pb_2) V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder T_a V_a_2 V_pb_2)))))))) :rule resolution :premises (t67 t70 a133))
% 1.46/1.64  (step t72 (cl (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____))))))) :rule resolution :premises (t66 t71))
% 1.46/1.64  (step t73 (cl (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))) :rule resolution :premises (t50 a1193 t72))
% 1.46/1.64  (step t74 (cl (not (or (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Oorder tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) tptp.v_q____)))))) :rule resolution :premises (t47 t48 t73))
% 1.46/1.64  (step t75 (cl (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) :rule resolution :premises (t45 t74))
% 1.46/1.64  (step t76 (cl (not (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) :rule or_pos)
% 1.46/1.64  (step t77 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (not (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule reordering :premises (t76))
% 1.46/1.64  (step t78 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) :rule not_symm :premises (a1))
% 1.46/1.64  (step t79 (cl (not (= (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (not (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule equiv_pos2)
% 1.46/1.64  (step t80 (cl (= (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) :rule refl)
% 1.46/1.64  (step t81 (cl (= (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)))) :rule refl)
% 1.46/1.64  (step t82 (cl (= (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule refl)
% 1.46/1.64  (step t83 (cl (= (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule cong :premises (t81 t54 t82))
% 1.46/1.64  (step t84 (cl (= (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule cong :premises (t80 t83))
% 1.46/1.64  (step t85 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t86)
% 1.46/1.64  (assume t86.a0 (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))
% 1.46/1.64  (step t86.t1 (cl (or (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule forall_inst :args ((:= V_a (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (:= T_a tptp.tc_Complex_Ocomplex)))
% 1.46/1.64  (step t86.t2 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule or :premises (t86.t1))
% 1.46/1.64  (step t86.t3 (cl (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule resolution :premises (t86.t2 t86.a0))
% 1.46/1.64  (step t86 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule subproof :discharge (t86.a0))
% 1.46/1.64  (step t87 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule resolution :premises (t85 t86))
% 1.46/1.64  (step t88 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (not (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule implies_neg2)
% 1.46/1.64  (step t89 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t87 t88))
% 1.46/1.64  (step t90 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule contraction :premises (t89))
% 1.46/1.64  (step t91 (cl (=> (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t79 t84 t90))
% 1.46/1.64  (step t92 (cl (not (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule implies :premises (t91))
% 1.46/1.64  (step t93 (cl (not (= (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)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) (not (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))))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) :rule equiv_pos2)
% 1.46/1.64  (anchor :step t94 :args ((V_a $$unsorted) (:= V_a V_a) (T_a $$unsorted) (:= T_a T_a)))
% 1.46/1.64  (step t94.t1 (cl (= V_a V_a)) :rule refl)
% 1.46/1.64  (step t94.t2 (cl (= T_a T_a)) :rule refl)
% 1.46/1.64  (step t94.t3 (cl (= (tptp.class_Rings_Odivision__ring T_a) (tptp.class_Rings_Odivision__ring T_a))) :rule refl)
% 1.46/1.64  (step t94.t4 (cl (= (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))))) :rule refl)
% 1.46/1.64  (step t94.t5 (cl (= (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))) :rule all_simplify)
% 1.46/1.64  (step t94.t6 (cl (= (not (= (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))) :rule cong :premises (t94.t5))
% 1.46/1.64  (step t94.t7 (cl (= (=> (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)))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) :rule cong :premises (t94.t4 t94.t6))
% 1.46/1.64  (step t94.t8 (cl (= (=> (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))))) (=> (tptp.class_Rings_Odivision__ring T_a) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) :rule cong :premises (t94.t3 t94.t7))
% 1.46/1.64  (step t94 (cl (= (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)))))) (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_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))))) :rule bind)
% 1.46/1.64  (step t95 (cl (= (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_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) :rule all_simplify)
% 1.46/1.64  (step t96 (cl (= (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)))))) (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a))))))) :rule trans :premises (t94 t95))
