TSTP Solution File: SWW197+1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW197+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n028.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 18:18:50 EDT 2024
% Result : Theorem 1.32s 1.51s
% Output : Proof 1.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.24/0.24 % Problem : SWW197+1 : TPTP v8.2.0. Released v5.2.0.
% 0.24/0.25 % Command : do_cvc5 %s %d
% 0.26/0.46 % Computer : n028.cluster.edu
% 0.26/0.46 % Model : x86_64 x86_64
% 0.26/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.46 % Memory : 8042.1875MB
% 0.26/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.26/0.46 % CPULimit : 300
% 0.26/0.46 % WCLimit : 300
% 0.26/0.46 % DateTime : Sun May 26 07:01:54 EDT 2024
% 0.26/0.46 % CPUTime :
% 0.58/0.87 %----Proving TF0_NAR, FOF, or CNF
% 1.32/1.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.32/1.51 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.5Q68rdGbnH/cvc5---1.0.5_16736.smt2
% 1.32/1.51 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.5Q68rdGbnH/cvc5---1.0.5_16736.smt2
% 1.32/1.51 (assume a0 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted)) (=> (forall ((B_x $$unsorted)) (= (tptp.hAPP V_f_2 B_x) (tptp.hAPP V_g_2 B_x))) (= V_f_2 V_g_2))))
% 1.32/1.51 (assume a1 (not (= tptp.v_na____ (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a2 (not (= tptp.v_b (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.32/1.51 (assume a3 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.32/1.51 (assume a4 (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat tptp.v_na____))
% 1.32/1.51 (assume a5 (not (= tptp.v_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a6 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.32/1.51 (assume a7 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.32/1.51 (assume a8 (not (forall ((B_z $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a9 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.32/1.51 (assume a10 (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_r V_s)))))))
% 1.32/1.51 (assume a11 (forall ((V_s $$unsorted) (V_y $$unsorted) (V_r $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) V_r) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_y) V_s) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r) V_s)))))))
% 1.32/1.51 (assume a12 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_ma_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_nb_2)) (= V_ma_2 V_nb_2))))))
% 1.32/1.51 (assume a13 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_ba_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_ba_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_ba_2) V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2))))))
% 1.32/1.51 (assume a14 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n))))))
% 1.32/1.51 (assume a15 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N)))))))
% 1.32/1.51 (assume a16 (forall ((V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.32/1.51 (assume a17 (not (= tptp.v_m____ (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a18 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat tptp.v_m____ tptp.v_na____))
% 1.32/1.51 (assume a19 (forall ((B_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_m tptp.v_na____) (=> (not (= B_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (exists ((B_z $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) B_m)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))))
% 1.32/1.51 (assume a20 (forall ((T_a $$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)))))
% 1.32/1.51 (assume a21 (forall ((V_nb_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_nb_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a22 (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))))))
% 1.32/1.51 (assume a23 (forall ((V_nb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Omult__zero T_a) (tptp.class_Rings_Ono__zero__divisors T_a) (tptp.class_Rings_Ozero__neq__one T_a)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_nb_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.32/1.51 (assume a24 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_i) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_i) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 1.32/1.51 (assume a25 (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))))))
% 1.32/1.51 (assume a26 (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)))))
% 1.32/1.51 (assume a27 (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)))))
% 1.32/1.51 (assume a28 (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)))))
% 1.32/1.51 (assume a29 (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)))))
% 1.32/1.51 (assume a30 (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)))))
% 1.32/1.51 (assume a31 (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)))))
% 1.32/1.51 (assume a32 (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)))))
% 1.32/1.51 (assume a33 (forall ((V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (= V_ba_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_ba_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a34 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.32/1.51 (assume a35 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 1.32/1.51 (assume a36 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_x))))
% 1.32/1.51 (assume a37 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_a))))
% 1.32/1.51 (assume a38 (forall ((V_n $$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)))))))
% 1.32/1.51 (assume a39 (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)))))))
% 1.32/1.51 (assume a40 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (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)))))))
% 1.32/1.51 (assume a41 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_p)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_p V_q))))))
% 1.32/1.51 (assume a42 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.32/1.51 (assume a43 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (V_r $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (=> (not (= V_r (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (and (= V_a V_b) (not (= V_c V_d))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_r) V_d)))))))))
% 1.32/1.51 (assume a44 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))
% 1.32/1.51 (assume a45 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.32/1.51 (assume a46 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.32/1.51 (assume a47 (forall ((V_a $$unsorted) (V_N $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_N) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_N) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n))))))))
% 1.32/1.51 (assume a48 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.32/1.51 (assume a49 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.32/1.51 (assume a50 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_rx)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ly) V_ry))))))
% 1.32/1.51 (assume a51 (forall ((V_ry $$unsorted) (V_rx $$unsorted) (V_ly $$unsorted) (V_lx $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) V_ry)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_rx) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_lx) V_ly)) V_ry))))))
% 1.32/1.51 (assume a52 (forall ((V_ry $$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)))))))
% 1.32/1.51 (assume a53 (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)))))
% 1.32/1.51 (assume a54 (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))))))
% 1.32/1.51 (assume a55 (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)))))
% 1.32/1.51 (assume a56 (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))))))
% 1.32/1.51 (assume a57 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)))))
% 1.32/1.51 (assume a58 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))))
% 1.32/1.51 (assume a59 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_b)))))
% 1.32/1.51 (assume a60 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 1.32/1.51 (assume a61 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) V_d)))))
% 1.32/1.51 (assume a62 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_d))))))
% 1.32/1.51 (assume a63 (forall ((V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)))))
% 1.32/1.51 (assume a64 (forall ((V_za_2 $$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.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_za_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_w_2) V_za_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_za_2))))))
% 1.32/1.51 (assume a65 (forall ((V_b $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_m)))))
% 1.32/1.51 (assume a66 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) V_ya) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 1.32/1.51 (assume a67 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 1.32/1.51 (assume a68 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 1.32/1.51 (assume a69 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct T_a) (= (and (not (= V_a_2 V_ba_2)) (not (= V_c_2 V_d_2))) (not (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_d_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_d_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_c_2))))))))
% 1.32/1.51 (assume a70 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 1.32/1.51 (assume a71 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Oplus__class_Oplus T_a V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_z))))))
% 1.32/1.51 (assume a72 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_b_H)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 1.32/1.51 (assume a73 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a))))
% 1.32/1.51 (assume a74 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oone__class_Oone T_a)) V_a) V_a))))
% 1.32/1.51 (assume a75 (forall ((V_q $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) V_q) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_q)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_q))))))
% 1.32/1.51 (assume a76 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_b) V_n))))))
% 1.32/1.51 (assume a77 (forall ((V_n $$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))))))
% 1.32/1.51 (assume a78 (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)))))
% 1.32/1.51 (assume a79 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__div__algebra T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y))))))
% 1.32/1.51 (assume a80 (forall ((V_n $$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)))))
% 1.32/1.51 (assume a81 (forall ((V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.32/1.51 (assume a82 (forall ((V_a $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_m (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_m)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))) V_m)))))
% 1.32/1.51 (assume a83 (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat tptp.v_m____ tptp.v_na____) (=> (not (= tptp.v_m____ (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (exists ((B_z $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) B_z) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a84 (forall ((V_nb_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) V_nb_2)) (or (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2)))))))
% 1.32/1.51 (assume a85 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a86 (forall ((V_nb_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) V_nb_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a87 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.32/1.51 (assume a88 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.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))))))))
% 1.32/1.51 (assume a89 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_y)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a90 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_y_2)) (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_x_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_y_2)))))
% 1.32/1.51 (assume a91 (forall ((V_n $$unsorted)) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n))))
% 1.32/1.51 (assume a92 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.32/1.51 (assume a93 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_m) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) V_n)))))))
% 1.32/1.51 (assume a94 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.32/1.51 (assume a95 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) V_n) V_n)))
% 1.32/1.51 (assume a96 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_ma_2) V_nb_2)) (and (= V_ma_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_nb_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a97 (forall ((V_n $$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)))
% 1.32/1.51 (assume a98 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m))))
% 1.32/1.51 (assume a99 (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))))
% 1.32/1.51 (assume a100 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_z)))))
% 1.32/1.51 (assume a101 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 1.32/1.51 (assume a102 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_ma_2) V_nb_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (and (= V_ma_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (= V_nb_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a103 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)))))
% 1.32/1.51 (assume a104 (forall ((V_k $$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)))))
% 1.32/1.51 (assume a105 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.32/1.51 (assume a106 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_nb_2)) (= V_ma_2 V_nb_2))))
% 1.32/1.51 (assume a107 (forall ((V_nb_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_k_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_nb_2 V_k_2)) (= V_ma_2 V_nb_2))))
% 1.32/1.51 (assume a108 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a109 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.32/1.51 (assume a110 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_m) (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a111 (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))))))
% 1.32/1.51 (assume a112 (forall ((V_nb_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_ma_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_nb_2) V_k_2)) (or (= V_ma_2 V_nb_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a113 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_ma_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_nb_2)) (or (= V_ma_2 V_nb_2) (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a114 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_ma_2) V_nb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (or (= V_ma_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a115 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_nb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (= V_ma_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a116 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 1.32/1.51 (assume a117 (forall ((V_m $$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))))
% 1.32/1.51 (assume a118 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) V_n)))
% 1.32/1.51 (assume a119 (forall ((V_n $$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))))
% 1.32/1.51 (assume a120 (forall ((V_P_2 $$unsorted) (V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_nb_2) V_ma_2))) (=> (=> (= V_ma_2 V_nb_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_nb_2) V_ma_2))) (=> (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_nb_2 V_ma_2) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_nb_2) V_ma_2))) (tptp.hBOOL (tptp.hAPP (tptp.hAPP V_P_2 V_nb_2) V_ma_2)))))))
% 1.32/1.51 (assume a121 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_k))))
% 1.32/1.51 (assume a122 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_l $$unsorted) (V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 1.32/1.51 (assume a123 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_k V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l))))))
% 1.32/1.51 (assume a124 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 1.32/1.51 (assume a125 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j)))))
% 1.32/1.51 (assume a126 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m)))))
% 1.32/1.51 (assume a127 (forall ((V_t $$unsorted) (V_s $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_s V_t) (not (= V_s V_t)))))
% 1.32/1.51 (assume a128 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_m) (not (= V_m V_n)))))
% 1.32/1.51 (assume a129 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 1.32/1.51 (assume a130 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_y V_x)))))
% 1.32/1.51 (assume a131 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2))))
% 1.32/1.51 (assume a132 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (not (= V_ma_2 V_nb_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_nb_2 V_ma_2)))))
% 1.32/1.51 (assume a133 (forall ((V_i $$unsorted) (V_j $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_i))))
% 1.32/1.51 (assume a134 (forall ((V_j $$unsorted) (V_i $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_i))))
% 1.32/1.51 (assume a135 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n V_n))))
% 1.32/1.51 (assume a136 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x_2 V_y_2)) (or (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_x_2) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_y_2)) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_x_2)) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_y_2)))))))
% 1.32/1.51 (assume a137 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_x_2) V_y_2)) (or (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_x_2) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_y_2)))))
% 1.32/1.51 (assume a138 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_nb_2)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_ma_2) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2)))))
% 1.32/1.51 (assume a139 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_nb_2))) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_ma_2) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2))))))
% 1.32/1.51 (assume a140 (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a141 (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)))))
% 1.32/1.51 (assume a142 (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)))))
% 1.32/1.51 (assume a143 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_ba_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_ba_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a144 (forall ((V_b $$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))))))))
% 1.32/1.51 (assume a145 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ono__zero__divisors T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)) (or (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_b (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a146 (forall ((T_a $$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))))))
% 1.32/1.51 (assume a147 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Ozero__neq__one T_a) (not (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.32/1.51 (assume a148 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))))))
% 1.32/1.51 (assume a149 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_e $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_e) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_e) V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)) V_e) V_c)))))
% 1.32/1.51 (assume a150 (forall ((V_n $$unsorted)) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n))))
% 1.32/1.51 (assume a151 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j))))))
% 1.32/1.51 (assume a152 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_k))))))
% 1.32/1.51 (assume a153 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a154 (forall ((V_nb_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_ma_2) V_k_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_nb_2) V_k_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a155 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_ma_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_nb_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a156 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a157 (forall ((V_nb_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) V_nb_2)) (or (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2)))))
% 1.32/1.51 (assume a158 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_ma_2) V_nb_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_ma_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_nb_2)))))
% 1.32/1.51 (assume a159 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 V_nb_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_ma_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_nb_2)))))
% 1.32/1.51 (assume a160 (forall ((V_nb_2 $$unsorted)) (= (not (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_nb_2))))
% 1.32/1.51 (assume a161 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a162 (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a163 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a164 (forall ((V_ba_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_c_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_ba_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_ba_2 V_a_2)))))))
% 1.32/1.51 (assume a165 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_ba_2)) (or (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_ba_2)) (and (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_ba_2 V_a_2)))))))
% 1.32/1.51 (assume a166 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_ba_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_ba_2))))))
% 1.32/1.51 (assume a167 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 1.32/1.51 (assume a168 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a169 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a170 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 1.32/1.51 (assume a171 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b))))))
% 1.32/1.51 (assume a172 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_ba_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_ba_2 V_a_2))))))
% 1.32/1.51 (assume a173 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a174 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)))))))
% 1.32/1.51 (assume a175 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 1.32/1.51 (assume a176 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 1.32/1.51 (assume a177 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__comm__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 1.32/1.51 (assume a178 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)))))))
% 1.32/1.51 (assume a179 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)))))))
% 1.32/1.51 (assume a180 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.32/1.51 (assume a181 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (= (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)))))))
% 1.32/1.51 (assume a182 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a183 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_y_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a184 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_z $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_z) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_y) (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))))))
% 1.32/1.51 (assume a185 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (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))))))
% 1.32/1.51 (assume a186 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x_2) V_za_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2)))))
% 1.32/1.51 (assume a187 (forall ((V_x_2 $$unsorted)) (= (not (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)))))