% 1.46/1.64  (step t97 (cl (forall ((V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Odivision__ring T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Rings_Oinverse__class_Oinverse T_a V_a)))))) :rule resolution :premises (t93 t96 a108))
% 1.46/1.64  (step t98 (cl (or (not (tptp.class_Rings_Odivision__ring tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule resolution :premises (t92 t97))
% 1.46/1.64  (step t99 (cl (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) :rule resolution :premises (t77 t78 a1177 t98))
% 1.46/1.64  (step t100 (cl (not (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule resolution :premises (t43 t75 t99))
% 1.46/1.64  (step t101 (cl (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))) (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule or_pos)
% 1.46/1.64  (step t102 (cl (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))))) :rule reordering :premises (t101))
% 1.46/1.64  (step t103 (cl (not (= (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))))) (not (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))))) :rule equiv_pos2)
% 1.46/1.64  (step t104 (cl (= (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))))) :rule refl)
% 1.46/1.64  (step t105 (cl (= (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) :rule all_simplify)
% 1.46/1.64  (step t106 (cl (= (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) :rule refl)
% 1.46/1.64  (step t107 (cl (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule cong :premises (t105 t106))
% 1.46/1.64  (step t108 (cl (= (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) :rule all_simplify)
% 1.46/1.64  (step t109 (cl (= (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule cong :premises (t107 t108))
% 1.46/1.64  (step t110 (cl (= (= (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))) :rule all_simplify)
% 1.46/1.64  (step t111 (cl (= (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))) :rule trans :premises (t109 t110))
% 1.46/1.64  (step t112 (cl (= (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))))) :rule cong :premises (t53 t111))
% 1.46/1.64  (step t113 (cl (= (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))))) :rule cong :premises (t104 t112))
% 1.46/1.64  (step t114 (cl (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t115)
% 1.46/1.64  (assume t115.a0 (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))))
% 1.46/1.64  (step t115.t1 (cl (or (not (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule forall_inst :args ((:= V_pb_2 tptp.v_q____) (:= V_a_2 (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (:= T_a tptp.tc_Complex_Ocomplex)))
% 1.46/1.64  (step t115.t2 (cl (not (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule or :premises (t115.t1))
% 1.46/1.64  (step t115.t3 (cl (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule resolution :premises (t115.t2 t115.a0))
% 1.46/1.64  (step t115 (cl (not (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule subproof :discharge (t115.a0))
% 1.46/1.64  (step t116 (cl (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule resolution :premises (t114 t115))
% 1.46/1.64  (step t117 (cl (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule implies_neg2)
% 1.46/1.64  (step t118 (cl (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule resolution :premises (t116 t117))
% 1.46/1.64  (step t119 (cl (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)) (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule contraction :premises (t118))
% 1.46/1.64  (step t120 (cl (=> (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t103 t113 t119))
% 1.46/1.64  (step t121 (cl (not (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))) :rule implies :premises (t120))
% 1.46/1.64  (step t122 (cl (not (= (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))))) (not (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) :rule equiv_pos2)
% 1.46/1.64  (anchor :step t123 :args ((V_pb_2 $$unsorted) (:= V_pb_2 V_pb_2) (V_a_2 $$unsorted) (:= V_a_2 V_a_2) (T_a $$unsorted) (:= T_a T_a)))
% 1.46/1.64  (step t123.t1 (cl (= V_pb_2 V_pb_2)) :rule refl)
% 1.46/1.64  (step t123.t2 (cl (= V_a_2 V_a_2)) :rule refl)
% 1.46/1.64  (step t123.t3 (cl (= T_a T_a)) :rule refl)
% 1.46/1.64  (step t123.t4 (cl (= (tptp.class_Rings_Oidom T_a) (tptp.class_Rings_Oidom T_a))) :rule refl)
% 1.46/1.64  (step t123.t5 (cl (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (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_Polynomial_Osmult T_a V_a_2 V_pb_2)))) :rule all_simplify)
% 1.46/1.64  (step t123.t6 (cl (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))) :rule refl)
% 1.46/1.64  (step t123.t7 (cl (= (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2)) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))) :rule cong :premises (t123.t5 t123.t6))
% 1.46/1.64  (step t123.t8 (cl (= (= (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2)) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) :rule all_simplify)
% 1.46/1.64  (step t123.t9 (cl (= (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))) :rule trans :premises (t123.t7 t123.t8))
% 1.46/1.64  (step t123.t10 (cl (= (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))))) (=> (tptp.class_Rings_Oidom T_a) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) :rule cong :premises (t123.t4 t123.t9))
% 1.46/1.64  (step t123 (cl (= (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))))) :rule bind)
% 1.46/1.64  (step t124 (cl (= (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)))) (= (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a)) (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))))) :rule all_simplify)
% 1.46/1.64  (step t125 (cl (= (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (= (= (tptp.c_Polynomial_Osmult T_a V_a_2 V_pb_2) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly T_a))))))) (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2))))))) :rule trans :premises (t123 t124))
% 1.46/1.64  (step t126 (cl (forall ((V_pb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (= (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_pb_2 (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_Polynomial_Osmult T_a V_a_2 V_pb_2)))))) :rule resolution :premises (t122 t125 a13))
% 1.46/1.64  (step t127 (cl (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))))) :rule resolution :premises (t121 t126))
% 1.46/1.64  (step t128 (cl (= (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))))) :rule resolution :premises (t102 a1193 t127))
% 1.46/1.64  (step t129 (cl (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))))) :rule resolution :premises (t41 t100 t128))
% 1.46/1.64  (step t130 (cl (=> (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule resolution :premises (t39 t129))
% 1.46/1.64  (step t131 (cl (not (=> (not (= (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))))) :rule resolution :premises (t37 t130))
% 1.46/1.64  (step t132 (cl (not (and (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))))) :rule resolution :premises (t21 t131))
% 1.46/1.64  (step t133 (cl (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) :rule implies_neg1)
% 1.46/1.64  (step t134 (cl (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule reordering :premises (t133))
% 1.46/1.64  (step t135 (cl (=> (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t134 t75))
% 1.46/1.64  (step t136 (cl (not (=> (not (= tptp.v_q____ (tptp.c_Groups_Ozero__class_Ozero (tptp.tc_Polynomial_Opoly tptp.tc_Complex_Ocomplex)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))))) :rule resolution :premises (t20 t132 t135))
% 1.46/1.64  (step t137 (cl (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t19 t136))
% 1.46/1.64  (step t138 (cl (not (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule or_pos)
% 1.46/1.64  (step t139 (cl (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (not (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule reordering :premises (t138))
% 1.46/1.64  (step t140 (cl (not (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule and_pos)
% 1.46/1.64  (step t141 (cl (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (not (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))) :rule reordering :premises (t140))
% 1.46/1.64  (step t142 (cl (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))) (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule or_pos)
% 1.46/1.64  (step t143 (cl (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))))) :rule reordering :premises (t142))
% 1.46/1.64  (step t144 (cl (not (= (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))))) (not (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))))) (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))))) :rule equiv_pos2)
% 1.46/1.64  (step t145 (cl (= (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))))) :rule refl)
% 1.46/1.64  (step t146 (cl (= (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) :rule cong :premises (t105))
% 1.46/1.64  (step t147 (cl (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule refl)
% 1.46/1.64  (step t148 (cl (= (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule cong :premises (t146 t147))
% 1.46/1.64  (step t149 (cl (= (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule all_simplify)
% 1.46/1.64  (step t150 (cl (= (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule cong :premises (t105 t149))
% 1.46/1.64  (step t151 (cl (= (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))) :rule cong :premises (t148 t150))
% 1.46/1.64  (step t152 (cl (= (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))))) :rule cong :premises (t53 t151))
% 1.46/1.64  (step t153 (cl (= (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))))) :rule cong :premises (t145 t152))
% 1.46/1.64  (step t154 (cl (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p))))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t155)
% 1.46/1.64  (assume t155.a0 (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))))
% 1.46/1.64  (step t155.t1 (cl (or (not (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))))) :rule forall_inst :args ((:= V_p tptp.v_q____) (:= V_a (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (:= T_a tptp.tc_Complex_Ocomplex)))
% 1.46/1.64  (step t155.t2 (cl (not (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) :rule or :premises (t155.t1))