% 1.32/1.51 (assume a188 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_ma_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a189 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_ma_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_nb_2)) (= V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a190 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a_2)))))
% 1.32/1.51 (assume a191 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a192 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a193 (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))))))
% 1.32/1.51 (assume a194 (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))))))
% 1.32/1.51 (assume a195 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (= V_b V_c)))))
% 1.32/1.51 (assume a196 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__ab__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 1.32/1.51 (assume a197 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (= V_b V_c)))))
% 1.32/1.51 (assume a198 (forall ((V_c_2 $$unsorted) (V_a_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_ba_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2)) (= V_ba_2 V_c_2)))))
% 1.32/1.51 (assume a199 (forall ((V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocancel__semigroup__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_ba_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2)) (= V_ba_2 V_c_2)))))
% 1.32/1.51 (assume a200 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__semigroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 1.32/1.51 (assume a201 (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))))))
% 1.32/1.51 (assume a202 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_z)))))
% 1.32/1.51 (assume a203 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_w) V_z))))
% 1.32/1.51 (assume a204 (forall ((V_z3 $$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)))))
% 1.32/1.51 (assume a205 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_y)) V_z) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_y) V_z)))))
% 1.32/1.51 (assume a206 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a207 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.32/1.51 (assume a208 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.32/1.51 (assume a209 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Olinordered__ab__group__add T_a) (= (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_a_2)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a210 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ocomm__monoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 1.32/1.51 (assume a211 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) V_a))))
% 1.32/1.51 (assume a212 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 1.32/1.51 (assume a213 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b)))))
% 1.32/1.51 (assume a214 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 1.32/1.51 (assume a215 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b))))))
% 1.32/1.51 (assume a216 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c))))))
% 1.32/1.51 (assume a217 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_ba_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_ba_2)))))
% 1.32/1.51 (assume a218 (forall ((V_ba_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a V_ba_2 V_c_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_ba_2)))))
% 1.32/1.51 (assume a219 (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))))
% 1.32/1.51 (assume a220 (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))))
% 1.32/1.51 (assume a221 (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))))
% 1.32/1.51 (assume a222 (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))))
% 1.32/1.51 (assume a223 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_ma_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_nb_2)) (or (= V_k_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a224 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_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_c_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_ba_2) V_c_2)) (= V_a_2 V_ba_2)))))
% 1.32/1.51 (assume a225 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted)) (=> (not (= V_c_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c_2) V_a_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c_2) V_ba_2)) (= V_a_2 V_ba_2)))))
% 1.32/1.51 (assume a226 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.32/1.51 (assume a227 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j)) V_u) V_k))))
% 1.32/1.51 (assume a228 (forall ((V_z $$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)))
% 1.32/1.51 (assume a229 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_z2) V_w)))))
% 1.32/1.51 (assume a230 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a231 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.32/1.51 (assume a232 (forall ((T_a $$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))))))
% 1.32/1.51 (assume a233 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 1.32/1.51 (assume a234 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x V_z) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z)))))
% 1.32/1.51 (assume a235 (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (exists ((B_r $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_r) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_r) V_n) V_a)))))))
% 1.32/1.51 (assume a236 (forall ((V_a $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (exists ((B_x $$unsorted)) (and (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 $$unsorted)) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_y) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) B_y) V_n) V_a)) (= B_y B_x)))))))))
% 1.32/1.51 (assume a237 (forall ((V_w_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (or (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2)) (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_x_2)))))))
% 1.32/1.51 (assume a238 (forall ((V_n $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a 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.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.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))))))))
% 1.32/1.51 (assume a239 (forall ((V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 1.32/1.51 (assume a240 (forall ((V_n $$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))))
% 1.32/1.51 (assume a241 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) V_z) V_z)))
% 1.32/1.51 (assume a242 (forall ((V_z $$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)))
% 1.32/1.51 (assume a243 (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))))
% 1.32/1.51 (assume a244 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a245 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 1.32/1.51 (assume a246 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Ominus__class_Ominus T_b V_b V_c)) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) V_c))))))
% 1.32/1.51 (assume a247 (forall ((V_c $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_c)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_c)))))
% 1.32/1.51 (assume a248 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_z2)) V_z3) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_z3)))))
% 1.32/1.51 (assume a249 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 1.32/1.51 (assume a250 (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Oring T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Groups_Ominus__class_Ominus T_b V_a V_b)) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)))))))
% 1.32/1.51 (assume a251 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_ma_2) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_ma_2) V_nb_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (and (= V_ma_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_nb_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 1.32/1.51 (assume a252 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_j))))))
% 1.32/1.51 (assume a253 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 1.32/1.51 (assume a254 (forall ((V_x_2 $$unsorted) (V_w_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber T_a) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2) V_x_2) (= V_x_2 (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))))))
% 1.32/1.51 (assume a255 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Int_Oring__char__0 T_a)) (= (= (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (= V_x_2 V_y_2)))))
% 1.32/1.51 (assume a256 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2) V_y_2))))))
% 1.32/1.51 (assume a257 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (= V_a_2 V_ba_2) (= V_c_2 V_d_2))))))
% 1.32/1.51 (assume a258 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_ba_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2) V_d_2)))))))
% 1.32/1.51 (assume a259 (forall ((V_w_2 $$unsorted) (V_v_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber T_a) (tptp.class_Orderings_Olinorder T_a)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2))) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v_2)))))))
% 1.32/1.51 (assume a260 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (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)))))
% 1.32/1.51 (assume a261 (forall ((V_y $$unsorted) (V_z $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z))))))
% 1.32/1.51 (assume a262 (forall ((V_z $$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.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_y V_z))))))
% 1.32/1.51 (assume a263 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)))))))
% 1.32/1.51 (assume a264 (forall ((V_n $$unsorted) (V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 1.32/1.51 (assume a265 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_k) V_j))))
% 1.32/1.51 (assume a266 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))))
% 1.32/1.51 (assume a267 (forall ((V_l $$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_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_l)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_l))))))
% 1.32/1.51 (assume a268 (forall ((V_n $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_n)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_i)) V_i))))
% 1.32/1.51 (assume a269 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_ma_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_nb_2)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_ma_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_nb_2 V_k_2)) (= V_ma_2 V_nb_2))))))
% 1.32/1.51 (assume a270 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_m)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 1.32/1.51 (assume a271 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_ma_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_nb_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_ma_2 V_k_2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_nb_2 V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2)))))))
% 1.32/1.51 (assume a272 (forall ((V_nb_2 $$unsorted) (V_ma_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_ma_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k_2) V_nb_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_ma_2 V_k_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_nb_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2))))))
% 1.32/1.51 (assume a273 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_c) V_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a V_c) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_b V_c))))))
% 1.32/1.51 (assume a274 (forall ((V_i $$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.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i)))))
% 1.32/1.51 (assume a275 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k) V_i) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_i) V_k)))))
% 1.32/1.51 (assume a276 (forall ((V_i $$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.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k))))))
% 1.32/1.51 (assume a277 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) V_j_2)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2) V_k_2) (= V_j_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_i_2))))))
% 1.32/1.51 (assume a278 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_n) V_m))))
% 1.32/1.51 (assume a279 (forall ((V_i_2 $$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.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.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2)) V_j_2))))))
% 1.32/1.51 (assume a280 (forall ((V_i $$unsorted) (V_j $$unsorted) (V_k $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_j)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_j) V_k)))))
% 1.32/1.51 (assume a281 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 1.32/1.51 (assume a282 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a283 (forall ((V_m $$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.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_k))))))
% 1.32/1.51 (assume a284 (forall ((V_i_2 $$unsorted) (V_k_2 $$unsorted) (V_j_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) V_i_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2))))))
% 1.32/1.51 (assume a285 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_ma_2 V_nb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2)))))
% 1.32/1.51 (assume a286 (forall ((V_i $$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.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k) V_j)))))
% 1.32/1.51 (assume a287 (forall ((V_d_2 $$unsorted) (V_ba_2 $$unsorted) (V_c_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.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_c_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_e_2) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_ba_2 V_a_2)) V_e_2) V_d_2)))))))
% 1.32/1.51 (assume a288 (forall ((V_d_2 $$unsorted) (V_ba_2 $$unsorted) (V_c_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.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_c_2)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_e_2) V_d_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2)) V_e_2) V_c_2)) V_d_2))))))
% 1.32/1.51 (assume a289 (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))))))))
% 1.32/1.51 (assume a290 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) V_j_2)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_nb_2)) (= V_ma_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_nb_2))))))
% 1.32/1.51 (assume a291 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_u $$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.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) V_m) (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_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_i)) V_u) V_n))))))
% 1.32/1.51 (assume a292 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) V_j_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_ma_2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_nb_2)))))))
% 1.32/1.51 (assume a293 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2) V_i_2)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_nb_2)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_ma_2) V_nb_2)))))
% 1.32/1.51 (assume a294 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_u $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j) V_i)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_u) V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_u) V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j)) V_u) V_m) V_n)))))
% 1.32/1.51 (assume a295 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2) V_i_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_ma_2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_ma_2)) V_nb_2))))))
% 1.32/1.51 (assume a296 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)))))))
% 1.32/1.51 (assume a297 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a))))
% 1.32/1.51 (assume a298 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.32/1.51 (assume a299 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (= V_a_2 V_ba_2) (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a300 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 V_ba_2)))))
% 1.32/1.51 (assume a301 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 V_y_2)))))
% 1.32/1.51 (assume a302 (forall ((V_d_2 $$unsorted) (V_c_2 $$unsorted) (V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (=> (= (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2) (tptp.c_Groups_Ominus__class_Ominus T_a V_c_2 V_d_2)) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_ba_2) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 V_d_2))))))
% 1.32/1.51 (assume a303 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 1.32/1.51 (assume a304 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_w))))))
% 1.32/1.51 (assume a305 (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) V_z)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_w))) V_z)))))
% 1.32/1.51 (assume a306 (forall ((V_b_H $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_b_H)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b_H))))))
% 1.32/1.51 (assume a307 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_xa $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_xa) V_y))))))
% 1.32/1.51 (assume a308 (forall ((V_b $$unsorted) (V_a_H $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_a_H)) V_b) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_H) V_b))))))
% 1.32/1.51 (assume a309 (forall ((V_ya $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) V_ya) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_ya) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_ya))))))
% 1.32/1.51 (assume a310 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 1.32/1.51 (assume a311 (forall ((V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w))))))
% 1.32/1.51 (assume a312 (forall ((V_z $$unsorted) (V_w $$unsorted) (V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_v) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w) V_z)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)) V_z)))))
% 1.32/1.51 (assume a313 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) V_b) V_a))))
% 1.32/1.51 (assume a314 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Ogroup__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) V_b) V_a))))
% 1.32/1.51 (assume a315 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (=> (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= V_m V_n)))))
% 1.32/1.51 (assume a316 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_m) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a317 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_m)))
% 1.32/1.51 (assume a318 (forall ((V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a319 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 1.32/1.51 (assume a320 (forall ((V_ba_2 $$unsorted) (V_c_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_c_2)) (tptp.c_Groups_Oplus__class_Oplus T_a V_ba_2 V_c_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_ba_2))))))
% 1.32/1.51 (assume a321 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_a_2)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c_2 V_ba_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_ba_2))))))
% 1.32/1.51 (assume a322 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_c)))))))
% 1.32/1.51 (assume a323 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__semigroup__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_b)))))))
% 1.32/1.51 (assume a324 (forall ((V_d $$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.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d))))))))
% 1.32/1.51 (assume a325 (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.c_Groups_Oplus__class_Oplus T_a V_a V_c)) (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))))))
% 1.32/1.51 (assume a326 (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.c_Groups_Oplus__class_Oplus T_a V_c V_a)) (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))))))
% 1.32/1.51 (assume a327 (forall ((V_l $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_l) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_n) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_l V_m))))))
% 1.32/1.51 (assume a328 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_j $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_j V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j V_n) V_k))))
% 1.32/1.51 (assume a329 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n) V_n) V_m)))
% 1.32/1.51 (assume a330 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m) V_n) V_m)))
% 1.32/1.51 (assume a331 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i V_j) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k)))))
% 1.32/1.51 (assume a332 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 1.32/1.51 (assume a333 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_k)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))
% 1.32/1.51 (assume a334 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_n)))))
% 1.32/1.51 (assume a335 (forall ((V_k $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_k) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_k) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_n) V_k)))))
% 1.32/1.51 (assume a336 (forall ((V_nb_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_nb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a337 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n))))
% 1.32/1.51 (assume a338 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (= V_m V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.32/1.51 (assume a339 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (=> (not (= V_m V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 1.32/1.51 (assume a340 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.32/1.51 (assume a341 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2) (= V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a342 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2)) (not (= V_ma_2 V_nb_2))))))
% 1.32/1.51 (assume a343 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)) (not (= V_x_2 V_y_2))))))
% 1.32/1.51 (assume a344 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2) (= V_x_2 V_y_2)))))
% 1.32/1.51 (assume a345 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 1.32/1.51 (assume a346 (forall ((V_m $$unsorted) (V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)))))
% 1.32/1.51 (assume a347 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2)) (exists ((B_k $$unsorted)) (= V_nb_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ma_2 B_k))))))
% 1.32/1.51 (assume a348 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_ma_2)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2)))))
% 1.32/1.51 (assume a349 (forall ((V_m $$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.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_m))))))
% 1.32/1.51 (assume a350 (forall ((V_m $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_j))))))
% 1.32/1.51 (assume a351 (forall ((V_k $$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.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_k))))))
% 1.32/1.51 (assume a352 (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.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_j V_l)))))))
% 1.32/1.51 (assume a353 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k)) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n)))))
% 1.32/1.51 (assume a354 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.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)))))
% 1.32/1.51 (assume a355 (forall ((V_n $$unsorted) (V_k $$unsorted) (V_m $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_k)) V_n)) (not (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_n))))))))
% 1.32/1.51 (assume a356 (forall ((V_m $$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)))))