% 1.46/1.64  (step t155.t3 (cl (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) :rule resolution :premises (t155.t2 t155.a0))
% 1.46/1.64  (step t155 (cl (not (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) :rule subproof :discharge (t155.a0))
% 1.46/1.64  (step t156 (cl (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) :rule resolution :premises (t154 t155))
% 1.46/1.64  (step t157 (cl (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) (not (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))))) :rule implies_neg2)
% 1.46/1.64  (step t158 (cl (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))))) :rule resolution :premises (t156 t157))
% 1.46/1.64  (step t159 (cl (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))))) :rule contraction :premises (t158))
% 1.46/1.64  (step t160 (cl (=> (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))))) :rule resolution :premises (t144 t153 t159))
% 1.46/1.64  (step t161 (cl (not (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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))))))) (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))) :rule implies :premises (t160))
% 1.46/1.64  (step t162 (cl (not (= (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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)))))))) (not (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p))))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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))))))) :rule equiv_pos2)
% 1.46/1.64  (anchor :step t163 :args ((V_p $$unsorted) (:= V_p V_p) (V_a $$unsorted) (:= V_a V_a) (T_a $$unsorted) (:= T_a T_a)))
% 1.46/1.64  (step t163.t1 (cl (= V_p V_p)) :rule refl)
% 1.46/1.64  (step t163.t2 (cl (= V_a V_a)) :rule refl)
% 1.46/1.64  (step t163.t3 (cl (= T_a T_a)) :rule refl)
% 1.46/1.64  (step t163.t4 (cl (= (tptp.class_Rings_Oidom T_a) (tptp.class_Rings_Oidom T_a))) :rule refl)
% 1.46/1.64  (step t163.t5 (cl (= (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)))) :rule refl)
% 1.46/1.64  (step t163.t6 (cl (= (= (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)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p))))) :rule all_simplify)
% 1.46/1.64  (step t163.t7 (cl (= (=> (= 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))) (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))))) :rule cong :premises (t163.t5 t163.t6))
% 1.46/1.64  (step t163.t8 (cl (= (=> (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))) (=> (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))))) :rule refl)
% 1.46/1.64  (step t163.t9 (cl (= (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)))) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (=> (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)))))) :rule cong :premises (t163.t7 t163.t8))
% 1.46/1.64  (step t163.t10 (cl (= (=> (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))))) (=> (tptp.class_Rings_Oidom T_a) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (=> (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))))))) :rule cong :premises (t163.t4 t163.t9))
% 1.46/1.64  (step t163 (cl (= (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)))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oidom T_a) (and (=> (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (=> (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))))) :rule bind)
% 1.46/1.64  (step t164 (cl (= (forall ((V_p $$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_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (=> (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)))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))))) :rule all_simplify)
% 1.46/1.64  (step t165 (cl (= (forall ((V_p $$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)))))) (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)) (tptp.c_Polynomial_Odegree T_a V_p)))))))) :rule trans :premises (t163 t164))
% 1.46/1.64  (step t166 (cl (forall ((V_p $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Rings_Oidom T_a)) (and (or (not (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree T_a (tptp.c_Polynomial_Osmult T_a V_a V_p)))) (or (= 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))))))) :rule resolution :premises (t162 t165 a374))
% 1.46/1.64  (step t167 (cl (or (not (tptp.class_Rings_Oidom tptp.tc_Complex_Ocomplex)) (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))) :rule resolution :premises (t161 t166))
% 1.46/1.64  (step t168 (cl (and (or (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule resolution :premises (t143 a1193 t167))
% 1.46/1.64  (step t169 (cl (or (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex) (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule resolution :premises (t141 t168))
% 1.46/1.64  (step t170 (cl (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule resolution :premises (t139 t99 t169))
% 1.46/1.64  (step t171 (cl (not (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule or_pos)
% 1.46/1.64  (step t172 (cl (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (not (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule reordering :premises (t171))