% 1.32/1.51 (assume a357 (forall ((V_m $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_m))))))
% 1.32/1.51 (assume a358 (forall ((V_k $$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))))))
% 1.32/1.51 (assume a359 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_i)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k) V_j))))))
% 1.32/1.51 (assume a360 (forall ((V_l $$unsorted) (V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_k) V_l)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j) V_l)))))))
% 1.32/1.51 (assume a361 (forall ((V_z $$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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_x)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_z V_y))))))
% 1.32/1.51 (assume a362 (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)))))))))
% 1.32/1.51 (assume a363 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_ba_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_ba_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_ba_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_ba_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)))))))
% 1.32/1.51 (assume a364 (forall ((V_n $$unsorted) (V_m $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oone__class_Oone T_a) V_a) (=> (tptp.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)))))))
% 1.32/1.51 (assume a365 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d))))))))
% 1.32/1.51 (assume a366 (forall ((V_w_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$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)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2)))) (or (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2)) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2))))))))
% 1.32/1.51 (assume a367 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_u_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_i_2) V_j_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_i_2)) V_u_2) V_nb_2))))))
% 1.32/1.51 (assume a368 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_u_2 $$unsorted) (V_i_2 $$unsorted) (V_j_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_j_2) V_i_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_i_2) V_u_2) V_ma_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_j_2) V_u_2) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_i_2 V_j_2)) V_u_2) V_ma_2) V_nb_2)))))
% 1.32/1.51 (assume a369 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_a_2 V_ba_2) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a370 (forall ((V_w_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (not (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2)) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.32/1.51 (assume a371 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_v $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Oplus__class_Oplus T_b V_b V_c)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) V_b) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) V_c))))))
% 1.32/1.51 (assume a372 (forall ((V_v $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Int_Onumber T_b) (tptp.class_Rings_Osemiring T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Groups_Oplus__class_Oplus T_b V_a V_b)) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.c_Groups_Oplus__class_Oplus T_b (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_a) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) V_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_v)))))))
% 1.32/1.51 (assume a373 (forall ((V_d_2 $$unsorted) (V_ba_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (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_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_e_2) V_d_2)) (= V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_ba_2 V_a_2)) V_e_2) V_d_2))))))
% 1.32/1.51 (assume a374 (forall ((V_d_2 $$unsorted) (V_ba_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (= (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_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_e_2) V_d_2)) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2)) V_e_2) V_c_2) V_d_2)))))
% 1.32/1.51 (assume a375 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)))))))
% 1.32/1.51 (assume a376 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_y) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) (tptp.c_Groups_Ominus__class_Ominus T_a V_y V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_a)) V_b))))))
% 1.32/1.51 (assume a377 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (or (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a378 (forall ((V_b $$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)))))))
% 1.32/1.51 (assume a379 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d))))))))))
% 1.32/1.51 (assume a380 (forall ((V_d $$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))))))))))
% 1.32/1.51 (assume a381 (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))))))))
% 1.32/1.51 (assume a382 (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))))))))
% 1.32/1.51 (assume a383 (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))))))))
% 1.32/1.51 (assume a384 (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))))))))
% 1.32/1.51 (assume a385 (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))))))))
% 1.32/1.51 (assume a386 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))))
% 1.32/1.51 (assume a387 (forall ((V_b $$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))))))))
% 1.32/1.51 (assume a388 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_a)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.32/1.51 (assume a389 (forall ((V_b $$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))))))))
% 1.32/1.51 (assume a390 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__cancel__semiring T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b))))))))
% 1.32/1.51 (assume a391 (forall ((V_ba_2 $$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_ba_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_ba_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_ba_2))))))))
% 1.32/1.51 (assume a392 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_ba_2))) (or (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_ba_2))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ba_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.32/1.51 (assume a393 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a))))))
% 1.32/1.51 (assume a394 (forall ((V_b $$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 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_Oplus__class_Oplus T_a V_a V_b)) (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.32/1.51 (assume a395 (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.c_Groups_Oplus__class_Oplus T_a V_a V_c))))))))
% 1.32/1.51 (assume a396 (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.c_Groups_Oplus__class_Oplus T_a V_a V_c))))))))
% 1.32/1.51 (assume a397 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y_2)) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a V_x_2 V_y_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.32/1.51 (assume a398 (forall ((V_b $$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.c_Groups_Oplus__class_Oplus T_a V_a V_b))))))))
% 1.32/1.51 (assume a399 (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_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)))))))
% 1.32/1.51 (assume a400 (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.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))))))
% 1.32/1.51 (assume a401 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__cancel__ab__semigroup__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_c) V_d)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 1.32/1.51 (assume a402 (forall ((V_d $$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.c_Orderings_Oord__class_Oless T_a V_c V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)))))))
% 1.32/1.51 (assume a403 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oone__class_Oone T_a))))))
% 1.32/1.51 (assume a404 (forall ((T_a $$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)))))))
% 1.32/1.51 (assume a405 (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))))))))
% 1.32/1.51 (assume a406 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.32/1.51 (assume a407 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_n) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_m) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n) V_m)))))
% 1.32/1.51 (assume a408 (forall ((V_ma_2 $$unsorted) (V_nb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_nb_2 V_ma_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2))))
% 1.32/1.51 (assume a409 (forall ((V_m $$unsorted) (V_n $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n V_m)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a410 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) V_m))))
% 1.32/1.51 (assume a411 (forall ((V_k_2 $$unsorted) (V_j_2 $$unsorted) (V_i_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_i_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_j_2 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_i_2 V_k_2) V_j_2))))
% 1.32/1.51 (assume a412 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) V_a)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)))))))
% 1.32/1.51 (assume a413 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2) (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_x_2) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_y_2)) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_x_2)) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_y_2)))))))
% 1.32/1.51 (assume a414 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_x))))))
% 1.32/1.51 (assume a415 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_n)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_n))))))))
% 1.32/1.51 (assume a416 (forall ((V_d_2 $$unsorted) (V_ba_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_e_2) V_d_2)) (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_ba_2 V_a_2)) V_e_2) V_d_2))))))
% 1.32/1.51 (assume a417 (forall ((V_d_2 $$unsorted) (V_ba_2 $$unsorted) (V_c_2 $$unsorted) (V_e_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a_2) V_e_2) V_c_2) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_ba_2) V_e_2) V_d_2)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_ba_2)) V_e_2) V_c_2) V_d_2)))))
% 1.32/1.51 (assume a418 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Groups_Ominus__class_Ominus T_a V_x (tptp.c_Groups_Oone__class_Oone T_a)))))))
% 1.32/1.51 (assume a419 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c_2) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_ba_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a_2) V_ba_2)))))))
% 1.32/1.51 (assume a420 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_c_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_a_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c_2) V_ba_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_ba_2) V_a_2)))))))
% 1.32/1.51 (assume a421 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.32/1.51 (assume a422 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.32/1.51 (assume a423 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (tptp.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.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.32/1.51 (assume a424 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_d) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_d)))))))))
% 1.32/1.51 (assume a425 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a426 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a427 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a428 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a429 (forall ((V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_c)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_b) V_c))) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))))
% 1.32/1.51 (assume a430 (forall ((V_b $$unsorted) (V_a $$unsorted) (V_c $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__strict T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_b))) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_c) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)))))))
% 1.32/1.51 (assume a431 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.32/1.51 (assume a432 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_b) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.32/1.51 (assume a433 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) V_c)) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.32/1.51 (assume a434 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c)))))))
% 1.32/1.51 (assume a435 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a436 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__comm__monoid__add T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a437 (forall ((V_y $$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.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)))))))
% 1.32/1.51 (assume a438 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__ring__strict T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x_2) V_x_2) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y_2) V_y_2))) (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a439 (forall ((V_y $$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))))))))
% 1.32/1.51 (assume a440 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x)) V_x))))))))
% 1.32/1.51 (assume a441 (forall ((V_w_2 $$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) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (not (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.32/1.51 (assume a442 (forall ((V_b $$unsorted) (V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.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.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a443 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_ba_2))) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_ba_2) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (forall ((B_d $$unsorted)) (=> (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ba_2 B_d)) (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))
% 1.32/1.51 (assume a444 (forall ((V_ba_2 $$unsorted) (V_a_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_a_2 V_ba_2))) (not (or (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_a_2 V_ba_2) (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))) (exists ((B_d $$unsorted)) (and (= V_a_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_ba_2 B_d)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_d))))))))))
% 1.32/1.51 (assume a445 (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)))
% 1.32/1.51 (assume a446 (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))))))
% 1.32/1.51 (assume a447 (forall ((V_x_2 $$unsorted) (V_nb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2)))))))
% 1.32/1.51 (assume a448 (forall ((V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Groups_Omonoid__mult T_a) (tptp.class_Rings_Olinordered__ring T_a)) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_n) (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_x) V_n)))))))
% 1.32/1.51 (assume a449 (forall ((V_nb_2 $$unsorted) (V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) V_nb_2))) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a_2)) (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2))))))
% 1.32/1.51 (assume a450 (forall ((V_nb_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$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)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) V_nb_2))) (or (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x_2))))))))
% 1.32/1.51 (assume a451 (forall ((V_nb_2 $$unsorted) (V_k_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_ma_2) V_k_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_nb_2) V_k_2))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2))))))
% 1.32/1.51 (assume a452 (forall ((V_nb_2 $$unsorted) (V_ma_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_ma_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_nb_2))) (=> (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_ma_2) V_nb_2))))))
% 1.32/1.51 (assume a453 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (V_k_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k_2) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_ma_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_k_2) V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2))))))
% 1.32/1.51 (assume a454 (forall ((V_y $$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)))))))
% 1.32/1.51 (assume a455 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_2) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_za_2) V_x_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_za_2) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2))))))
% 1.32/1.51 (assume a456 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_za_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_za_2)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_y_2) V_za_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2))))))
% 1.32/1.51 (assume a457 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_x) (tptp.c_RealVector_Onorm__class_Onorm T_a V_y)))))))
% 1.32/1.51 (assume a458 (forall ((V_n $$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))))))
% 1.32/1.51 (assume a459 (forall ((V_w_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (or (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_x_2)))))
% 1.32/1.51 (assume a460 (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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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))))))
% 1.32/1.51 (assume a461 (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.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.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))))))))))
% 1.32/1.51 (assume a462 (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Power_Opower T_a) (tptp.class_Rings_Osemiring__0 T_a)) (and (=> (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w) (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)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w) (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)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a463 (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.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))))))))
% 1.32/1.51 (assume a464 (forall ((V_w_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2)) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w_2))) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a465 (forall ((V_n $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) V_n)))))))
% 1.32/1.51 (assume a466 (forall ((V_nb_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) V_nb_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (and (not (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (or (and (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)))) (and (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2) (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))))
% 1.32/1.51 (assume a467 (forall ((V_nb_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_nb_2) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2) (not (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_nb_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))
% 1.32/1.51 (assume a468 (forall ((V_p $$unsorted) (V_m $$unsorted)) (and (=> (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (=> (not (= V_m (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_p) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_p) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))))
% 1.32/1.51 (assume a469 (forall ((V_v $$unsorted) (V_u $$unsorted) (V_y $$unsorted) (V_a $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semiring__1__strict T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_u)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_v)) (=> (= (tptp.c_Groups_Oplus__class_Oplus T_a V_u V_v) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_u) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_v) V_y)) V_a)))))))))
% 1.32/1.51 (assume a470 (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Power_Opower T_a) (and (=> (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.c_Groups_Oone__class_Oone T_a))) (=> (not (= V_n (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_m) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_m) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 1.32/1.51 (assume a471 (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)))))))
% 1.32/1.51 (assume a472 (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)))))
% 1.32/1.51 (assume a473 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oab__group__add T_a) (= (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_c) (tptp.c_Groups_Oplus__class_Oplus T_a V_b V_d)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b) (tptp.c_Groups_Ominus__class_Ominus T_a V_c V_d))))))
% 1.32/1.51 (assume a474 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 1.32/1.51 (assume a475 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 1.32/1.51 (assume a476 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_z) V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 1.32/1.51 (assume a477 (forall ((V_za_2 $$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_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2))))
% 1.32/1.51 (assume a478 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k_2 V_l_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a479 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_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_za_2)))))
% 1.32/1.51 (assume a480 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2))))
% 1.32/1.51 (assume a481 (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_w)))))
% 1.32/1.51 (assume a482 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2))))
% 1.32/1.51 (assume a483 (forall ((V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z)))))
% 1.32/1.51 (assume a484 (forall ((V_z $$unsorted) (V_w $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w V_z) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_z)))))
% 1.32/1.51 (assume a485 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i) V_j)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_i)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_j))))))
% 1.32/1.51 (assume a486 (forall ((V_z $$unsorted) (V_z_H $$unsorted) (V_w $$unsorted) (V_w_H $$unsorted)) (=> (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.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_H V_z_H) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))))
% 1.32/1.51 (assume a487 (forall ((V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w) V_w))))
% 1.32/1.51 (assume a488 (forall ((V_w $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_w) V_w))))
% 1.32/1.51 (assume a489 (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)))))
% 1.32/1.51 (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)))))
% 1.32/1.51 (assume a491 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) V_l_2)))))
% 1.32/1.51 (assume a492 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i) V_j)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_j) V_k)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_i) V_k))))))
% 1.32/1.51 (assume a493 (forall ((V_k $$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))))))
% 1.32/1.51 (assume a494 (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)))))
% 1.32/1.51 (assume a495 (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)))))
% 1.32/1.51 (assume a496 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))))
% 1.32/1.51 (assume a497 (forall ((V_w_2 $$unsorted) (V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 V_w_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_za_2) V_w_2)) (not (= V_za_2 V_w_2))))))
% 1.32/1.51 (assume a498 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_n))))