% 1.46/1.64  (step t173 (cl (not (= (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))) (not (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule equiv_pos2)
% 1.46/1.64  (step t174 (cl (= (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))) :rule refl)
% 1.46/1.64  (step t175 (cl (= (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)))) :rule refl)
% 1.46/1.64  (step t176 (cl (= (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule all_simplify)
% 1.46/1.64  (step t177 (cl (= (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule cong :premises (t175 t176))
% 1.46/1.64  (step t178 (cl (= (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))))) :rule cong :premises (t174 t177))
% 1.46/1.64  (step t179 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t180)
% 1.46/1.64  (assume t180.a0 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.46/1.64  (step t180.t1 (cl (or (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule forall_inst :args ((:= V_pb_2 (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (:= T_a tptp.tc_Complex_Ocomplex)))
% 1.46/1.64  (step t180.t2 (cl (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule or :premises (t180.t1))
% 1.46/1.64  (step t180.t3 (cl (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t180.t2 t180.a0))
% 1.46/1.64  (step t180 (cl (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule subproof :discharge (t180.a0))
% 1.46/1.64  (step t181 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t179 t180))
% 1.46/1.64  (step t182 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg2)
% 1.46/1.64  (step t183 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t181 t182))
% 1.46/1.64  (step t184 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule contraction :premises (t183))
% 1.46/1.64  (step t185 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))))) :rule resolution :premises (t173 t178 t184))
% 1.46/1.64  (step t186 (cl (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule implies :premises (t185))
% 1.46/1.64  (step t187 (cl (not (= (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))) (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) :rule equiv_pos2)
% 1.46/1.64  (step t188 (cl (= (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ozero T_a) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))) :rule all_simplify)
% 1.46/1.64  (step t189 (cl (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) :rule resolution :premises (t187 t188 a271))
% 1.46/1.64  (step t190 (cl (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))))) :rule resolution :premises (t186 t189))
% 1.46/1.64  (step t191 (cl (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____)))) :rule resolution :premises (t172 a1192 t190))
% 1.46/1.64  (step t192 (cl (not (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))) (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) :rule or_pos)
% 1.46/1.64  (step t193 (cl (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)) (not (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))) :rule reordering :premises (t192))
% 1.46/1.64  (step t194 (cl (not (= (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) (not (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))) :rule equiv_pos2)
% 1.46/1.64  (step t195 (cl (= (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))) :rule all_simplify)
% 1.46/1.64  (step t196 (cl (= (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))) :rule cong :premises (t175 t195))
% 1.46/1.64  (step t197 (cl (= (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))))) :rule cong :premises (t174 t196))
% 1.46/1.64  (step t198 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t199)
% 1.46/1.64  (assume t199.a0 (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.46/1.64  (step t199.t1 (cl (or (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule forall_inst :args ((:= V_pb_2 tptp.v_q____) (:= T_a tptp.tc_Complex_Ocomplex)))
% 1.46/1.64  (step t199.t2 (cl (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule or :premises (t199.t1))
% 1.46/1.64  (step t199.t3 (cl (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t199.t2 t199.a0))
% 1.46/1.64  (step t199 (cl (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule subproof :discharge (t199.a0))
% 1.46/1.64  (step t200 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t198 t199))
% 1.46/1.64  (step t201 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg2)
% 1.46/1.64  (step t202 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t200 t201))
% 1.46/1.64  (step t203 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule contraction :premises (t202))
% 1.46/1.64  (step t204 (cl (=> (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))))) :rule resolution :premises (t194 t197 t203))
% 1.46/1.64  (step t205 (cl (not (forall ((V_pb_2 $$unsorted) (T_a $$unsorted)) (or (not (tptp.class_Groups_Ozero T_a)) (= (tptp.c_Polynomial_Odegree T_a V_pb_2) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat T_a tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB T_a (tptp.tc_fun T_a tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff T_a V_pb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))) (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))) :rule implies :premises (t204))