% 1.32/1.51 (assume a499 (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)))))
% 1.32/1.51 (assume a500 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= V_m V_n) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_m) V_n)))))
% 1.32/1.51 (assume a501 (forall ((V_k $$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))))))
% 1.32/1.51 (assume a502 (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)))))
% 1.32/1.51 (assume a503 (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_y V_x))))
% 1.32/1.51 (assume a504 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_i V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_j V_k)))))
% 1.32/1.51 (assume a505 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_za_2) V_za_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a506 (forall ((V_z3 $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 V_z2) V_z3) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z2 V_z3)))))
% 1.32/1.51 (assume a507 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_y (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_z)))))
% 1.32/1.51 (assume a508 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_za_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2) (= V_w_2 V_za_2)))))
% 1.32/1.51 (assume a509 (forall ((V_w $$unsorted) (V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_w) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w V_z))))
% 1.32/1.51 (assume a510 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)))
% 1.32/1.51 (assume a511 (forall ((V_z $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_z) V_z)))
% 1.32/1.51 (assume a512 (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)))
% 1.32/1.51 (assume a513 (forall ((V_z $$unsorted)) (not (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_z) V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a514 (not (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a515 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x_2 V_y_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a516 (forall ((V_w $$unsorted) (V_z2 $$unsorted) (V_z1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z1) V_w) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z2) V_w)))))
% 1.32/1.51 (assume a517 (forall ((V_z2 $$unsorted) (V_z1 $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z1 V_z2)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z1) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z2)))))
% 1.32/1.51 (assume a518 (forall ((V_w $$unsorted) (V_v $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_w)))))
% 1.32/1.51 (assume a519 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$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_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b))) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b)))))))
% 1.32/1.51 (assume a520 (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 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 B_x)) (tptp.hAPP V_g_2 B_x))))))))
% 1.32/1.51 (assume a521 (forall ((V_y $$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))))))
% 1.32/1.51 (assume a522 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (= V_x_2 V_y_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y_2) V_x_2)))))))
% 1.32/1.51 (assume a523 (forall ((V_y $$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))))))
% 1.32/1.51 (assume a524 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2)))))))
% 1.32/1.51 (assume a525 (forall ((V_x_2 $$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))))))
% 1.32/1.51 (assume a526 (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)))))))
% 1.32/1.51 (assume a527 (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)))))))
% 1.32/1.51 (assume a528 (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)))))))
% 1.32/1.51 (assume a529 (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)))))))
% 1.32/1.51 (assume a530 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (= V_x V_y))))))
% 1.32/1.51 (assume a531 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_z)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_z)))))))
% 1.32/1.51 (assume a532 (forall ((V_x $$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))))))
% 1.32/1.51 (assume a533 (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)))))))
% 1.32/1.51 (assume a534 (forall ((V_x_2 $$unsorted) (V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_b (tptp.hAPP V_f_2 V_x_2)) (tptp.hAPP V_g_2 V_x_2)))))))
% 1.32/1.51 (assume a535 (forall ((V_y $$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))))))
% 1.32/1.51 (assume a536 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (=> (not (= V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.32/1.51 (assume a537 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.32/1.51 (assume a538 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_z V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_z V_x))))))
% 1.32/1.51 (assume a539 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_y V_z) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 1.32/1.51 (assume a540 (forall ((V_c $$unsorted) (V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 1.32/1.51 (assume a541 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (=> (= V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 1.32/1.51 (assume a542 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_c V_b) (tptp.c_Orderings_Oord__class_Oless T_a V_c V_a))))))
% 1.32/1.51 (assume a543 (forall ((V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oord T_a) (=> (= V_a V_b) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_c) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_c))))))
% 1.32/1.51 (assume a544 (forall ((V_a $$unsorted) (V_b $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a545 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b) (not (tptp.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 1.32/1.51 (assume a546 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_y V_x))))))
% 1.32/1.51 (assume a547 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))))
% 1.32/1.51 (assume a548 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.32/1.51 (assume a549 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.32/1.51 (assume a550 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (not (= V_x V_y))))))
% 1.32/1.51 (assume a551 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (= V_x V_y)) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x))))))
% 1.32/1.51 (assume a552 (forall ((V_x_2 $$unsorted) (V_y_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))))
% 1.32/1.51 (assume a553 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y) (tptp.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 1.32/1.51 (assume a554 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2) (= V_x_2 V_y_2))))))
% 1.32/1.51 (assume a555 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (= V_x_2 V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2))))))
% 1.32/1.51 (assume a556 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_x)))))
% 1.32/1.51 (assume a557 (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 $$unsorted)) (= V_l_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_k_2 B_n))))))
% 1.32/1.51 (assume a558 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (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))))))
% 1.32/1.51 (assume a559 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (= (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2))) (tptp.c_Orderings_Oord__class_Oless T_a V_y_2 V_x_2)))))
% 1.32/1.51 (assume a560 (forall ((V_y $$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.c_Orderings_Oord__class_Oless T_a V_y V_x)))))
% 1.32/1.51 (assume a561 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (not (= V_x_2 V_y_2)))))))
% 1.32/1.51 (assume a562 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (= (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))))))))
% 1.32/1.51 (assume a563 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (or (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2) (= V_x_2 V_y_2))))))
% 1.32/1.51 (assume a564 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (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))))))
% 1.32/1.51 (assume a565 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x))) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y)))))
% 1.32/1.51 (assume a566 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (not (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))))))
% 1.32/1.51 (assume a567 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (not (= V_a V_b)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a568 (forall ((V_b $$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.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 1.32/1.51 (assume a569 (forall ((V_x $$unsorted) (V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_y) V_x)) (not (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))))
% 1.32/1.51 (assume a570 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (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))))))
% 1.32/1.51 (assume a571 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Olinorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x_2) V_y_2)) (= (not (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 V_y_2)) (= V_x_2 V_y_2))))))
% 1.32/1.51 (assume a572 (forall ((V_y $$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.c_Orderings_Oord__class_Oless T_a V_x V_y) (= V_x V_y))))))
% 1.32/1.51 (assume a573 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Oorder T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b)) (=> (not (= V_a V_b)) (tptp.c_Orderings_Oord__class_Oless T_a V_a V_b))))))
% 1.32/1.51 (assume a574 (forall ((V_a $$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.c_Orderings_Oord__class_Oless T_a V_b V_a))))))
% 1.32/1.51 (assume a575 (forall ((V_z $$unsorted) (V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_a) (=> (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.c_Orderings_Oord__class_Oless T_a V_x V_z))))))
% 1.32/1.51 (assume a576 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_a) (=> (= V_a (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_r (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_a) V_q))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))))))
% 1.32/1.51 (assume a577 (forall ((V_q $$unsorted) (V_r $$unsorted) (V_a $$unsorted)) (=> (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.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.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)))))))
% 1.32/1.51 (assume a578 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b_H) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_q_H)))))))
% 1.32/1.51 (assume a579 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_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.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))))))))
% 1.32/1.51 (assume a580 (forall ((V_k $$unsorted)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_k) V_k)))
% 1.32/1.51 (assume a581 (forall ((V_g_2 $$unsorted) (V_f_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (tptp.class_Orderings_Oord T_b) (= (tptp.c_Orderings_Oord__class_Oless (tptp.tc_fun T_a T_b) V_f_2 V_g_2) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_f_2) V_g_2)) (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq (tptp.tc_fun T_a T_b) V_g_2) V_f_2))))))))
% 1.32/1.51 (assume a582 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b_H) V_q_H) V_r_H) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_b_H) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_b_H) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) V_q))))))))))
% 1.32/1.51 (assume a583 (forall ((V_r $$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.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.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.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_b V_r) (=> (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))))))))
% 1.32/1.51 (assume a584 (forall ((V_r_H $$unsorted) (V_q_H $$unsorted) (V_b_H $$unsorted) (V_r $$unsorted) (V_q $$unsorted) (V_b $$unsorted)) (=> (= (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.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.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_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.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))))))))))
% 1.32/1.51 (assume a585 (forall ((V_r $$unsorted) (V_q $$unsorted) (V_r_H $$unsorted) (V_q_H $$unsorted) (V_b $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q_H) V_r_H)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_b) V_q) V_r))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_r_H)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r_H V_b) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_r V_b) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_q_H) V_q))))))))
% 1.32/1.51 (assume a586 (forall ((V_a $$unsorted) (V_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_b V_a)) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_b))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_a)))))
% 1.32/1.51 (assume a587 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n))))))
% 1.32/1.51 (assume a588 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)))))))
% 1.32/1.51 (assume a589 (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a590 (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a591 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)))))))
% 1.32/1.51 (assume a592 (forall ((V_z $$unsorted)) (=> (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex V_z) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_z (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_z (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_z tptp.c_Complex_Oii)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Complex_Ocomplex V_z tptp.c_Complex_Oii)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a593 (forall ((V_y $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$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)))))))))
% 1.32/1.51 (assume a594 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_x $$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)))))))))
% 1.32/1.51 (assume a595 (forall ((V_w $$unsorted)) (not (= tptp.c_Complex_Oii (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Complex_Ocomplex V_w)))))
% 1.32/1.51 (assume a596 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))))
% 1.32/1.51 (assume a597 (not (= tptp.c_Complex_Oii (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.32/1.51 (assume a598 (forall ((T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra T_a) (exists ((B_K $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_a $$unsorted) (B_b $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K)))))))))
% 1.32/1.51 (assume a599 (forall ((V_x $$unsorted) (V_y $$unsorted)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y) V_x)) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y) V_x))) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.32/1.51 (assume a600 (forall ((V_nb_2 $$unsorted) (V_P_2 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))) (=> (tptp.hBOOL (tptp.hAPP V_P_2 V_nb_2)) (exists ((B_k $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_k V_nb_2) (forall ((B_i $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i) B_k)) (not (tptp.hBOOL (tptp.hAPP V_P_2 B_i))))) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_k (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))))))))
% 1.32/1.51 (assume a601 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Nat__Transfer_Otsub V_x V_y)))))))
% 1.32/1.51 (assume a602 (forall ((V_x $$unsorted) (V_y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_y) V_x)) (= (tptp.c_Nat__Transfer_Otsub V_x V_y) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_y)))))
% 1.32/1.51 (assume a603 (forall ((V_y $$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 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_x) V_y))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))))
% 1.32/1.51 (assume a604 (forall ((V_x $$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 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) B_x))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_x)) B_K)))))))))
% 1.32/1.51 (assume a605 (forall ((T_a $$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 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) B_a) B_b))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_a B_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a B_b))) B_K)))))))))
% 1.32/1.51 (assume a606 (= (tptp.c_Complex_Oexpi (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex)))
% 1.32/1.51 (assume a607 (forall ((V_x $$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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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))))))
% 1.32/1.51 (assume a608 (forall ((V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (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_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v))) (=> (not (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_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)))) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a609 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a610 (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatceiling V_x)))))
% 1.32/1.51 (assume a611 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x)) (tptp.c_RComplete_Onatceiling V_y))))))
% 1.32/1.51 (assume a612 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Nat_Osemiring__char__0 T_a) (= (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_ma_2) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_nb_2)) (= V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a613 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__algebra__1 T_a) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_RealDef_Oreal) V_n)))))
% 1.32/1.51 (assume a614 (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a615 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n))))
% 1.32/1.51 (assume a616 (forall ((V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m))))))
% 1.32/1.51 (assume a617 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))))))
% 1.32/1.51 (assume a618 (forall ((V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a619 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.32/1.51 (assume a620 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n)))))
% 1.32/1.51 (assume a621 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_m V_n) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))))))
% 1.32/1.51 (assume a622 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_ma_2) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2)))))
% 1.32/1.51 (assume a623 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_ma_2)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2))))))
% 1.32/1.51 (assume a624 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))))))
% 1.32/1.51 (assume a625 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_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_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n))))))
% 1.32/1.51 (assume a626 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.32/1.51 (assume a627 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a628 (forall ((V_nb_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_nb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a629 (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))
% 1.32/1.51 (assume a630 (forall ((V_P_2 $$unsorted)) (= (forall ((B_x $$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)) B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (forall ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) B_x)))))))
% 1.32/1.51 (assume a631 (forall ((V_P_2 $$unsorted)) (= (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x)))) (exists ((B_x $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) B_x)))))))
% 1.32/1.51 (assume a632 (forall ((V_z $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_z)))))
% 1.32/1.51 (assume a633 (forall ((V_n $$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.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n)))))
% 1.32/1.51 (assume a634 (forall ((V_k $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_k) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a635 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x_2) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2))))
% 1.32/1.51 (assume a636 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 V_nb_2))))
% 1.32/1.51 (assume a637 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x_2)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_x_2) V_y_2)))))
% 1.32/1.51 (assume a638 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_ma_2) V_nb_2)))))
% 1.32/1.51 (assume a639 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2) V_za_2)) (exists ((B_n $$unsorted)) (= V_za_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_w_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) B_n)))))))
% 1.32/1.51 (assume a640 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_y)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_x V_y)))))
% 1.32/1.51 (assume a641 (forall ((V_z $$unsorted) (V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n) V_z)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) V_z))))
% 1.32/1.51 (assume a642 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)))))
% 1.32/1.51 (assume a643 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_y)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_x) V_y)))))
% 1.32/1.51 (assume a644 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.32/1.51 (assume a645 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n)))))
% 1.32/1.51 (assume a646 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume a647 (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))
% 1.32/1.51 (assume a648 (forall ((V_n $$unsorted) (V_m $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (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 T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m)) V_n)))))
% 1.32/1.51 (assume a649 (forall ((V_n $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x)) V_n) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_x) V_n)))))
% 1.32/1.51 (assume a650 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m)) V_n) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.32/1.51 (assume a651 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (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_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m)) V_n))))
% 1.32/1.51 (assume a652 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.c_Nat__Transfer_Otsub (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_y)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_x V_y)))))
% 1.32/1.51 (assume a653 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a654 (forall ((V_m $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1 T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)))))))
% 1.32/1.51 (assume a655 (forall ((V_nb_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_nb_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a656 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n))))))
% 1.32/1.51 (assume a657 (forall ((V_x_2 $$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))))))
% 1.32/1.51 (assume a658 (forall ((V_nb_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_nb_2)))))
% 1.32/1.51 (assume a659 (forall ((V_nb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_nb_2))))
% 1.32/1.51 (assume a660 (forall ((V_k $$unsorted) (V_j $$unsorted) (V_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i V_j) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_k) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_k)) V_i) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_k)) V_j))))))