% 1.46/1.64  (step t206 (cl (or (not (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex)) (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____)))) :rule resolution :premises (t205 t189))
% 1.46/1.64  (step t207 (cl (= (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))) (tptp.c_Polynomial_Odegree tptp.tc_Complex_Ocomplex tptp.v_q____))) :rule resolution :premises (t193 a1192 t206))
% 1.46/1.64  (step t208 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) :rule implies_neg1)
% 1.46/1.64  (anchor :step t209)
% 1.46/1.64  (assume t209.a0 (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))))
% 1.46/1.64  (step t209.t1 (cl (or (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule forall_inst :args ((:= V_n (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))
% 1.46/1.64  (step t209.t2 (cl (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule or :premises (t209.t1))
% 1.46/1.64  (step t209.t3 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t209.t2 t209.a0))
% 1.46/1.64  (step t209 (cl (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule subproof :discharge (t209.a0))
% 1.46/1.64  (step t210 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t208 t209))
% 1.46/1.64  (step t211 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg2)
% 1.46/1.64  (step t212 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t210 t211))
% 1.46/1.65  (step t213 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule contraction :premises (t212))
% 1.46/1.65  (step t214 (cl (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule implies :premises (t213))
% 1.46/1.65  (step t215 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex tptp.v_q____)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t214 a614))
% 1.46/1.65  (step t216 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) :rule implies_neg1)
% 1.46/1.65  (anchor :step t217)
% 1.46/1.65  (assume t217.a0 (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))))
% 1.46/1.65  (step t217.t1 (cl (or (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule forall_inst :args ((:= V_n (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))
% 1.46/1.65  (step t217.t2 (cl (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule or :premises (t217.t1))
% 1.46/1.65  (step t217.t3 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t217.t2 t217.a0))
% 1.46/1.65  (step t217 (cl (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule subproof :discharge (t217.a0))
% 1.46/1.65  (step t218 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t216 t217))
% 1.46/1.65  (step t219 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (not (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule implies_neg2)
% 1.46/1.65  (step t220 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule resolution :premises (t218 t219))
% 1.46/1.65  (step t221 (cl (=> (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))))))) :rule contraction :premises (t220))
% 1.46/1.65  (step t222 (cl (not (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Nat_OSuc V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n)))) (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule implies :premises (t221))
% 1.46/1.65  (step t223 (cl (= (tptp.hAPP tptp.c_Nat_OSuc (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_OLeast tptp.tc_Nat_Onat (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) tptp.tc_HOL_Obool tptp.tc_Nat_Onat (tptp.c_HOL_OAll tptp.tc_Nat_Onat)) (tptp.c_COMBC tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.tc_fun (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBS tptp.tc_Nat_Onat tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) (tptp.hAPP (tptp.c_COMBB (tptp.tc_fun tptp.tc_Nat_Onat tptp.tc_HOL_Obool) (tptp.tc_fun tptp.tc_Nat_Onat (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool)) tptp.tc_Nat_Onat (tptp.c_COMBB tptp.tc_HOL_Obool (tptp.tc_fun tptp.tc_HOL_Obool tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fimplies)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat))) (tptp.c_COMBC tptp.tc_Nat_Onat tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool (tptp.hAPP (tptp.c_COMBB tptp.tc_Complex_Ocomplex (tptp.tc_fun tptp.tc_Complex_Ocomplex tptp.tc_HOL_Obool) tptp.tc_Nat_Onat tptp.c_fequal) (tptp.c_Polynomial_Ocoeff tptp.tc_Complex_Ocomplex (tptp.c_Polynomial_Osmult tptp.tc_Complex_Ocomplex (tptp.c_Rings_Oinverse__class_Oinverse tptp.tc_Complex_Ocomplex (tptp.hAPP (tptp.c_Polynomial_Opoly tptp.tc_Complex_Ocomplex tptp.v_q____) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))) tptp.v_q____))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)))))))) :rule resolution :premises (t222 a614))
% 1.46/1.65  (step t224 (cl) :rule resolution :premises (t18 t137 t170 t191 t207 t215 t223))
% 1.46/1.65  
% 1.46/1.65  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.nO8QCaxKt7/cvc5---1.0.5_22881.smt2
% 1.46/1.65  % cvc5---1.0.5 exiting
% 1.46/1.66  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------