% 1.32/1.51 (assume a661 (forall ((V_b $$unsorted) (V_a $$unsorted)) (= (tptp.c_Complex_Oexpi (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Complex_Ocomplex V_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Oexpi V_a)) (tptp.c_Complex_Oexpi V_b)))))
% 1.32/1.51 (assume a662 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_x_2 V_y_2)))) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_y_2) V_x_2)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x_2) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_y_2))))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_x_2 V_y_2) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))))
% 1.32/1.51 (assume a663 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_n))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n)))))))
% 1.32/1.51 (assume a664 (forall ((V_x $$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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (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))))))
% 1.32/1.51 (assume a665 (forall ((V_n $$unsorted)) (not (tptp.c_Nat__Numeral_Oneg (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n)))))
% 1.32/1.51 (assume a666 (forall ((V_nb_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_nb_2)) (= V_ma_2 V_nb_2))))
% 1.32/1.51 (assume a667 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_x_2) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_y_2)) (= V_x_2 V_y_2))))
% 1.32/1.51 (assume a668 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n))))
% 1.32/1.51 (assume a669 (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a670 (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a671 (forall ((V_x_2 $$unsorted)) (= (not (tptp.c_Nat__Numeral_Oneg V_x_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x_2)))))
% 1.32/1.51 (assume a672 (forall ((V_Z_2 $$unsorted)) (= (tptp.c_Nat__Numeral_Oneg V_Z_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_Z_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a673 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a674 (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_RComplete_Onatfloor V_x)))))
% 1.32/1.51 (assume a675 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_RComplete_Onatfloor V_y))))))
% 1.32/1.51 (assume a676 (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a677 (forall ((V_x_2 $$unsorted) (V_nb_2 $$unsorted)) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_nb_2))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_nb_2)) (tptp.c_RComplete_Onatfloor V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_nb_2)) V_x_2)))))))
% 1.32/1.51 (assume a678 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_n))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_n))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_n)))))))
% 1.32/1.51 (assume a679 (forall ((V_v $$unsorted)) (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a680 (forall ((V_v $$unsorted)) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))))))
% 1.32/1.51 (assume a681 (forall ((V_x $$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)))))
% 1.32/1.51 (assume a682 (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_H_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_2))) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_H_2)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_H_2))) (= V_v_2 V_v_H_2))))))))
% 1.32/1.51 (assume a683 (forall ((V_k $$unsorted) (V_v_H $$unsorted) (V_v $$unsorted)) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H) V_k))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_H)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) V_k))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_H))) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H) V_k)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_v_H)) V_k))))))))
% 1.32/1.51 (assume a684 (forall ((V_x_2 $$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)))))
% 1.32/1.51 (assume a685 (forall ((V_v $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_v)))))))
% 1.32/1.51 (assume a686 (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))))))))
% 1.32/1.51 (assume a687 (forall ((V_x_2 $$unsorted) (V_nb_2 $$unsorted)) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_nb_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)) 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)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_nb_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_nb_2))))))))
% 1.32/1.51 (assume a688 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (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.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))))
% 1.32/1.51 (assume a689 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_d_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint B_x V_d_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_k_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_d_2)))))))))))
% 1.32/1.51 (assume a690 (forall ((V_k_2 $$unsorted) (V_P_2 $$unsorted) (V_d_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d_2) (=> (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x V_d_2))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_k_2)) (forall ((B_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP V_P_2 B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint B_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k_2) V_d_2)))))))))))
% 1.32/1.51 (assume a691 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)))))
% 1.32/1.51 (assume a692 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatfloor (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)) V_n)))
% 1.32/1.51 (assume a693 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_RealDef_Oreal)))
% 1.32/1.51 (assume a694 (= (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_RealDef_Oreal)))
% 1.32/1.51 (assume a695 (= (tptp.hAPP (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)))
% 1.32/1.51 (assume a696 (forall ((V_nb_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a697 (forall ((V_n $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))))
% 1.32/1.51 (assume a698 (forall ((V_ma_2 $$unsorted) (V_nb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_ma_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_nb_2 V_ma_2))))
% 1.32/1.51 (assume a699 (forall ((V_ma_2 $$unsorted) (V_nb_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2)) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_ma_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_nb_2) V_ma_2)))))
% 1.32/1.51 (assume a700 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (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.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_m)) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)))))
% 1.32/1.51 (assume a701 (forall ((V_ma_2 $$unsorted) (V_nb_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_ma_2)) (= V_nb_2 V_ma_2))))
% 1.32/1.51 (assume a702 (forall ((V_n $$unsorted)) (= (tptp.c_RComplete_Onatceiling (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)) V_n)))
% 1.32/1.51 (assume a703 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)))))
% 1.32/1.51 (assume a704 (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.32/1.51 (assume a705 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_m)) V_n) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)))))
% 1.32/1.51 (assume a706 (forall ((V_n $$unsorted) (V_m $$unsorted)) (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) V_m) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_m)) V_n))))
% 1.32/1.51 (assume a707 (forall ((V_x $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatceiling V_x))))))
% 1.32/1.51 (assume a708 (forall ((V_nb_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a709 (forall ((V_m $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_n) V_m)) (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat V_m V_n)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_m) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n))))))
% 1.32/1.51 (assume a710 (forall ((V_x $$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.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x))) V_x)))))
% 1.32/1.51 (assume a711 (forall ((V_a $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (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))))))
% 1.32/1.51 (assume a712 (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.hAPP (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)))))
% 1.32/1.51 (assume a713 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (= V_x (tptp.hAPP (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)))))
% 1.32/1.51 (assume a714 (forall ((V_nb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) V_nb_2))))
% 1.32/1.51 (assume a715 (forall ((V_ma_2 $$unsorted) (V_nb_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_nb_2 V_ma_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_ma_2))))))
% 1.32/1.51 (assume a716 (forall ((V_ma_2 $$unsorted) (V_nb_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_nb_2) V_ma_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_nb_2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_ma_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a717 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat V_a_2) (tptp.c_RComplete_Onatfloor V_x_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a_2)) V_x_2))))))
% 1.32/1.51 (assume a718 (forall ((V_a_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x_2)) V_a_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_x_2) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a_2)))))))
% 1.32/1.51 (assume a719 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.32/1.51 (assume a720 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a)) V_x)) (= (tptp.c_RComplete_Onatfloor (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))))
% 1.32/1.51 (assume a721 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_RComplete_Onatfloor V_x)))))
% 1.32/1.51 (assume a722 (forall ((V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a)) V_x)) (= (tptp.c_RComplete_Onatceiling (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a))) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a)))))
% 1.32/1.51 (assume a723 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_n)))))
% 1.32/1.51 (assume a724 (forall ((V_v $$unsorted)) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))) (= (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_v))))))
% 1.32/1.51 (assume a725 (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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatfloor V_x) V_a)))))
% 1.32/1.51 (assume a726 (forall ((V_n $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (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.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_z (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)))))
% 1.32/1.51 (assume a727 (forall ((V_x $$unsorted) (V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)) V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (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)))))
% 1.32/1.51 (assume a728 (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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_a))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_RComplete_Onatceiling V_x) V_a)))))
% 1.32/1.51 (assume a729 (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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) V_n))))))
% 1.32/1.51 (assume a730 (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.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat B_n (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) V_r)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_r (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) B_n)))))))
% 1.32/1.51 (assume a731 (forall ((V_n $$unsorted) (V_a $$unsorted) (V_r $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r V_a)) V_n) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_r) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)) V_a)))))
% 1.32/1.51 (assume a732 (forall ((V_a $$unsorted)) (= (tptp.c_Complex_Orcis (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_a) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Complex_Ocomplex))))
% 1.32/1.51 (assume a733 (forall ((V_b $$unsorted) (V_r2 $$unsorted) (V_a $$unsorted) (V_r1 $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) (tptp.c_Complex_Orcis V_r1 V_a)) (tptp.c_Complex_Orcis V_r2 V_b)) (tptp.c_Complex_Orcis (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_r1) V_r2) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_a V_b)))))
% 1.32/1.51 (assume a734 (forall ((V_X_2 $$unsorted) (V_M_2 $$unsorted) (T_a $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_RealVector_Oreal__normed__vector T_b) (tptp.class_Orderings_Oord T_a)) (=> (forall ((B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_M_2) B_n)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.c_Groups_Ominus__class_Ominus T_b (tptp.hAPP V_X_2 V_M_2) (tptp.hAPP V_X_2 B_n))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (forall ((B_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_M_2) B_n)) (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_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_RealVector_Onorm__class_Onorm T_b (tptp.hAPP V_X_2 V_M_2))))))))))
% 1.32/1.51 (assume a735 (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)))))))))
% 1.32/1.51 (assume a736 (forall ((V_k $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_k) (exists ((B_n $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) B_n) (= V_k (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) B_n)))))))
% 1.32/1.51 (assume a737 (forall ((V_n $$unsorted) (V_v $$unsorted)) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) V_n))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) V_n) (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) V_n)))))))
% 1.32/1.51 (assume a738 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a739 (forall ((V_z $$unsorted)) (=> (tptp.c_Nat__Numeral_Oneg V_z) (= (tptp.hAPP tptp.c_Int_Onat V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a740 (forall ((V_w $$unsorted)) (= (tptp.hAPP tptp.c_Int_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w))))
% 1.32/1.51 (assume a741 (forall ((V_v $$unsorted)) (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)))))
% 1.32/1.51 (assume a742 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y_2)) (= (= (tptp.hAPP tptp.c_Int_Onat V_x_2) (tptp.hAPP tptp.c_Int_Onat V_y_2)) (= V_x_2 V_y_2))))))
% 1.32/1.51 (assume a743 (forall ((V_P_2 $$unsorted)) (= (forall ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x1))) (forall ((B_x $$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)) B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP tptp.c_Int_Onat B_x))))))))
% 1.32/1.51 (assume a744 (forall ((V_P_2 $$unsorted)) (= (exists ((B_x1 $$unsorted)) (tptp.hBOOL (tptp.hAPP V_P_2 B_x1))) (exists ((B_x $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) B_x)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP tptp.c_Int_Onat B_x))))))))
% 1.32/1.51 (assume a745 (forall ((V_z_H_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_za_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z_H_2)) (= (= (tptp.hAPP tptp.c_Int_Onat V_za_2) (tptp.hAPP tptp.c_Int_Onat V_z_H_2)) (= V_za_2 V_z_H_2))))))
% 1.32/1.51 (assume a746 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a747 (= (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a748 (forall ((V_n $$unsorted)) (= (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_n)) V_n)))
% 1.32/1.51 (assume a749 (forall ((V_z $$unsorted)) (=> (not (tptp.c_Nat__Numeral_Oneg V_z)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP tptp.c_Int_Onat V_z)) V_z))))
% 1.32/1.51 (assume a750 (forall ((V_i_2 $$unsorted)) (= (= (tptp.hAPP tptp.c_Int_Onat V_i_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (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))))))
% 1.32/1.51 (assume a751 (forall ((V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= (tptp.hAPP tptp.c_Int_Onat V_z) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))
% 1.32/1.51 (assume a752 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_w_2) (tptp.hAPP tptp.c_Int_Onat V_za_2)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2)))))
% 1.32/1.51 (assume a753 (forall ((V_w_2 $$unsorted) (V_za_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_w_2) (tptp.hAPP tptp.c_Int_Onat V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2)))))
% 1.32/1.51 (assume a754 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y_2)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_x_2)) (tptp.hAPP tptp.c_Int_Onat V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2) V_y_2)))))))
% 1.32/1.51 (assume a755 (forall ((V_z $$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.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP tptp.c_Int_Onat V_z)) V_z))))
% 1.32/1.51 (assume a756 (forall ((V_za_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2) V_za_2) (and (= V_ma_2 (tptp.hAPP tptp.c_Int_Onat V_za_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_za_2))))))
% 1.32/1.51 (assume a757 (forall ((V_z $$unsorted)) (and (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP tptp.c_Int_Onat V_z)) V_z)) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z))) (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.hAPP tptp.c_Int_Onat V_z)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))))
% 1.32/1.51 (assume a758 (forall ((V_za_2 $$unsorted) (V_ma_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat V_ma_2 (tptp.hAPP tptp.c_Int_Onat V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2) V_za_2))))
% 1.32/1.51 (assume a759 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_za_2))))
% 1.32/1.51 (assume a760 (forall ((V_za_2 $$unsorted) (V_w_2 $$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_w_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_w_2) (tptp.hAPP tptp.c_Int_Onat V_za_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 V_za_2)))))
% 1.32/1.51 (assume a761 (forall ((V_y_2 $$unsorted) (V_x_2 $$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_x_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_y_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_x_2) (tptp.hAPP tptp.c_Int_Onat V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 V_y_2))))))
% 1.32/1.51 (assume a762 (forall ((V_za_2 $$unsorted) (V_w_2 $$unsorted)) (=> (or (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_w_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_za_2))) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_w_2)) (tptp.hAPP tptp.c_Int_Onat V_za_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_w_2) V_za_2))))))
% 1.32/1.51 (assume a763 (forall ((V_ma_2 $$unsorted) (V_w_2 $$unsorted)) (= (= (tptp.hAPP tptp.c_Int_Onat V_w_2) V_ma_2) (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_w_2)) (= V_w_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2))) (=> (not (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_w_2))) (= V_ma_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.32/1.51 (assume a764 (forall ((V_w_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= V_ma_2 (tptp.hAPP tptp.c_Int_Onat V_w_2)) (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_w_2)) (= V_w_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2))) (=> (not (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_w_2))) (= V_ma_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))))))
% 1.32/1.51 (assume a765 (forall ((V_i_2 $$unsorted) (V_P_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.hAPP tptp.c_Int_Onat V_i_2))) (and (forall ((B_n $$unsorted)) (=> (= V_i_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) B_n)) (tptp.hBOOL (tptp.hAPP V_P_2 B_n)))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_i_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.hBOOL (tptp.hAPP V_P_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))))
% 1.32/1.51 (assume a766 (forall ((V_z_H $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z_H)) (= (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_z V_z_H)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_z) (tptp.hAPP tptp.c_Int_Onat V_z_H)))))))
% 1.32/1.51 (assume a767 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_x) (tptp.hAPP tptp.c_Int_Onat V_y)) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x V_y)))))))
% 1.32/1.51 (assume a768 (forall ((V_z_H $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (= (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_z) V_z_H)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat V_z)) (tptp.hAPP tptp.c_Int_Onat V_z_H))))))
% 1.32/1.51 (assume a769 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat V_x)) (tptp.hAPP tptp.c_Int_Onat V_y)) (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_x) V_y)))))))
% 1.32/1.51 (assume a770 (forall ((V_v_2 $$unsorted) (V_ma_2 $$unsorted)) (= (= (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_2)) (and (= V_ma_2 (tptp.hAPP tptp.c_Int_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v_2)))))))
% 1.32/1.51 (assume a771 (forall ((V_z $$unsorted) (V_z_H $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z_H)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_z_H) V_z)) (= (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_z V_z_H)) (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_z) (tptp.hAPP tptp.c_Int_Onat V_z_H)))))))
% 1.32/1.51 (assume a772 (forall ((V_n $$unsorted) (V_z $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_z)) (= (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_z) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat V_z)) V_n)))))
% 1.32/1.51 (assume a773 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat V_x)) V_n) (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) V_x) V_n))))))
% 1.32/1.51 (assume a774 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_x)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_y)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_x) (tptp.hAPP tptp.c_Int_Onat V_y)) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Nat__Transfer_Otsub V_x V_y)))))))
% 1.32/1.51 (assume a775 (forall ((V_ma_2 $$unsorted) (V_w_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) V_w_2)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_w_2) V_ma_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_ma_2))))))
% 1.32/1.51 (assume a776 (forall ((V_w $$unsorted) (V_v $$unsorted)) (and (=> (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)))) (=> (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)) (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w))))))))
% 1.32/1.51 (assume a777 (forall ((V_n $$unsorted) (V_i $$unsorted)) (= (tptp.c_Int_Onat__aux V_i V_n) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.hAPP tptp.c_Int_Onat V_i) V_n))))
% 1.32/1.51 (assume a778 (tptp.c_Nat__Transfer_Otransfer__morphism tptp.tc_Int_Oint tptp.tc_Nat_Onat tptp.c_Int_Onat (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a779 (forall ((V_n $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)) (tptp.c_Transcendental_Oln V_x))))))
% 1.32/1.51 (assume a780 (forall ((V_z $$unsorted) (V_x $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d)) V_z))))
% 1.32/1.51 (assume a781 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (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_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y_2) (= (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.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 V_y_2))))))
% 1.32/1.51 (assume a782 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (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_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))))))
% 1.32/1.51 (assume a783 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) V_x))))
% 1.32/1.51 (assume a784 (= (tptp.c_Transcendental_Oln (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)))
% 1.32/1.51 (assume a785 (forall ((V_n $$unsorted) (V_m $$unsorted)) (=> (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_m) V_n)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_m) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a786 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_a)) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 1.32/1.51 (assume a787 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a788 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))))
% 1.32/1.51 (assume a789 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a790 (forall ((T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.32/1.51 (assume a791 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 1.32/1.51 (assume a792 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 1.32/1.51 (assume a793 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))))))
% 1.32/1.51 (assume a794 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.32/1.51 (assume a795 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) V_n)))))
% 1.32/1.51 (assume a796 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)))))
% 1.32/1.51 (assume a797 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a))))))
% 1.32/1.51 (assume a798 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) V_b)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_a) V_b))))))
% 1.32/1.51 (assume a799 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a))))))
% 1.32/1.51 (assume a800 (forall ((V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_n) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 1.32/1.51 (assume a801 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_a)))))))
% 1.32/1.51 (assume a802 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b))) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)))))))
% 1.32/1.51 (assume a803 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)))))))
% 1.32/1.51 (assume a804 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))))))
% 1.32/1.51 (assume a805 (forall ((V_d $$unsorted) (V_b $$unsorted) (V_c $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_c) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_b) V_d) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_c) V_d)))))))
% 1.32/1.51 (assume a806 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a807 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a_2)) (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a808 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) V_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a V_a) V_a)))))
% 1.32/1.51 (assume a809 (forall ((V_m $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) V_m))))
% 1.32/1.51 (assume a810 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n)))))
% 1.32/1.51 (assume a811 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oordered__ring__abs T_a) (=> (and (or (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_Ozero__class_Ozero T_a)))) (or (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_b) (tptp.c_Groups_Ozero__class_Ozero T_a))))) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_b)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))))))
% 1.32/1.51 (assume a812 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_x)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_y)) V_x) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_y) V_x)))))))
% 1.32/1.51 (assume a813 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$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)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) V_n))))))
% 1.32/1.51 (assume a814 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_b)))))))
% 1.32/1.51 (assume a815 (forall ((V_d $$unsorted) (V_c $$unsorted) (V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Oordered__ab__group__add__abs T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a V_a V_b) (tptp.c_Groups_Oplus__class_Oplus T_a V_c V_d)))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_c)) (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_b V_d))))))))
% 1.32/1.51 (assume a816 (forall ((V_r_2 $$unsorted) (V_a_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_x_2 V_a_2)) V_r_2) (and (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a_2 V_r_2) V_x_2) (tptp.c_Orderings_Oord__class_Oless T_a V_x_2 (tptp.c_Groups_Oplus__class_Oplus T_a V_a_2 V_r_2)))))))
% 1.32/1.51 (assume a817 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_n $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_n) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) (tptp.c_Groups_Oabs__class_Oabs T_a V_y))) (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_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) V_n))))))))
% 1.32/1.51 (assume a818 (forall ((V_x $$unsorted) (V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_x)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_w)))))))
% 1.32/1.51 (assume a819 (forall ((V_za_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_za_2) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)) (= V_za_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a820 (forall ((V_z $$unsorted) (V_w $$unsorted)) (= (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_w) V_z))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_w))) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_z))))))
% 1.32/1.51 (assume a821 (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)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x)) V_n)))))
% 1.32/1.51 (assume a822 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (=> (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_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)))))))
% 1.32/1.51 (assume a823 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x))))))
% 1.32/1.51 (assume a824 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x) (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)))))
% 1.32/1.51 (assume a825 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x_2)))))
% 1.32/1.51 (assume a826 (forall ((V_x_2 $$unsorted)) (=> (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))))))
% 1.32/1.51 (assume a827 (forall ((V_x_2 $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x_2) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x_2 (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a828 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (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))))))
% 1.32/1.51 (assume a829 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Transcendental_Oln V_x)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x)))))
% 1.32/1.51 (assume a830 (forall ((V_nb_2 $$unsorted) (V_x_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Int_Oint) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint V_x_2)) V_nb_2)) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))) (= V_nb_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))))))
% 1.32/1.51 (assume a831 (forall ((V_x_2 $$unsorted)) (=> (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))))))
% 1.32/1.51 (assume a832 (forall ((V_x $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (tptp.c_Transcendental_Oln V_x))) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))))
% 1.32/1.51 (assume a833 (forall ((V_y $$unsorted) (V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_y) (= (tptp.c_Transcendental_Oln (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_x) V_y)) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Transcendental_Oln V_x) (tptp.c_Transcendental_Oln V_y)))))))
% 1.32/1.51 (assume a834 (forall ((V_x $$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.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) V_x))) V_x)))))
% 1.32/1.51 (assume a835 (forall ((V_x $$unsorted) (V_z $$unsorted) (V_d $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) V_d) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_z (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_x (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_x V_z)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))) V_d))))))
% 1.32/1.51 (assume a836 (forall ((V_X_2 $$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.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.hAPP V_X_2 B_n))) B_K)))))))))
% 1.32/1.51 (assume a837 (forall ((V_X_2 $$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 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_m) B_n)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP V_X_2 B_m)) (tptp.hAPP V_X_2 B_n)))))))))
% 1.32/1.51 (assume a838 (forall ((V_a $$unsorted) (V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (tptp.c_Complex_Orcis V_r V_a)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))
% 1.32/1.51 (assume a839 (forall ((V_x $$unsorted)) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_x)) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_x))))
% 1.32/1.51 (assume a840 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (= (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)) (tptp.c_RealVector_Onorm__class_Onorm T_a V_a)))))
% 1.32/1.51 (assume a841 (forall ((V_y $$unsorted) (V_x $$unsorted) (V_c $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_c) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) V_c) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_y)))) (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a842 (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_RealVector_Oreal__normed__algebra__1 T_a)) (= (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal V_w))))))
% 1.32/1.51 (assume a843 (forall ((V_x $$unsorted)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) V_x))))
% 1.32/1.51 (assume a844 (forall ((V_b $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm T_a V_a) (tptp.c_RealVector_Onorm__class_Onorm T_a V_b)))) (tptp.c_RealVector_Onorm__class_Onorm T_a (tptp.c_Groups_Ominus__class_Ominus T_a V_a V_b)))))))
% 1.32/1.51 (assume a845 (forall ((V_x $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x)))))
% 1.32/1.51 (assume a846 (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 $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_K) (forall ((B_n $$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)))))))))
% 1.32/1.51 (assume a847 (forall ((V_X_2 $$unsorted) (V_K_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_RealVector_Oreal__normed__vector T_a) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) V_K_2) (=> (forall ((B_n $$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))))))
% 1.32/1.51 (assume a848 (forall ((V_r $$unsorted)) (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_RealDef_Oreal V_r) (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_r))))
% 1.32/1.51 (assume a849 (forall ((V_b $$unsorted) (V_x $$unsorted) (V_a $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_a V_x) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal V_x V_b) (exists ((B_d $$unsorted)) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal) B_d) (forall ((B_y $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal (tptp.c_Groups_Ominus__class_Ominus tptp.tc_RealDef_Oreal V_x B_y)) B_d) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal V_a) B_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal B_y) V_b)))))))))))
% 1.32/1.51 (assume a850 (forall ((V_k_2 $$unsorted) (V_f_2 $$unsorted) (V_nb_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i V_nb_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP V_f_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_i (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.hAPP V_f_2 B_i)))) (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 (tptp.hAPP V_f_2 (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_Int_Oint V_k_2) (tptp.hAPP V_f_2 V_nb_2))) (exists ((B_i $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i) V_nb_2)) (= (tptp.hAPP V_f_2 B_i) V_k_2))))))))
% 1.32/1.51 (assume a851 (forall ((V_k_2 $$unsorted) (V_f_2 $$unsorted) (V_nb_2 $$unsorted)) (=> (forall ((B_i $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat B_i V_nb_2) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Oabs__class_Oabs tptp.tc_Int_Oint (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.hAPP V_f_2 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat B_i (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.hAPP V_f_2 B_i)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.hAPP V_f_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) V_k_2)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) (tptp.hAPP V_f_2 V_nb_2))) (exists ((B_i $$unsorted)) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat B_i) V_nb_2)) (= (tptp.hAPP V_f_2 B_i) V_k_2))))))))
% 1.32/1.51 (assume a852 (forall ((V_k $$unsorted) (V_v_H $$unsorted) (V_v $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) V_k)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) V_k)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_v_H))) V_k))))))
% 1.32/1.51 (assume a853 (not (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OPls))))
% 1.32/1.51 (assume a854 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls tptp.c_Int_OPls)))
% 1.32/1.51 (assume a855 (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k tptp.c_Int_OPls) V_k)))
% 1.32/1.51 (assume a856 (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint tptp.c_Int_OPls V_k) V_k)))
% 1.32/1.51 (assume a857 (= tptp.c_Int_OPls (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))
% 1.32/1.51 (assume a858 (forall ((V_w $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) tptp.c_Int_OPls) V_w) tptp.c_Int_OPls)))
% 1.32/1.51 (assume a859 (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls) tptp.c_Int_OPls)))
% 1.32/1.51 (assume a860 (forall ((V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k tptp.c_Int_OPls) V_k)))
% 1.32/1.51 (assume a861 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OPls)))
% 1.32/1.51 (assume a862 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint))))
% 1.32/1.51 (assume a863 (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat tptp.c_Int_OPls)))
% 1.32/1.51 (assume a864 (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat tptp.c_Int_OPls) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a865 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) V_a) V_a))))
% 1.32/1.51 (assume a866 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a V_a (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)) V_a))))
% 1.32/1.51 (assume a867 (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls)))))
% 1.32/1.51 (assume a868 (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a tptp.c_Int_OPls) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.32/1.51 (assume a869 (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2) tptp.c_Int_OPls)))))
% 1.32/1.51 (assume a870 (forall ((V_v_2 $$unsorted)) (= (= (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2) tptp.c_Int_OPls)))))
% 1.32/1.51 (assume a871 (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_2 V_v_H_2) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_H_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_2 V_v_H_2)))))
% 1.32/1.51 (assume a872 (forall ((V_v_H_2 $$unsorted) (V_v_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H_2))) (=> (not (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2) V_v_H_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_v_2) tptp.c_Int_OPls))))))
% 1.32/1.51 (assume a873 (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint tptp.c_Int_OPls))))
% 1.32/1.51 (assume a874 (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls) V_y_2))))))
% 1.32/1.51 (assume a875 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2)) (tptp.c_Groups_Ozero__class_Ozero T_a))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_x_2) tptp.c_Int_OPls))))))
% 1.32/1.51 (assume a876 (forall ((V_x_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Int_Onumber__class_Onumber__of T_a V_x_2) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x_2 tptp.c_Int_OPls)))))
% 1.32/1.51 (assume a877 (forall ((V_y_2 $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_y_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_y_2)))))
% 1.32/1.51 (assume a878 (forall ((V_v_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_v_2))))
% 1.32/1.51 (assume a879 (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_H tptp.c_Int_OPls) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v_H tptp.c_Int_OPls)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_v V_v_H)))))))))
% 1.32/1.51 (assume a880 (forall ((V_v_H $$unsorted) (V_v $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v_H)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_v) V_v_H)))))))
% 1.32/1.51 (assume a881 (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))
% 1.32/1.51 (assume a882 (forall ((V_v $$unsorted)) (and (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (=> (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_v tptp.c_Int_OPls)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat V_v) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_Osucc V_v)))))))
% 1.32/1.51 (assume a883 (forall ((V_n $$unsorted)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n))))
% 1.32/1.51 (assume a884 (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))))
% 1.32/1.51 (assume a885 (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))))
% 1.32/1.51 (assume a886 (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls V_k_2))))
% 1.32/1.51 (assume a887 (= (tptp.c_Int_OBit0 tptp.c_Int_OPls) tptp.c_Int_OPls))
% 1.32/1.51 (assume a888 (= (tptp.c_Int_Osucc tptp.c_Int_OPls) (tptp.c_Int_OBit1 tptp.c_Int_OPls)))
% 1.32/1.51 (assume a889 (forall ((V_l $$unsorted)) (not (= tptp.c_Int_OPls (tptp.c_Int_OBit1 V_l)))))
% 1.32/1.51 (assume a890 (forall ((V_l_2 $$unsorted)) (= (= tptp.c_Int_OPls (tptp.c_Int_OBit0 V_l_2)) (= tptp.c_Int_OPls V_l_2))))
% 1.32/1.51 (assume a891 (forall ((V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) tptp.c_Int_OPls))))
% 1.32/1.51 (assume a892 (forall ((V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) tptp.c_Int_OPls) (= V_k_2 tptp.c_Int_OPls))))
% 1.32/1.51 (assume a893 (forall ((V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2)) tptp.c_Int_OPls)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) tptp.c_Int_OPls)))))
% 1.32/1.51 (assume a894 (forall ((V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls) (tptp.c_Int_OBit1 V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls) V_k_2)))))
% 1.32/1.51 (assume a895 (forall ((V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls) (tptp.c_Int_OBit0 V_k_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls) V_k_2)))))
% 1.32/1.51 (assume a896 (forall ((V_l $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint tptp.c_Int_OPls V_l)))))
% 1.32/1.51 (assume a897 (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))
% 1.32/1.51 (assume a898 (tptp.c_Orderings_Oord__class_Oless tptp.tc_Nat_Onat (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))
% 1.32/1.51 (assume a899 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (not (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a900 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a901 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y)) (tptp.c_Orderings_Oord__class_Oless T_a V_x V_y))))))
% 1.32/1.51 (assume a902 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (or (not (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a))) (not (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))))
% 1.32/1.51 (assume a903 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (not (tptp.c_Orderings_Oord__class_Oless T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a904 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))))
% 1.32/1.51 (assume a905 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (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)))))))
% 1.32/1.51 (assume a906 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z)))
% 1.32/1.51 (assume a907 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted)) (= (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_y_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_RealDef_Oreal))))))
% 1.32/1.51 (assume a908 (forall ((V_n $$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.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) V_n))))))
% 1.32/1.51 (assume a909 (forall ((V_w $$unsorted) (T_b $$unsorted)) (=> (and (tptp.class_Groups_Omonoid__mult T_b) (tptp.class_Int_Onumber T_b)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_w)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_b) (tptp.c_Int_Onumber__class_Onumber__of T_b V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_b V_w))))))
% 1.32/1.51 (assume a910 (forall ((V_y_2 $$unsorted) (V_x_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.c_Groups_Ozero__class_Ozero T_a)) (and (= V_x_2 (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_y_2 (tptp.c_Groups_Ozero__class_Ozero T_a)))))))
% 1.32/1.51 (assume a911 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (=> (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)) (= V_x V_y)))))))
% 1.32/1.51 (assume a912 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__semidom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) V_y)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a V_x) V_y)))))))
% 1.32/1.51 (assume a913 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))))
% 1.32/1.51 (assume a914 (forall ((V_nb_2 $$unsorted)) (= (tptp.c_Parity_Oeven__odd__class_Oeven tptp.tc_Nat_Onat V_nb_2) (exists ((B_m $$unsorted)) (= V_nb_2 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) B_m))))))
% 1.32/1.51 (assume a915 (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))
% 1.32/1.51 (assume a916 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_z V_z))))
% 1.32/1.51 (assume a917 (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) V_z) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Nat_Onat V_z V_z))))
% 1.32/1.51 (assume a918 (forall ((V_n $$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.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) 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_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))
% 1.32/1.51 (assume a919 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.32/1.51 (assume a920 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Groups_Omonoid__mult T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) V_a)))))
% 1.32/1.51 (assume a921 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Ocomm__semiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_x) V_x) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))
% 1.32/1.51 (assume a922 (forall ((V_a_2 $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Oring__1__no__zero__divisors T_a) (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a_2) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Ozero__class_Ozero T_a)) (= V_a_2 (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a923 (forall ((T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Ozero__class_Ozero T_a)))))
% 1.32/1.51 (assume a924 (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))
% 1.32/1.51 (assume a925 (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_z) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))))
% 1.32/1.51 (assume a926 (forall ((V_z $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z) (tptp.c_Groups_Oplus__class_Oplus T_a V_z V_z)))))
% 1.32/1.51 (assume a927 (forall ((V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))
% 1.32/1.51 (assume a928 (forall ((V_n $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_RealDef_Oreal (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)))))
% 1.32/1.51 (assume a929 (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))
% 1.32/1.51 (assume a930 (forall ((V_n $$unsorted) (T_a $$unsorted)) (=> (and (tptp.class_Int_Onumber__ring T_a) (tptp.class_Rings_Olinordered__idom T_a)) (tptp.c_Orderings_Oord__class_Oless T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) V_n) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)))))
% 1.32/1.51 (assume a931 (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))) (tptp.hAPP tptp.c_Int_Onat (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))
% 1.32/1.51 (assume a932 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oabs__class_Oabs T_a V_a)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))
% 1.32/1.51 (assume a933 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (= (tptp.c_Groups_Oabs__class_Oabs T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))
% 1.32/1.51 (assume a934 (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit1 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) V_k) V_k))))
% 1.32/1.51 (assume a935 (forall ((V_w_2 $$unsorted)) (= (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_w_2))) (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w_2)))))
% 1.32/1.51 (assume a936 (forall ((V_w_2 $$unsorted)) (= (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_w_2))) (tptp.c_Nat__Numeral_Oneg (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_w_2)))))
% 1.32/1.51 (assume a937 (forall ((V_n $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint V_n))) (and (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_n)))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_n))))))))
% 1.32/1.51 (assume a938 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k V_l)))))
% 1.32/1.51 (assume a939 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k V_l)))))
% 1.32/1.51 (assume a940 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Ominus__class_Ominus tptp.tc_Int_Oint V_k V_l)))))
% 1.32/1.51 (assume a941 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Int_OBit0 V_l_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) V_l_2)))))
% 1.32/1.51 (assume a942 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2)) (tptp.c_Int_OBit1 V_l_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) V_l_2)))))
% 1.32/1.51 (assume a943 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2)) (tptp.c_Int_OBit0 V_k2_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2) V_k2_2)))))
% 1.32/1.51 (assume a944 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2)) (tptp.c_Int_OBit1 V_k2_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2) V_k2_2)))))
% 1.32/1.51 (assume a945 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Int_OBit1 V_l_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) V_l_2)))))
% 1.32/1.51 (assume a946 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2)) (tptp.c_Int_OBit1 V_k2_2))) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2) V_k2_2)))))
% 1.32/1.51 (assume a947 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (= V_k_2 V_l_2))))
% 1.32/1.51 (assume a948 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (= (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (= V_k_2 V_l_2))))
% 1.32/1.51 (assume a949 (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)))))
% 1.32/1.51 (assume a950 (forall ((V_l $$unsorted) (V_k $$unsorted)) (not (= (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)))))
% 1.32/1.51 (assume a951 (forall ((V_k $$unsorted)) (= (tptp.c_Int_Osucc (tptp.c_Int_OBit1 V_k)) (tptp.c_Int_OBit0 (tptp.c_Int_Osucc V_k)))))
% 1.32/1.51 (assume a952 (forall ((V_k $$unsorted)) (= (tptp.c_Int_Osucc (tptp.c_Int_OBit0 V_k)) (tptp.c_Int_OBit1 V_k))))
% 1.32/1.51 (assume a953 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Int_OBit0 V_k)) V_l) (tptp.c_Int_OBit0 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_l)))))
% 1.32/1.51 (assume a954 (forall ((V_k $$unsorted)) (= (tptp.c_Int_OBit0 V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_k))))
% 1.32/1.51 (assume a955 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))))
% 1.32/1.51 (assume a956 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))))
% 1.32/1.51 (assume a957 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit0 V_l)) (tptp.c_Int_OBit1 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k V_l)))))
% 1.32/1.51 (assume a958 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k) (tptp.c_Int_OBit1 V_l)) (tptp.c_Int_OBit0 (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k (tptp.c_Int_Osucc V_l))))))
% 1.32/1.51 (assume a959 (forall ((V_l $$unsorted) (V_k $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Int_OBit1 V_k)) V_l) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) V_k) V_l)) V_l))))
% 1.32/1.51 (assume a960 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))))
% 1.32/1.51 (assume a961 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))))
% 1.32/1.51 (assume a962 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit0 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))))
% 1.32/1.51 (assume a963 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))))
% 1.32/1.51 (assume a964 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit0 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))))
% 1.32/1.51 (assume a965 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))))
% 1.32/1.51 (assume a966 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k_2) (tptp.c_Int_OBit1 V_l_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k_2) V_l_2)))))
% 1.32/1.51 (assume a967 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_k1_2) (tptp.c_Int_OBit1 V_k2_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint V_k1_2) V_k2_2)))))
% 1.32/1.51 (assume a968 (forall ((V_l_2 $$unsorted) (V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2)) (tptp.c_Int_OBit0 V_l_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 V_l_2))))
% 1.32/1.51 (assume a969 (forall ((V_k2_2 $$unsorted) (V_k1_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k1_2)) (tptp.c_Int_OBit0 V_k2_2))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k1_2 V_k2_2))))
% 1.32/1.51 (assume a970 (forall ((V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_w_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a971 (forall ((V_w_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint (tptp.c_Int_OBit0 V_w_2) (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_w_2 (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a972 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Oplus__class_Oplus T_a V_x V_y)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x)) V_y))))))
% 1.32/1.51 (assume a973 (forall ((V_k $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (=> (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.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) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_k))) (tptp.c_Groups_Ozero__class_Ozero T_a))) (= V_a (tptp.c_Groups_Ozero__class_Ozero T_a))))))
% 1.32/1.51 (assume a974 (forall ((V_n $$unsorted) (V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Olinordered__idom T_a) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq T_a (tptp.c_Groups_Ozero__class_Ozero T_a)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_n)))))))
% 1.32/1.51 (assume a975 (forall ((V_x $$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.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_x (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (or (= V_x (tptp.c_Groups_Ozero__class_Ozero tptp.tc_Int_Oint)) (= V_x (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))))
% 1.32/1.51 (assume a976 (forall ((V_n $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) V_n)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) V_n)))))
% 1.32/1.51 (assume a977 (forall ((V_y $$unsorted) (V_x $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal V_x V_y)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.c_Groups_Oplus__class_Oplus tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_RealDef_Oreal) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_RealDef_Oreal (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x)) V_y)))))
% 1.32/1.51 (assume a978 (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Ozero__class_Ozero T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 1.32/1.51 (assume a979 (forall ((V_x $$unsorted)) (=> (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_Groups_Oabs__class_Oabs tptp.tc_RealDef_Oreal V_x) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_RealDef_Oreal) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))
% 1.32/1.51 (assume a980 (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 V_w)) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w))))))
% 1.32/1.51 (assume a981 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a) V_a))))
% 1.32/1.51 (assume a982 (forall ((V_a $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) V_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))) V_a))))
% 1.32/1.51 (assume a983 (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))
% 1.32/1.51 (assume a984 (forall ((T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit1 tptp.c_Int_OPls)) (tptp.c_Groups_Oone__class_Oone T_a)))))
% 1.32/1.51 (assume a985 (forall ((V_k_2 $$unsorted)) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint tptp.c_Int_OPls (tptp.c_Int_OBit1 V_k_2)) (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint tptp.c_Int_OPls) V_k_2)))))
% 1.32/1.51 (assume a986 (forall ((V_k_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.c_Orderings_Oord__class_Oless__eq tptp.tc_Int_Oint (tptp.c_Int_OBit1 V_k_2)) tptp.c_Int_OPls)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_Int_Oint V_k_2 tptp.c_Int_OPls))))
% 1.32/1.51 (assume a987 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 tptp.c_Int_OPls))))
% 1.32/1.51 (assume a988 (= (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 tptp.c_Int_OPls)) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))
% 1.32/1.51 (assume a989 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 tptp.c_Int_OPls))))
% 1.32/1.51 (assume a990 (forall ((V_y $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) (tptp.c_Groups_Ominus__class_Ominus T_a V_x V_y)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.c_Groups_Ominus__class_Ominus T_a (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_x) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower T_a) V_y) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x)) V_y))))))
% 1.32/1.51 (assume a991 (forall ((V_k $$unsorted)) (= (tptp.c_Int_Osucc V_k) (tptp.c_Groups_Oplus__class_Oplus tptp.tc_Int_Oint V_k (tptp.c_Groups_Oone__class_Oone tptp.tc_Int_Oint)))))
% 1.32/1.51 (assume a992 (forall ((V_x $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Rings_Osemiring__1 T_a) (=> (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.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.hAPP tptp.c_Int_Onat (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Int_Oint) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_x))) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.hAPP tptp.c_Int_Onat V_x)) (tptp.hAPP (tptp.c_Nat_Osemiring__1__class_Oof__nat T_a) (tptp.hAPP tptp.c_Int_Onat V_x))))))))
% 1.32/1.51 (assume a993 (forall ((V_w $$unsorted) (T_a $$unsorted)) (=> (tptp.class_Int_Onumber__ring T_a) (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes T_a) (tptp.c_Groups_Oplus__class_Oplus T_a (tptp.c_Groups_Oone__class_Oone T_a) (tptp.c_Groups_Oone__class_Oone T_a))) (tptp.c_Int_Onumber__class_Onumber__of T_a V_w)) (tptp.c_Int_Onumber__class_Onumber__of T_a (tptp.c_Int_OBit0 V_w))))))
% 1.32/1.51 (assume a994 (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_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (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_a)) V_a)))))
% 1.32/1.51 (assume a995 (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_Int_Onumber__class_Onumber__of tptp.tc_Int_Oint (tptp.c_Int_OBit1 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))
% 1.32/1.51 (assume a996 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Opreorder T_1) (tptp.class_Orderings_Opreorder (tptp.tc_fun T_2 T_1)))))
% 1.32/1.51 (assume a997 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oorder T_1) (tptp.class_Orderings_Oorder (tptp.tc_fun T_2 T_1)))))
% 1.32/1.51 (assume a998 (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (tptp.class_Orderings_Oord T_1) (tptp.class_Orderings_Oord (tptp.tc_fun T_2 T_1)))))
% 1.32/1.51 (assume a999 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1000 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1001 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1002 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1003 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1004 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1005 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1006 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1007 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1008 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1009 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1010 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1011 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1012 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1013 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1014 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1015 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1016 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1017 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1018 (tptp.class_Rings_Olinordered__semiring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1019 (tptp.class_Rings_Olinordered__semidom tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1020 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1021 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1022 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1023 (tptp.class_Rings_Oordered__semiring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1024 (tptp.class_Rings_Oordered__ring__abs tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1025 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1026 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1027 (tptp.class_Rings_Olinordered__ring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1028 (tptp.class_Rings_Olinordered__idom tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1029 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1030 (tptp.class_Rings_Ocomm__semiring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1031 (tptp.class_Nat_Osemiring__char__0 tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1032 (tptp.class_Groups_Oab__group__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1033 (tptp.class_Rings_Ozero__neq__one tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1034 (tptp.class_Rings_Oordered__ring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1035 (tptp.class_Orderings_Opreorder tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1036 (tptp.class_Orderings_Olinorder tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1037 (tptp.class_Groups_Omonoid__mult tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1038 (tptp.class_Groups_Omonoid__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1039 (tptp.class_Rings_Osemiring__1 tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1040 (tptp.class_Rings_Osemiring__0 tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1041 (tptp.class_Groups_Ogroup__add tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1042 (tptp.class_Rings_Omult__zero tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1043 (tptp.class_Orderings_Oorder tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1044 (tptp.class_Int_Oring__char__0 tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1045 (tptp.class_Int_Onumber__ring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1046 (tptp.class_Rings_Osemiring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1047 (tptp.class_Orderings_Oord tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1048 (tptp.class_Rings_Oring__1 tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1049 (tptp.class_Power_Opower tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1050 (tptp.class_Groups_Ozero tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1051 (tptp.class_Rings_Oring tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1052 (tptp.class_Int_Onumber tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1053 (tptp.class_Groups_Oone tptp.tc_Int_Oint))
% 1.32/1.51 (assume a1054 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1055 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1056 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1057 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1058 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1059 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1060 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1061 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1062 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1063 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1064 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1065 (tptp.class_Rings_Olinordered__semiring tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1066 (tptp.class_Rings_Olinordered__semidom tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1067 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1068 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1069 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1070 (tptp.class_Rings_Oordered__semiring tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1071 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1072 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1073 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1074 (tptp.class_Rings_Ocomm__semiring tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1075 (tptp.class_Nat_Osemiring__char__0 tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1076 (tptp.class_Rings_Ozero__neq__one tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1077 (tptp.class_Orderings_Opreorder tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1078 (tptp.class_Orderings_Olinorder tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1079 (tptp.class_Groups_Omonoid__mult tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1080 (tptp.class_Groups_Omonoid__add tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1081 (tptp.class_Rings_Osemiring__1 tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1082 (tptp.class_Rings_Osemiring__0 tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1083 (tptp.class_Rings_Omult__zero tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1084 (tptp.class_Orderings_Oorder tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1085 (tptp.class_Rings_Osemiring tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1086 (tptp.class_Orderings_Oord tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1087 (tptp.class_Power_Opower tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1088 (tptp.class_Groups_Ozero tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1089 (tptp.class_Int_Onumber tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1090 (tptp.class_Groups_Oone tptp.tc_Nat_Onat))
% 1.32/1.51 (assume a1091 (tptp.class_Orderings_Opreorder tptp.tc_HOL_Obool))
% 1.32/1.51 (assume a1092 (tptp.class_Orderings_Oorder tptp.tc_HOL_Obool))
% 1.32/1.51 (assume a1093 (tptp.class_Orderings_Oord tptp.tc_HOL_Obool))
% 1.32/1.51 (assume a1094 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1095 (tptp.class_Groups_Oordered__cancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1096 (tptp.class_Groups_Oordered__ab__semigroup__add__imp__le tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1097 (tptp.class_Rings_Olinordered__comm__semiring__strict tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1098 (tptp.class_Rings_Olinordered__semiring__1__strict tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1099 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1100 (tptp.class_Rings_Olinordered__semiring__strict tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1101 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1102 (tptp.class_Groups_Oordered__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1103 (tptp.class_Groups_Oordered__ab__group__add__abs tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1104 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1105 (tptp.class_Groups_Oordered__comm__monoid__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1106 (tptp.class_Groups_Olinordered__ab__group__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1107 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1108 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1109 (tptp.class_Rings_Oordered__cancel__semiring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1110 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1111 (tptp.class_Rings_Olinordered__ring__strict tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1112 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1113 (tptp.class_Rings_Oordered__comm__semiring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1114 (tptp.class_Rings_Olinordered__semiring__1 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1115 (tptp.class_Groups_Oordered__ab__group__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1116 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1117 (tptp.class_Rings_Olinordered__semiring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1118 (tptp.class_Rings_Olinordered__semidom tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1119 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1120 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1121 (tptp.class_Groups_Oab__semigroup__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1122 (tptp.class_Rings_Oordered__semiring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1123 (tptp.class_Rings_Oordered__ring__abs tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1124 (tptp.class_Rings_Ono__zero__divisors tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1125 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1126 (tptp.class_Rings_Olinordered__ring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1127 (tptp.class_Rings_Olinordered__idom tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1128 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1129 (tptp.class_Rings_Ocomm__semiring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1130 (tptp.class_Nat_Osemiring__char__0 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1131 (tptp.class_Groups_Oab__group__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1132 (tptp.class_Rings_Ozero__neq__one tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1133 (tptp.class_Rings_Oordered__ring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1134 (tptp.class_Orderings_Opreorder tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1135 (tptp.class_Orderings_Olinorder tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1136 (tptp.class_Groups_Omonoid__mult tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1137 (tptp.class_Groups_Omonoid__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1138 (tptp.class_Rings_Osemiring__1 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1139 (tptp.class_Rings_Osemiring__0 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1140 (tptp.class_Groups_Ogroup__add tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1141 (tptp.class_Rings_Omult__zero tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1142 (tptp.class_Orderings_Oorder tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1143 (tptp.class_Int_Oring__char__0 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1144 (tptp.class_Int_Onumber__ring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1145 (tptp.class_Rings_Osemiring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1146 (tptp.class_Orderings_Oord tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1147 (tptp.class_Rings_Oring__1 tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1148 (tptp.class_Power_Opower tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1149 (tptp.class_Groups_Ozero tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1150 (tptp.class_Rings_Oring tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1151 (tptp.class_Int_Onumber tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1152 (tptp.class_Groups_Oone tptp.tc_RealDef_Oreal))
% 1.32/1.51 (assume a1153 (tptp.class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1154 (tptp.class_RealVector_Oreal__normed__div__algebra tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1155 (tptp.class_RealVector_Oreal__normed__algebra__1 tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1156 (tptp.class_RealVector_Oreal__normed__algebra tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1157 (tptp.class_Groups_Ocancel__ab__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1158 (tptp.class_Rings_Oring__1__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1159 (tptp.class_RealVector_Oreal__normed__vector tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1160 (tptp.class_Rings_Oring__no__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1161 (tptp.class_Groups_Ocancel__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1162 (tptp.class_Groups_Oab__semigroup__mult tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1163 (tptp.class_Groups_Ocomm__monoid__mult tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1164 (tptp.class_Groups_Oab__semigroup__add tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1165 (tptp.class_Rings_Ono__zero__divisors tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1166 (tptp.class_Groups_Ocomm__monoid__add tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1167 (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1168 (tptp.class_Rings_Ocomm__semiring tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1169 (tptp.class_Nat_Osemiring__char__0 tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1170 (tptp.class_Groups_Oab__group__add tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1171 (tptp.class_Rings_Ozero__neq__one tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1172 (tptp.class_Groups_Omonoid__mult tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1173 (tptp.class_Groups_Omonoid__add tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1174 (tptp.class_Rings_Osemiring__1 tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1175 (tptp.class_Rings_Osemiring__0 tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1176 (tptp.class_Groups_Ogroup__add tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1177 (tptp.class_Rings_Omult__zero tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1178 (tptp.class_Int_Oring__char__0 tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1179 (tptp.class_Int_Onumber__ring tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1180 (tptp.class_Rings_Osemiring tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1181 (tptp.class_Rings_Oring__1 tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1182 (tptp.class_Power_Opower tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1183 (tptp.class_Groups_Ozero tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1184 (tptp.class_Rings_Oring tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1185 (tptp.class_Int_Onumber tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1186 (tptp.class_Groups_Oone tptp.tc_Complex_Ocomplex))
% 1.32/1.51 (assume a1187 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.32/1.51 (assume a1188 true)
% 1.32/1.51 (step t1 (cl (not (= (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) (not (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule equiv_pos2)
% 1.32/1.51 (step t2 (cl (= (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule refl)
% 1.32/1.51 (step t3 (cl (= (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule refl)
% 1.32/1.51 (step t4 (cl (= (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) true) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule equiv_simplify)
% 1.32/1.51 (step t5 (cl (not (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) true)) (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule equiv1 :premises (t4))
% 1.32/1.51 (step t6 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))) :rule all_simplify)
% 1.32/1.51 (step t7 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule refl)
% 1.32/1.51 (step t8 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule all_simplify)
% 1.32/1.51 (step t9 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule cong :premises (t7 t8))
% 1.32/1.51 (step t10 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) true)) :rule all_simplify)
% 1.32/1.51 (step t11 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) true)) :rule trans :premises (t9 t10))
% 1.32/1.51 (step t12 (cl (= (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) true)) :rule trans :premises (t6 t11))
% 1.32/1.51 (step t13 (cl (= (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule resolution :premises (t5 t12))
% 1.32/1.51 (step t14 (cl (= (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))) :rule refl)
% 1.32/1.51 (step t15 (cl (= (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))))) :rule refl)
% 1.32/1.51 (step t16 (cl (= (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule refl)
% 1.32/1.51 (step t17 (cl (= (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) :rule cong :premises (t2 t3 t13 t14 t15 t16))
% 1.32/1.51 (step t18 (cl (not (= (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) (not (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule equiv_pos2)
% 1.32/1.51 (step t19 (cl (= (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule refl)
% 1.32/1.51 (step t20 (cl (= (= (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))) :rule equiv_simplify)
% 1.32/1.51 (step t21 (cl (= (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) (not (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))) :rule equiv2 :premises (t20))
% 1.32/1.51 (step t22 (cl (not (not (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule not_not)
% 1.32/1.51 (step t23 (cl (= (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t21 t22))
% 1.32/1.51 (step t24 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule implies_neg1)
% 1.32/1.51 (anchor :step t25)
% 1.32/1.51 (assume t25.a0 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.32/1.51 (assume t25.a1 (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))
% 1.32/1.51 (assume t25.a2 (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))
% 1.32/1.51 (assume t25.a3 (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))
% 1.32/1.51 (assume t25.a4 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume t25.a5 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.32/1.51 (step t25.t1 (cl (not (= (= false true) false)) (not (= false true)) false) :rule equiv_pos2)
% 1.32/1.51 (step t25.t2 (cl (= (= false true) false)) :rule all_simplify)
% 1.32/1.51 (step t25.t3 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) false) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule equiv_simplify)
% 1.32/1.51 (step t25.t4 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) false) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule equiv2 :premises (t25.t3))
% 1.32/1.51 (step t25.t5 (cl (not (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) :rule not_not)
% 1.32/1.51 (step t25.t6 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) false) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) :rule resolution :premises (t25.t4 t25.t5))
% 1.32/1.51 (step t25.t7 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) false)) :rule resolution :premises (t25.t6 t25.a5))
% 1.32/1.51 (step t25.t8 (cl (= false (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule symm :premises (t25.t7))
% 1.32/1.51 (step t25.t9 (cl (= tptp.tc_RealDef_Oreal tptp.tc_RealDef_Oreal)) :rule refl)
% 1.32/1.51 (step t25.t10 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))))) :rule refl)
% 1.32/1.51 (step t25.t11 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))) :rule cong :premises (t25.t9 t25.t10 t25.a4))
% 1.32/1.51 (step t25.t12 (cl (= tptp.tc_Complex_Ocomplex tptp.tc_Complex_Ocomplex)) :rule refl)
% 1.32/1.51 (step t25.t13 (cl (= (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex) (tptp.c_Groups_Oone__class_Oone tptp.tc_Complex_Ocomplex))) :rule refl)
% 1.32/1.51 (step t25.t14 (cl (= (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.v_b) (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.v_b))) :rule refl)
% 1.32/1.51 (step t25.t15 (cl (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)))) :rule refl)
% 1.32/1.51 (step t25.t16 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____) tptp.v_na____)) :rule symm :premises (t25.a3))
% 1.32/1.51 (step t25.t17 (cl (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) :rule symm :premises (t25.t16))
% 1.32/1.51 (step t25.t18 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) :rule cong :premises (t25.t15 t25.t17))
% 1.32/1.51 (step t25.t19 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____))) :rule symm :premises (t25.a2))
% 1.32/1.51 (step t25.t20 (cl (= (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex))) :rule refl)
% 1.32/1.51 (step t25.t21 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_z____)) :rule symm :premises (t25.a1))
% 1.32/1.51 (step t25.t22 (cl (= (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____))) :rule cong :premises (t25.t20 t25.t21))
% 1.32/1.51 (step t25.t23 (cl (= tptp.v_m____ tptp.v_m____)) :rule refl)
% 1.32/1.51 (step t25.t24 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____))) :rule cong :premises (t25.t22 t25.t23))
% 1.32/1.51 (step t25.t25 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____))) :rule trans :premises (t25.t18 t25.t19 t25.t24))
% 1.32/1.51 (step t25.t26 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Complex_Ocomplex) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) :rule cong :premises (t25.t14 t25.t25))
% 1.32/1.51 (step t25.t27 (cl (= (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____))) (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____))))) :rule cong :premises (t25.t12 t25.t13 t25.t26))
% 1.32/1.51 (step t25.t28 (cl (= (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))))) :rule cong :premises (t25.t12 t25.t27))
% 1.32/1.51 (step t25.t29 (cl (= (tptp.hAPP (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))) :rule symm :premises (t25.a4))
% 1.32/1.51 (step t25.t30 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule cong :premises (t25.t9 t25.t28 t25.t29))
% 1.32/1.51 (step t25.t31 (cl (= (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) true) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule equiv_simplify)
% 1.32/1.51 (step t25.t32 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) true) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule equiv2 :premises (t25.t31))
% 1.32/1.51 (step t25.t33 (cl (= (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) true)) :rule resolution :premises (t25.t32 t25.a0))
% 1.32/1.51 (step t25.t34 (cl (= false true)) :rule trans :premises (t25.t8 t25.t11 t25.t30 t25.t33))
% 1.32/1.51 (step t25.t35 (cl false) :rule resolution :premises (t25.t1 t25.t2 t25.t34))
% 1.32/1.51 (step t25 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) :rule subproof :discharge (t25.a0 t25.a1 t25.a2 t25.a3 t25.a4 t25.a5))
% 1.32/1.51 (step t26 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) :rule and_pos)
% 1.32/1.51 (step t27 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule and_pos)
% 1.32/1.51 (step t28 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) :rule and_pos)
% 1.32/1.51 (step t29 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) :rule and_pos)
% 1.32/1.51 (step t30 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) :rule and_pos)
% 1.32/1.51 (step t31 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 1.32/1.51 (step t32 (cl false (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule resolution :premises (t25 t26 t27 t28 t29 t30 t31))
% 1.32/1.51 (step t33 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) false) :rule reordering :premises (t32))
% 1.32/1.51 (step t34 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) false) :rule contraction :premises (t33))
% 1.32/1.51 (step t35 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) false) :rule resolution :premises (t24 t34))
% 1.32/1.51 (step t36 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) (not false)) :rule implies_neg2)
% 1.32/1.51 (step t37 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false)) :rule resolution :premises (t35 t36))
% 1.32/1.51 (step t38 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false)) :rule contraction :premises (t37))
% 1.32/1.51 (step t39 (cl (= (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))))) :rule implies_simplify)
% 1.32/1.51 (step t40 (cl (not (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false)) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule equiv1 :premises (t39))
% 1.32/1.51 (step t41 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule resolution :premises (t38 t40))
% 1.32/1.51 (step t42 (cl (= (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) false)) :rule resolution :premises (t23 t41))
% 1.32/1.51 (step t43 (cl (= (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) false))) :rule cong :premises (t19 t42))
% 1.32/1.51 (step t44 (cl (= (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) false) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) :rule all_simplify)
% 1.32/1.51 (step t45 (cl (= (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))))) :rule trans :premises (t43 t44))
% 1.32/1.51 (step t46 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule implies_neg1)
% 1.32/1.51 (anchor :step t47)
% 1.32/1.51 (assume t47.a0 (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))
% 1.32/1.51 (assume t47.a1 (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))
% 1.32/1.51 (assume t47.a2 (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))
% 1.32/1.51 (assume t47.a3 (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))))
% 1.32/1.51 (assume t47.a4 (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))
% 1.32/1.51 (assume t47.a5 (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))
% 1.32/1.51 (step t47.t1 (cl (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule and_neg)
% 1.32/1.51 (step t47.t2 (cl (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t47.t1 t47.a0 t47.a5 t47.a4 t47.a1 t47.a3 t47.a2))
% 1.32/1.51 (step t47 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule subproof :discharge (t47.a0 t47.a1 t47.a2 t47.a3 t47.a4 t47.a5))
% 1.32/1.51 (step t48 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) :rule and_pos)
% 1.32/1.51 (step t49 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) :rule and_pos)
% 1.32/1.51 (step t50 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) :rule and_pos)
% 1.32/1.51 (step t51 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) :rule and_pos)
% 1.32/1.51 (step t52 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) :rule and_pos)
% 1.32/1.51 (step t53 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule and_pos)
% 1.32/1.51 (step t54 (cl (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule resolution :premises (t47 t48 t49 t50 t51 t52 t53))
% 1.32/1.51 (step t55 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule reordering :premises (t54))
% 1.32/1.51 (step t56 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule contraction :premises (t55))
% 1.32/1.51 (step t57 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule resolution :premises (t46 t56))
% 1.32/1.51 (step t58 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule implies_neg2)
% 1.32/1.51 (step t59 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule resolution :premises (t57 t58))
% 1.32/1.51 (step t60 (cl (=> (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule contraction :premises (t59))
% 1.32/1.51 (step t61 (cl (not (and (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat))) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule resolution :premises (t18 t45 t60))
% 1.32/1.51 (step t62 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule not_and :premises (t61))
% 1.32/1.51 (step t63 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))))) :rule or_neg)
% 1.32/1.51 (step t64 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule or_neg)
% 1.32/1.51 (step t65 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))))) :rule or_neg)
% 1.32/1.51 (step t66 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))))) :rule or_neg)
% 1.32/1.51 (step t67 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))))) :rule or_neg)
% 1.32/1.51 (step t68 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (not (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule or_neg)
% 1.32/1.51 (step t69 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule resolution :premises (t62 t63 t64 t65 t66 t67 t68))
% 1.32/1.51 (step t70 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule contraction :premises (t69))
% 1.32/1.51 (step t71 (cl (or (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule resolution :premises (t1 t17 t70))
% 1.32/1.51 (step t72 (cl (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule or :premises (t71))
% 1.32/1.51 (step t73 (cl (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) tptp.v_na____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal)) (not (tptp.c_Orderings_Oord__class_Oless tptp.tc_RealDef_Oreal (tptp.c_RealVector_Onorm__class_Onorm tptp.tc_Complex_Ocomplex (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) tptp.v_b) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) tptp.v_z____) tptp.v_m____)))) (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal))) (not (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) (not (= tptp.v_na____ (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule reordering :premises (t72))
% 1.32/1.51 (step t74 (cl (not (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) :rule or_pos)
% 1.32/1.51 (step t75 (cl (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))) (not (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))))) :rule reordering :premises (t74))
% 1.32/1.51 (step t76 (cl (=> (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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)))))) :rule implies_neg1)
% 1.32/1.51 (anchor :step t77)
% 1.32/1.51 (assume t77.a0 (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))))
% 1.32/1.51 (step t77.t1 (cl (or (not (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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)))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))))) :rule forall_inst :args ((:= V_q tptp.v_m____) (:= V_p (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) (:= V_x (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (:= T_a tptp.tc_Complex_Ocomplex)))
% 1.32/1.51 (step t77.t2 (cl (not (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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)))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule or :premises (t77.t1))
% 1.32/1.51 (step t77.t3 (cl (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule resolution :premises (t77.t2 t77.a0))
% 1.32/1.51 (step t77 (cl (not (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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)))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule subproof :discharge (t77.a0))
% 1.32/1.51 (step t78 (cl (=> (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule resolution :premises (t76 t77))
% 1.32/1.51 (step t79 (cl (=> (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) (not (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))))) :rule implies_neg2)
% 1.32/1.51 (step t80 (cl (=> (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) (=> (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))))) :rule resolution :premises (t78 t79))
% 1.32/1.51 (step t81 (cl (=> (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))))) :rule contraction :premises (t80))
% 1.32/1.51 (step t82 (cl (not (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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)))))) (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule implies :premises (t81))
% 1.32/1.51 (step t83 (cl (not (= (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))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))))) (not (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)))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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)))))) :rule equiv_pos2)
% 1.32/1.51 (step t84 (cl (= (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))))) (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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))))))) :rule all_simplify)
% 1.32/1.51 (step t85 (cl (forall ((V_q $$unsorted) (V_p $$unsorted) (V_x $$unsorted) (T_a $$unsorted)) (or (not (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)))))) :rule resolution :premises (t83 t84 a25))
% 1.32/1.51 (step t86 (cl (or (not (tptp.class_Rings_Ocomm__semiring__1 tptp.tc_Complex_Ocomplex)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____))))) :rule resolution :premises (t82 t85))
% 1.32/1.51 (step t87 (cl (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))) tptp.v_m____) (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.hAPP (tptp.hAPP (tptp.c_Groups_Otimes__class_Otimes tptp.tc_Nat_Onat) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) tptp.v_m____)))) :rule resolution :premises (t75 a1167 t86))
% 1.32/1.51 (step t88 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule implies_neg1)
% 1.32/1.51 (anchor :step t89)
% 1.32/1.51 (assume t89.a0 (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))
% 1.32/1.51 (step t89.t1 (cl (or (not (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule forall_inst :args ((:= V_z tptp.v_z____)))
% 1.32/1.51 (step t89.t2 (cl (not (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule or :premises (t89.t1))
% 1.32/1.51 (step t89.t3 (cl (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule resolution :premises (t89.t2 t89.a0))
% 1.32/1.51 (step t89 (cl (not (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule subproof :discharge (t89.a0))
% 1.32/1.51 (step t90 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule resolution :premises (t88 t89))
% 1.32/1.51 (step t91 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (not (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule implies_neg2)
% 1.32/1.51 (step t92 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (=> (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule resolution :premises (t90 t91))
% 1.32/1.51 (step t93 (cl (=> (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule contraction :premises (t92))
% 1.32/1.51 (step t94 (cl (not (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule implies :premises (t93))
% 1.32/1.51 (step t95 (cl (not (= (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z)) (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) (not (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z))) (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule equiv_pos2)
% 1.32/1.51 (anchor :step t96 :args ((V_z $$unsorted) (:= V_z V_z)))
% 1.32/1.51 (step t96.t1 (cl (= V_z V_z)) :rule refl)
% 1.32/1.51 (step t96.t2 (cl (= (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule all_simplify)
% 1.32/1.51 (step t96 (cl (= (forall ((V_z $$unsorted)) (= (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))) V_z)) (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))))) :rule bind)
% 1.32/1.51 (step t97 (cl (forall ((V_z $$unsorted)) (= V_z (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt V_z)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls))))))) :rule resolution :premises (t95 t96 a906))
% 1.32/1.51 (step t98 (cl (= tptp.v_z____ (tptp.hAPP (tptp.hAPP (tptp.c_Power_Opower__class_Opower tptp.tc_Complex_Ocomplex) (tptp.c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt tptp.v_z____)) (tptp.c_Int_Onumber__class_Onumber__of tptp.tc_Nat_Onat (tptp.c_Int_OBit0 (tptp.c_Int_OBit1 tptp.c_Int_OPls)))))) :rule resolution :premises (t94 t97))
% 1.32/1.52 (step t99 (cl (= (tptp.c_Groups_Oone__class_Oone tptp.tc_RealDef_Oreal) (tptp.hAPP (tptp.c_RealDef_Oreal tptp.tc_Nat_Onat) (tptp.c_Groups_Oone__class_Oone tptp.tc_Nat_Onat)))) :rule symm :premises (a704))
% 1.32/1.52 (step t100 (cl) :rule resolution :premises (t73 t87 t98 a1187 a881 t99 a3))
% 1.32/1.52
% 1.32/1.52 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.5Q68rdGbnH/cvc5---1.0.5_16736.smt2
% 1.32/1.52 % cvc5---1.0.5 exiting
% 1.32/1.53 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------